Adv Inorganic Chemistry I
Adv Inorganic Chemistry I CHM 448
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Chromium Discovered In 1797 by LN Vauquelin as its oxide He isolated it in 1798 by charcoal reduction of the oxide Name From the Greek word chroma meaning quotcolorquot because of the variety of colors its compounds display Occurrence Moderate abundance Its only important mineral is chromite FeCr204 which is found principally in southern Africa 96 of known reserves nations of the former USSR and the Philippines Isolation FeCrZO4 02 alkali bNazCrzO4 NazCrzO4 H20 gt NaZCrZO7 need to balance NazCrzO7 2C gt CrzO3 NaZCO3 CO Cr203 2A1 gt A1203 2Cr Natural Isotopes 50Cr 43 52Cr 838 53Cr 96 54Cr 24 Cost of 1 gram 1 mole 015 766 Physical and Shiny and silvery in color Chemical Soft and brittle Properties High melting and boiling points Oxidation states from 2 to 6 are known Most stable oxidation state is 3 Corrosion resistant Reactions Cr3 forms thousands of complex ions that for the most part are 6 coordinate eg Cr3 6 H20 gt CrHZO63 The chromates and dichromates are important oxidizing agents The half reaction for dichromate oxidation is Cr207239 14 H 6 e39 gt 2 Cr3 7 H20 Uses Production of non ferrous alloys Ornamental plating Green colored glass Nate Compounds of CrVl are known to be both toxic and potent carcinogens Cobalt Discovered First isolated by G Brandt in 1735 It was identi ed as an element in 1780 by TD Bergman Name From the German word kabald for quotgoblinquot or quotevil spiritquot Several of the cobalt ores contain arsenic vide infra and the processing of them led to the formation of highly toxic gaseous As406 The miners attributed this to evil spirits Cobalt is also extremely similar to the Greek word cabalas meaning quotminequot but no connection is believed to exist between the two Occurrence Moderate abundance Over 200 minerals are known to contain cobalt Important ones are smaltite CoAs4 cobaltite CoAsS and linnaeite Co3S4 These minerals almost always occur with nickel ores and frequently with copper silver and lead ores Found in Africa and Canada small reserves also exist in Australia and nations of the former USSR Isolation Usually obtained as a by product of iron or nickel production The general ore is roasted to give a mixture of metals and oxides Leaching with H2S04 removes Cu and puts Fe and Co in solution The iron is precipitated with lime and cobalt with NaOCl 2 Co2 0C1quot 4 OHquot H20 gt 2 CoOH3 C1quot Natural Isotopes 59Co 100 Cost of 1 gram 1 mole 036 2145 Physical and Lustrous with a bluish silvery color Chemical Hard and brittle Properties 2 allotropes Ferromagnetic Much less reactive than iron Dissolves slowly in dilute mineral acids giving CoH in solution Reacts when heated with halogens B C P As S and O No binary Co hydride or nitride is known Stable oxidation states range from 1 to 5 with 2 and 3 most common Reactions Like chromium cobalt has an extensive coordination chemistry for the 3 oxidation state A CoH2063 6 NH3 gtH20 CoNH363 6 H20 Co X2 4A Con X C1 or Br 2 Co 02 4A 2 C00 M C0304 Uses In blue pigments dyes and glasses Co compounds are used as catalysts in hydrogenation dehydrogenation and hydroformylation reactions High temperature alloys 30 Magnetic alloys 20 Electroplating because of its inertness 60Co is used as a y ray source Vitamin B12 is an organic molecule containing a CoHI as an octahedral complex Discovered It has probably been in use since 5000 BC Name Both the name quotcopperquot and cupmm Latin are derived from aes cyprium because the Romans first obtained their copper from the island of Cyprus Occurrence It is found in moderate abundance Some is found in elemental form The principle copper containing minerals are chalcopyrite CuFeSZ cat 50 of all copper deposits chalcopyrite CuZS cuprite CuZO and malachite CuZCO3OH2 Large deposits of these ores are found in North and South America Africa and nations of the former USSR Isolation Most copper comes from the extraction of low grade ca 12 copper ores After initial extraction cuprous sulfide is converted into copper by the following series of reactions that occur at 1400 C 2Cu2S 3024A 2Cu20 2502 2Cu20 CuZS 6Cu SO2 Natural Isotopes 63Cu 691 65Cu 309 Cost of 1 gram 1 mole 005 300 Physical and Reddish color Chemical Good electrical 2nd only to silver and thermal conductor Properties Soft and ductile Relatively low oxidation potentials to 1 and 2 Fairly resistant to air oxidation because the oxide adheres strongly to the metal Forms numerous alloys Reacts With halogens and oxygen and sulfur at high temperatures Stable oxidation states range from 1 to 4 With 1 and 2 most stable Reactions 2 Cu 02 gt 2 CuO e g corrosion of copper such as on pennies Cu Sn 4Agt bronze Cu Zn A brass Uses Coinage in the USA new pennies contain 25 Cu While quotsilverquot coins contain a majority of copper Production of brass and bronze alloys Electrical conductance applications Copper sulfate is used as an agricultural poison Some shellfish use copper complexes in their oxygen transport systems Iron Discovered Known since prehistoric times lron beads from around 4000 BC are known Name Derived from an Anglo Saxon word iren which means quotholy metal so named from what I can tell because it was used to make swords for the Crusades Fe the atomic symbol is derived from the Latin word ferrum which is probably derived from an unknown Hebrew or Arabic word Occurrence It is the Earth39s second most abundant element in the crust and the most abundant element in the core Common minerals include haematite Fe203 magnetite Fe204 limonite 2Fe203 3H20 siderite FeCO3 and pyrite FeSZ quotfool39s gold It is common throughout the universe because one of its isotopes 56Fe is the most stable nucleus and is produced in signi cant amounts when stars explode Isolation lron was first smelted around 3000 BC in the Hittite empire The iron ore is converted into iron by the following reactions 3 FeZO3 CO A 2 Fe3O4 CO2 Fe304 CO 4A 3 quotFeOquot CO2 C CO2 4A 2 CO quotFeOquot CO A Fe CO2 Natural Isotopes 54Fe 58 56Fe 917 57Fe 22 58Fe 03 Cost of 1 gram 1 mole 006 314 Physical and Silvery in color with a lustrous finish Chemical Relatively hard and brittle Properties Ferromagnetic to 768 C Comparatively reactive Soluble as Fe2 in dilute mineral acids Strong oxidizing acids passivate iron through formation of an oxide coating Oxidation states range from 2 to 6 with 2 and 3 the most common Pyrophoric when finely divided Reactions 4 Fe 3 02 gt 2 FeZO3 rust Fe X2 gt FeX2 X Br or I or FeX3 X F or Cl Fe 5C0 gs FeCO5 I Uses Steel 700 million tons annually worldwide in 1984 Active site in Hemoglobin Manganese Discovered In 1774 CW Scheele recognized a new element in the mineral pyrolusite MnOZ JG Gahn heated it with charcoal and oil to yield metallic manganese Name Derived from the Latin word magnes meaning magnet for the magnetic properties of pyrolusite Occurrence It is moderately abundant It occurs in over 300 minerals of which about a dozen are important eg pyrolusite MnOZ hausmannite Mn3O4 rhodochrosite MnCO3 all are found in nations of the former USSR Gabon South Africa Brazil Australia India and China Isolation a Electrolysis of aqueous MnSO4 solutions b 3MnO2 4N4Agt3Mn 2A1203 c Mn used in steel alloys comes from the in situ reduction of MnO2 in a blast furnace Natural Isotopes 55Mn 100 Cost of 1 gram 1 mole 007 401 Physical and Gray to white color Chemical Hard and very brittle Properties Comparatively electropositive Physical properties are similar to iron Oxidation states range from 3 to 7 with high spin 2 most stable Relatively active i Dissolves in dilute non oxidizing acids Mn2 ii Burns in 02 when finely divided iii Slowly reacts with cold water iv Reacts with many non metals at elevated temperatures Pure metal exists in 4 allotropic forms Reactions Mn 2H gt Mn2 3 Mn 202 gt Mn3O4 note that manganese is in 2 different oxidation states in this compound 2MnOH2 02 gt 2MnO2 2H20 2 Mn2 5 H202 gt MnO4 6 H 2 H20 Note the variety of oxidation states shown above Uses Steel alloys ca 95 Oxidant KMnO4 Dry cell batteries MnOZ Colorizing agent in glass bricks MnOZ and the gemstone amethyst Mn2 Nickel Discovered In 1751 AP Cronstedt first isolated and named nickel Name NiAs ore resembles CuZO Which was a desired mineral Saxon miners attributed their inability to extract copper from it to the work of the devil Old Nick39s copper Occurrence It is moderately abundant Important ores gamierite NiMg6 nickeliferrous limonite FeNiOOH6 nHZO pentlandite NiFe9S8 The most important deposit in Canada Isolation Very complicated This one is not required Cost of 1 gram 1 mole 012 675 Naturallsotopes 58Ni683 6ONi261 61Ni11 62Ni36 64Ni09 Physical and Silvery White in color Chemical Hard Properties Ferromagnetic Does not corrode at room temperature Reacts With some non metals steam Soluble in dilute mineral acids Oxidation states from 1 to 4 With 2 most common High electrical and thermal conductivities Finely divided metal burns in air Atomic mass is smaller than that of the preceding element Co 587 amu vs 589 amu Nickel complexes tend to be either 4 coordinate tetrahedral complexes or 6 coordinate octahedral complexes Reactions Ni 4C0 50 C NiCO4 a liquid at RT very toxic NiH206C12 6NH3 gt NiNH36C12 6H20 Uses Monel alloy very corrosion resistant Nichrome alloy very low temperature coefficient of electrical resistance lnvar alloy very small coefficient of expansion Catalyst for the hydrogenation of unsaturated vegetable oils Storage batteries Coinage Alloy in alnico magnets aluminum nickel cobalt alloy get it Nickel steel Colors glass green Scandium Discovered Oxide first isolated in 1879 by LF Nilsen Pure element was first isolated in 1937 from the electrolysis of a mixture of KClNaClScCl3 at 700 C by Fischer Brunger and Grieneisen Name From the oxide Sc203 called scandia for the location of the ore Occurrence Rare element and Widely distributed It39s only rich mineral is thortveitite SczSi207 Which is found in Norway Isolation As a by product of uranium processing contains car 002 Sc203 Cost of 1 gram 1 mole 164 7350 Natural Isotopes 55Sc 100 Physical and Soft silvery White metal Chemical Moderately electropositive Properties Unexpectedly high melting and boiling points compared to calcium Reacts With most non metals at elevated temperatures Only chemically important oxidation state is 3 Complexing properties similar to aluminum Chemistry anomalous compared to the other transition metals lts chemistry is closer to that of the main group metals Reactions 4 Sc 3 02 gt ZScZO3 28c 3F2 gt ZScF3 ScF3 3NaF gt Na3ScF6 Uses The oxide is used in the production of high intensity lights Titanium Discovered By William Gregor of England in 1791 in TiOZ First isolated by 1 Berzelius in 1825 but not made pure until 1910 by Mathew Hunter Name Named by a German chemist MH Klaproth in 1795 after the Titans people of Greek mythology that were children of Heaven and Earth condemned to live amongst the hidden fires of the earth Occurrence It is abundant Two most significant minerals are ilmenite Canada US Australia Scandinavia Malaysia and rutile Australia Isolation This method was developed by Wilhelm Kroll in 1932 in Luxemburg 2FeTiO3 7C12 6C gt 2TiC14 2FeCl3 6C0 TiCi4 2Mg gt Ti 2MgC12 Cost of 1 gram 1 mole 021 996 Naturallsotopes 46Ti79 47Ti73 48Ti739 49Ti55 50Ti53 Physical and Lustrous silvery metal Chemical High melting and boiling points Properties Not especially good conductor relative to other metals Low density Very resistant to corrosion Relatively unreactive at normal temperatures Oxidation states range from 1 to 4 except 1 4 is the most significant Burns in N2 at high temperatures Reactions Ti 2 C12 4A TiCl4 mp 23 C TiCl4 2 H20 gt TiO2 4 HCl smoke screens for ships in W W 11 Uses Form high strength construction alloys Low density lightweight high temperature alloys for aircraft TiO2 is the principle pignent in white paint It replaced PbOH2 2PbCO3 and 2PbSO4 PbO in that role when many commercial uses of lead were phased out in the 1970s Uranium Discovered MH Klaproth identi ed it as a component of pitchblende in 1789 It is believed that B Peligot first isolated uranium metal in 1841 Name It was named after the planet Uranus by Klaproth because the planet had been discovered shortly before he discovered uranium Uranus was the god of the heavens in Greek mythology Occurrence It is fairly abundant more so than tin Its most important minerals include pitchblende or uraninite U308 and carnotite K2UOZVO42 3HZO Principle sources are the US Canada South Africa and Australia Isolation ore 4 H2304 U022 300 C U03 70 U02 U02 4 HF 4 U14 70184 U 2MgF2 Cost for 1 gram 1 mole 588 281 Natural Isotopes 234U 00054 235U 071 238U 9928 Physical and Radioactive 234U tl2 25 X 105 yr Chemical 235U tl2 71 X 108 yr Properties 238U tl2 45 X 109 yr Very dense 191 gcm3 Silvery white color Ductile and malleable Pyrophoric when finely divided Soluble in acids Last naturally occurring element Electropositive Tarnishes rapidly in air OXidation states of 3 to 6 are known with 4 most stable Toxic beyond its radioactivity 250 Reactions 2U 3 H2 c 2UH3 238U 1n 4 239U 239Np 239131 UC6 2H20 gt U02C12 4HC1 Uses Electrical power generation fuel 1 lb U E 1500 lb coal Used in inertial guidance devices gyro compasses counter weights for aircraft control surfaces as ballast for missile reentry vehicles and to generate high energy X rays Photographic toner UNO33 Uranium salts are used as yellow glass colorants Alloy with titanium is used in armor piercing shells Vanadium Discovered By AM del Rio in 1801 and named it erythranium but he withdrew his claim after someone else incorrectly suggested that his results were in error In 1830 NG Sefstrom rediscovered the element and gave it its current name Name From Vanadis the Scandinavian goddess of beauty because its compounds come in a variety of colors Occurrence It is moderately abundant and is widely distributed in nature Common minerals patronite VS4 vanadinate Pb5VO43Cl2 PbClZ 3Pb3VO42 carnotite KUOZVO4 32HZO Venezuelan crude oil Chief exporters US nations of the former USSR China and South Africa Isolation carnotite NaCl 850 C NaVO3 pH 273 H2304 V M V205 m a polyvanadate Cost ofl gram 1 mole 256 130 Natural Isotopes 50V 024 51V 9976 Physical and Shiny silvery appearance Chemical Soft and ductile Properties Highest melting point boiling point and enthalpy of atomization of the first row transition metals Last first row transition metal in which its d electrons don39t enter the inert core and whose group oxidation state 5 is not highly oxidizing Corrosion resistant VO2 is possibly the most stable diatomic ion Has stable oxidation states ranging from 5 to 1 with 4 the most stable Reactions V205 60Hquot gt 2VO4339 3 H20 V205 2H3O gt 2V02 3 H20 V 2 C12 gt VCl4 VCl4 6H20 gt VOH2052 2H 4Cl39 Uses Alloy in steel to yield strong high temperature performance Mordant in dyeing V205 V205 is used as a catalyst in the contact process for the production of HZSO4 Zinc Discovered First isolated by the 13Lh century in India Early brass ca 1400 BC was made With out isolating the zinc Rediscovered in Europe by Marggraf in 1746 Name The origin of the name is not certain but it appears to be derived from the German word Zinke meaning quotspikequot or quottoot referring to the shape of the metal When it crystallizes Occurrence It is relatively non abundant lt39s major minerals include zinc blende sphalerite ZnS calamine silicate and smithsonite ZnCO3 Large deposits are found in Canada the USA and Australia Isolation Most Zn is derived from ZnS ore The method is not important Natural Isotopes 64Zn 489 66Zn 278 67Zn 41 68Zn 186 Cost for 1 gram 1 mole 004 235 Physical and Low melting and boiling points Chemical Silvery solid With a bluish tint When freshly made Properties Brittle at room temperature Only chemically important oxidation state is 2 Alloys With a variety of other metals Chemically similar to the alkaline earth metals Reactions Zn 2H gt Zn2 H2 Zn 20Hquot gtZn02239 H2 Uses Anti corrosion coating galvanizing Carbon zinc batteries Brass alloy With copper ZnO has a Wide variety of uses incl paints cosmetics plastics textiles and pharmaceuticals Chapter 11 Coordination Chemistry Bonding Spectra and Magnetism Read through the top of p 391 on your own This is a description of the beginnings of modern inorganic chemistry It is mostly history but there is some interesting chemistry in there as well You will be able to see the logic of how Alfred Werner was able to figure out the structures of coordination complexes with no modern spectroscopic or crystallographic instrumentation Bonding in Coordination F amp Valence Bond Theory Read to the top of p 393 on your own With the exception of the hybridization scheme that leads to square planar geometry spzd this is review The F 4139 v Principle and Back Bonding Before we begin this section here are three important definitions coordination complex a molecule or ion in which a metal atom is covalently bound to one or more ligands g d a molecule atom or ion that is covalently bound in a coordination complex Most ligands donate 2 electrons coordinate covalent bond 7 a covalent bond that results from one of the atoms providing all of the electrons in a bond It is sometimes called a dative bond Consider a generic coordination complex ML 2 where the ligands are neutral 2 electron donors Since all of the electrons in a coordinate covalent bond come from one of the atoms formal charges suggest that each bond should place a 1 charge on the M2 yielding a formal M4quot for an octahedral complex How can this be As you would probably guess since donor atoms on the ligand are more electronegative than the metal they do not share their electron density equally Calculations suggest that the ligands help to lower the charge on the metal from its oxidation state by spreading it out over several atoms but not by so much as to place signi cant negative charge on the electropositive metal center The closer the oxidation number of a metal is to zero the closer will its actual charge be to zero As you can see in the example for Be2 and Al3 p 394 the actual charges wind up very near zero For 0304 where the oxidation state is 2 8 the actual charge on osmium may be as high as only 1 to 2 As a result metal ligand bonds are typically about 50 covalent in character and 50 ionic A second way to remove electron density from a metal center is called back bonding If a metal has electron density in its d orbitals the electron density may be transferred to a ligand through the latter s 7M orbitals e g CO lt 39CEO 76 orbital This feeding of electron density into 7cquot orbitals on the ligand affects bond lengths in the complex The M C bond will shorten while the C 0 bond will lengthen This can be easily seen using VB resonance structures M39lt CEO lt gt MCo The more electron rich a metal is the more the right hand form contributes to the actual structure We can see this empirically through crystal structures and infrared spectroscopy vide infra Cgstal Field Theory This is a relatively simplistic theory that does an amazingly good job of making predictions about complexes Unfortunately most of its underlying assumptions are wrong even if their application has merit It turns out the errors just about cancel each other out Crystal field theory treats the metal atom as a point charge with five d orbitals The ligands are treated as negative point charges Thus the bonds are thought of as purely ionic in character The book shows representations of the d orbitals on pp 396 97 You should commit these to memory There is also discussion about the fact that mathematically one can come up with 6 equations to describe d orbitals This should be a bit of a review from earlier in the semester Recall that the d d Ky XZ dyz and dx2y2 orbitals all look the same because mathematically the only difference between them is their orientation in space The dzz orbital looks different because it is the average of the two remaining mathematical functions The doughnut traditionally shown in 3 general chemistry texts is inaccurate The shape is more akin to a teardrop rotated around the nucleus with the tip pointing towards the metal The averaging causes the lobes along the z axis to be larger ie thicker than the torus Henceforth the d orbitals will be designated by their subscripts ie xy dxy Cgstal Field Effects Octahedral smetg In your mind39s eye imagine 6 ligands interacting with a d1 metal ion As I hope you will see if this works for a d1 metal ion it will work for any transition metal atom or ion How do we arrange the ligands They lie on opposite ends of the coordinate axes at an infinite distance from the origin The transition metal ion resides at the origin Where is the transition metal d electron lt spends 15 of the time in each orbital in the absence of an outside interaction What happens as we bring the ligands towards the metal ion Two things i M ligand attraction lowers the energy of d orbitals and ii electron electron repulsion w the energy of the d orbitals Let s ignore point i for a moment As the ligands approach the ion their electrons repel the metal d electron Repulsion is greatest in orbitals lying along the x y and z axes zz xZ yz and less in the orbitals directed between the axes xy xz yz Thus the orbitals are split in relative energies As you might guess the electrons in all orbitals are repelled so all orbitals increase in energy When the first factor is added in i above all orbitals lower in energy Now let s step back for a minute Imagine instead of 6 discreet ligands the pairs of electrons were smeared out in a spherical shell around the metal atom If the shell were contracted all 5 orbitals would increase in energy at exact equal rates Now the 6 ligands described above are distributed spherically ie They come as close as 6 ligands can to simulating a spherical distribution As a result the average energy of the d orbitals in the real complex is the same as the average energy of the d orbitals in the hypothetical complex called the barycenter So what does this mean When the metal ligand electrostatic attractions are figured in the xy xz and yz orbitals go down in energy relative to the average and the z2 and xz y2 go up lmportantly the total energy decrease of the xy xz and yz orbitals exactly equals the total energy 4 increase of the z2 and xZ yz Individually xy xz and yz orbitals drop below the average by 25 A0 and z2 and xz y2 increase by 35 A0 This can be seen graphically as Finally these groups of degenerate orbitals are named t2g for the lower energy orbitals and eg for the higher energy orbitals The labels come from group theory To generate the labels begin with the molecular point group 011 Since there are three equal energy orbitals they must belong to a T irreducible representation Tlg ng Tlu and T211 exist for 011 Then treating the three orbitals as a group perform the various symmetry operations and keep track of the results They will generate a set of characters identical to one of the irreducible representations in this case tzg Cgstal Field Stabilization Energy Now that we see that the d orbitals split in energy and why they do so we need to explore how the orbitals fill All of the examples in this section possess an octahedral coordination geometry In the case of a one electron d1 atom or ion the answer is simple the electron drops into the t2g set This electron is more stable than in the free ion by 04AO This stabilization is called the cgstal field stabilization energy CFSE A0 is measured from the electronic spectrum UV visible where the t2g a eg transition is observed Likewise in d2 and d3 complexes the second and third electrons go into the t2g set with CFSEs of 08 A0 and 12 A0 respectively So far this is just like filling the 2p orbitals from boron through nitrogen Now things get interesting What happens with d4 The electron may go into either the t2g or eg set depending on the magnitude of A0 We will talk about this more later but in a nutshell ligands with strong associations to metal ions have larger AOs than those with weaker associations We ll discuss the 5 nature of these associations shortly Factors Affecting the Magnitude of A0 If A0 is greater than the spin pairing energy P the electron goes into the t2g set Conversely if P gt A0 the electron goes into the eg A0 gt P is called the strong field or w case and P gt A0 is the weak field or high spin case We begin with the latter scenario i The filling for d4 is ill t2 egl Thus CFSE 304A0 106AO 06AO For d5 CFSE 0 because the fifth electron also goes into the e For d6 the next electron goes into t2g g so CFSE 04AO For d7 CFSE 08AO Let s stop here and go back to the low spin case It merges with the high spin configuration at d8 The d4 case looks like ll so CFSE 16AO P For d5 CFSE 20A0 2P d6 yields a result that is a little surprising at first glance lt s CFSE 24AO 2P Why not 3P For the same reason you do not subtract IP from the high spin d6 case Remember we are measuring CFSE m to the unsplit case In the unsplit case d6 would have one spin paired anyway so only the additional paired spins are counted The book is in error here For d7 CFSE 18AO P 604AO 106AO Once eight electrons are placed in the orbitals the low spin and high spin configurations are identical and the labels no longer are relevant Thus high and low spin applies only to d4 d7 ln d8 complexes CFSE 12AO d9 CFSE 06AO dloz CFSE 0 Tetrahedral smmetry We can use the same approach here as for octahedral symmetry The ligands are placed on alternating corners of a cube and are then brought in towards the metal ion If the coordination axes are passed through the faces of the cube then the incoming ligands will interact more strongly with the xy xz and yz orbitals than z2 and xz y2 orbitals Thus the splitting will be reversed T quot 39 note the changes in labels AT 6 Note that because the point group is now Td the labels have changed slightly The presence of only four ligands causes AT to be smaller than A0 under almost all conditions That the ligands do not exactly align with the orbitals also reduces the value of AT versus A0 This causes tetrahedral complexes to be almost exclusively high spin Tetragonal smetg Square Planar Complexes The book mentions the Jahn Teller effect here I and the book will put it off for a while The easiest way to think about square complexes is as octahedra with one pair of trans ligands removed Mathematically it is easiest to remove the two ligands on the z axis When this happens orbitals with a z component drop in energy To maintain the barycenter those without a z component increase in energy by an equal amount I v quot 52 lt I h I h lt xz yz spherical octahedral tetra gonal coordination Coordlnatlon coordination The spacing of energy gaps is somewhat different for square planar complexes than for the two previous cases One might conclude from the discussion on tetrahedral complexes that the top to bottom gap would be small because there are only 4 ligands That is only partially true For the four orbitals that don t point at the ligands xy xz yz zz the splitting is indeed small see Table 115 p 405 for details The xz y2 orbital however bears the full brunt of the repulsion in the complex and is therefore elevated in energy by a significant amount Furthermore since there are now four energy levels the gaps between any two tend to be fairly small Factors Affecting the Magnitude of A All of these factors will have something in common the stronger the M L interactions the larger will be A Metal ion oxidation state A increases with oxidation state higher charged ions draw ligands in closer 7 Nature of MH A increases down a group for Mn with constant charge Probably because there is more overlap with larger d orbitals Note that this trend is opposite to what occurs for main group elements Number and Geometry of Ligand A increases with increasing number of ligands as discussed previously Nature of Ligands memorize the basic outline of the spectrochemical series I39 lt Brquot lt Clquot lt Fquot lt 0239 lt H20 lt N compounds lt alkylsaryls lt CN39 lt CO This ordering is generally true although there are exceptions depending on the metal Note this is the reverse from what is expected in crystal field theory We will talk about why later Applications of Cgstal Field Theog Skip pp 408 4 413 top Molecular Orbital Theog The notion that metal ligand interactions are purely ionic is clearly inaccurate cf electroneutrality vide supra In fact for most ligands the interactions are primarily covalent e g neutral ligands and there is significant experimental evidence consistent with this assertion In fact the spectrochemical series is essentially backwards from what it should be for a reasonable prediction based on the assumptions of crystal field theory The book discusses this brie y Read it on your own Octahedral Complexes The MO diagram of an octahedral complex probably seems like it would be very difficult to construct In fact it is not so hard to generate The first question to ask is what orbitals are involved The 6 ligand 6 donors and the 3d 43 and 4p orbitals on the metal this is for a first row transition metal with 6 2 electron donor ligands The ligands can be treated in terms of ligand group orbitals see pp 175 182 to review We ve already seen that the metal d orbitals can be broken into eg and t2g sets The 43 orbital is spherically symmetrical and will be described by the A1g irreducible representation as a sphere any operation will give back a sphere therefore all characters in the reversible representation will 8 be 1 Given the high symmetry of an octahedron it s a good bet that the p orbitals would be treated together They yield a T111 irreducible representation The lobes on the ligands used to donate to the metal may have positive or negative signs on the wave function These signs are used to make up the group orbitals The ligands generate a reducible representation that can be broken into A1 g Eg and T111 irreducible representations The LGOs are displayed on p 416 quot t j 4p 39 39 I 39 I g 48 I gru Note here the tzg set does not change in energy This is because there is no net 6 bonding With the ligand orbitals see p 415 Fig 17 These are non bonding orbitals When filling the MO diagram remember the ligands will contribute 12 electrons 62e so the alg tlu and eg sets will always be filled Filling of the tzg and egquot will depend on the number of the metal d electrons A result is that the same final d orbital pattern is generated as existed for crystal field theory The crystal field eg orbitals become egquot orbitals in molecular orbital theory Be sure to remember this distinction Tetrahedral and Square Planar Read this section on your own You are not required to memorize these MO diagrams but understand how they are constructed Pi Bonding and MO Theory Your book only looks at an octahedral system but Tc bonding also exists for tetrahedral and square planar complexes The MO treatment for these systems is very similar to What is observed for an octahedral system First there are four plausible L M Tc interactions p d d d Tc d o d The book 9 gives examples of each in Table 11 on p 421 The pW dI interaction involves ligand to metal 7c donation While the other three are metal to ligand 7c donations 7c bonds will involve the t2g set not the egquot This is because the egquot orbitals point directly at the ligands and are set up for o overlap See pictures on p 420 The direction of electron donation and the energy levels of ligand Tc bonding orbitals will have a pronounced effect on molecules We will consider a molecule With six Tc donor ligands e g halide ions and then 6 Tc acceptor ligands e g CO MX6H39 The halide p orbitals are lower in energy than the metal d orbitals and they are filled While metal d orbitals may or may not contain electrons Thus When the MOs form the ligand p electrons fill the t2g orbitals thus metal t2g electrons go into the tzgquot MOs The result of this type of interaction is a small A0 MCO6 The CO 76 orbitals are empty and are high in energy remember CO bond energy tzg 39 t I e 2g 6 39 g 39 g I l 1 39 A0 I 391 s t2g 39 I Since the CO 76 orbitals are empty the t2g MO is filled With metal t2g electrons and promotion is then a relatively high energy process These diagrams explain the relative placements of the halides and CN39ICO in the spectrochemical series In an electrostatic model the reverse would be expected Experimental Evidence For Pi Bonding So what evidence is there for Tc bonding ie what do we look for We begin by asking what would the interaction look like without Tc bonding Then what happens with full Tc bonding ML a ML Since the bonding between metal and ligand changes between these forms bonding within the ligand must change see the figures on p 2 of these notes If electron density is fed into a it or o orbital on the metal a bond within the ligand will be weakened The strongest evidence for 7c bonding comes from metal carbonyl complexes C stallography The greater the extent of Tc back bonding the more MC character there will be and the more CEO will resemble C20 The difference in CEO and C20 bond lengths is about 01 A and should be useable for quantification Unfortunately this has not been observed In contrast M C bond lengths do change Consider the complexes CrCO6 and CrCO5PR3 In the absence of Tc backbonding the Cr C bond lengths should be the same If it does occur then the bond lengths should be shorter in CrCO5PMe3 Why Two reasons PMe3 is at best a very poor Tc acceptor so only 5 COs are competing for electron density from the metal not 6 and PR3 is a very good 6 donor CO is not Thus the Cr has more electron density to share with fewer acceptors One other trend is expected The Cr CO bond trans to PR3 should be shorter than those cis This is because the trans CO will bind to the same d orbital as the PR3 and the effect will be greatest there As can be seen in Table 12 p 427 all of this is observed Infrared Spectroscopy Evidence for CO character is most clearly seen in IR spectroscopy VCO for CEO is about 2150 cm39l while in R2CO VCO is about 1700 cm39l Thus the greater the extent of backbonding the lower the expected VCEO This is seen dramatically for two series of complexes MCO6 39 and MCO4 39 in Table 13 on p 428 This can also be seen when a CO is substituted for by another ligand as seen in crystallography The only problem with using this 11 technique is that the CO stretching band is almost always split into several components making interpretation difficult Read the section in the book on le of substituted complexes Skip the subsection on photoelectron spectroscopy pp 431 433 1 Flectronic Spectra of F quotTanabe Sur39ano Diagrams Skip pp 433 447 Tetragonal Distortions from Octahedral Smmetg The sections we just passed over discussed how energy levels are affected by having different ligands bound to the central metal atom or ion As I said earlier this is more complex than we need to get into however energy level distortions can occur even if the ligands are all the same The Jahn Teller theorem predicts these distortions It states that for a non linear molecule in a non degenerate state the molecule must distort such that the symmetry of the molecule is lowered the degeneracy is removed and the energy of the molecule is lowered So what does this mean First a non degenerate state is one in which all sets of orbitals are E full empty or half qu eg 1 or 2 electrons in t2g or 1 electron in egquot Let39s assume for a moment you have 1 electron in an eg set That electron spends 50 of the time in the z2 and 50 of the time in the xZ yz Now what would happen if the two z axis ligands were pulled slightly away from the metal The X and y axis ligands would be pulled in a little closer to replace lost electron density With the z2 ligands further away the z2 drops in energy The xz y2 will rise in energy by an equal amount because its ligands are drawn closer The reverse may also happen That is z ligands move in and X y ligands move out There will also be an effect on the t2g set Fig 47 p 450 This is shown graphically below z out octahedral z in 152 zz gt 39 2 z2 eg XZy xy xzyz 12 Note the average energy of each split set equals the energy of the unsplit set These splittings are quite small and so do not affect pairings Altering spin pairings could conceivably happen in a d4 case where to avoid spin pairing energy the fourth electron moved into a lowered egquot orbital However the square planar geometry can be viewed as an extreme Jahn Teller distortion with the z ligands moved to infinite distance Lastly the number of electrons in a tzg set will govern the type of distortion 1equot 4equot LS or 6equot HS z out and 2equot 5equot LS or 7equot HS z in What about the egquot set This brings us to an important point about the Jahn Teller theorem It tells us neither the type nor the size of the distortion only that it will occur with the proviso that the center of symmetry will remain For the eg set either distortion can occur depending on the complex The book brie y discusses some experimental evidence for Jahn Teller distortions Read it Charge Transfer Spectra The previous discussion centered on d d transitions That is transferring an electron from one metal d based orbital to another eg t2g a egquot But other types of electron promotions can occur For an electron in a metal based MO excited to a ligand based M0 the electron is effectively moved from the metal to the ligands This is called a metal to ligand charge transfer MLCT The converse is a ligand to metal charge transfer LMCT LMCT are favored for metals in high oxidation states that are bound to electron rich low electronegativity ligands MLCT is favored for electron metals bound to ligands with low lying 7c orbitals eg CO heteroarenes eg pyridine These complexes are frequently highly colored A functional use of these compounds is as photoreducing agents Basically an electron is promoted to a high energy excited state by shining light on the compound which then transfers the electron to another species Following this two things can happen i the electron can return to the first molecule or ii if either molecule undergoes some irreversible rearrangement the electron transfer becomes permanent MLquot LgtMLngtk L MLnMAn gt 7 13 When applicable this method has advantages over traditional methods i The reducing power can be varied by promoting into different energy levels That is the higher the electron is promoted the more powerful the complex is as a reductant and ii the reaction can easily be stopped in progress by simply turning the light off November 6 2003 Chapter 5 Bonding Models in Inorganic Chemist 2 The Covalent Bond Lewis Structures Do this pp 1389 as a review Valance Bond 1 y B Theory VB theory begins with the assumption that the atomic orbitals of two bound atoms overlap to form a bond Mathematically atomic orbitals overlap by multiplying the wave functions Thus for H21 WH2 WA1 VB2 where WAG refers to the rst hydrogen atom and its electron and where 432 refers to the second hydrogen atom and its electron The next thing that is done is to correct for inaccuracies in this equation For example in the equation it is assumed that each electron remains closely associated with the nucleus to which it was initially assigned In fact there is no reason why the electrons cannot switch positions Likewise while not very energetically favorable there is no reason why both electrons cannot be on the same nucleus for brief periods The result can be thought of as an ionic correction ie H H39 41 WA1VB2 WA2VB1 XWAOWAQ KWBOWBQ where 7 ltlt 1 A third correction is for the electrons shielding each other These corrections yield about 85 of the experimental energy and come within 0008 A of the experimental bond length Other more involved corrections provide more accurate predictions The best wave function to date has over 100 terms and is accurate to within 0002 It s worth noting that unlike the sum you ve been shown here not all of those one hundred terms have physically explainable meanings Resonance occurs when more than one energetically reasonable structure can be drawn for a molecule There are two possible types of resonance structures One takes charge separation into account For example for the molecule HCl there will be a signi cant ionic contribution from HCl39 There will also be a very small contribution by H39Cl w awcov waC1 cwHCH where a gt b gtgt 0 The second resonance type is the more familiar type The book uses a classic example the carbonate ion Here three equivalent structures can be drawn 0 O IOI H C H c 39ljci39i Q o 9 o o 9 I II 111 average w dull 6qu p1H where d e f since the structures are equivalent Here the double bond is delocalized over 4 atoms In the case of carbonate all three structures are equivalent so each contributes equally to the actual structure As we will see next this is not necessarily so When structures contribute different amounts the relative contributions must be determined General rules to yield resonance structures in order of importance include 1 The number of bonds should be maximized consistent with other structure drawing rules e g no pentavalent carbons 2 The atoms must always occupy the same relative positions 3 Formal charges on atoms should be minimized and should be placed reasonably according to atom electronegativities ie negative charges on more electronegative atoms ng0 1 O IP O Opposite charges should reside as close to each other as possible 4 The number of unpaired electrons should be the same usually zero Formal Charges These are charges assigned to atoms as if each atom possessed half of the electrons in bonds it makes Q N AE NLPE 12NBPE N AE number of atomic electrons NLPE number of lone pair electrons NBPE number of bonding pair electrons Example CH4 QC40124x20 QHl012lx20 3 Remember that formal charges are just that they should not be taken literally What formal charges really tell us is something about the charge distribution within a molecule Typically you can do this by simply looking at electronegativities but that doesn t always work For example the formal charges on carbon monoxide are reversed from the electronegativities p 148 resulting in a nearly nonpolar molecule Thus if the formal charges are reversed based on electronegativity bond polarity will be reduced Conversely if they align as expected the bond will be more polar than expected Nonetheless while formal charges may provide you information about where nucleophilic or electrophilic attack may occur these sites should not be viewed as ionic On p 148 the book shows a way to calculate formal charges that is interesting but not required Hybridization This is a central feature of VB theory We will rst address how then why Hybridization can be viewed as a three step process i Promote each electron into its own atomic orbital ii Randomize the spins iii Mix the orbitals Pictorially for carbon E i i 41L i i i L ZS 2p ZS 2p lei SP3 2 2 But why does this occur or more specifically why is it energetically favorable First look at the shape of the hybrid on p 150 It is formed by adding the wave functions of an s and a p orbital 4 Do p orbital to yield an Sp hybrid v orbital w 4 Where the signs of the wave functions are the same the waves add constructive interference and a large lobe is obtained Where the signs are opposite they cancel destructive interference and a small lobe is generated The resulting hybrid has a huge lobe for overlap and consequently larger bond energies are obtained An interesting feature of these orbitals is their shape p 150 As you can see they are blunter than p orbitals which accounts for their improved overlap See Table 53 on p 153 hybridH bonds 410500 ldmol vs p H at 335 kJmol Overlap order Sp gt Sp2 gt SP3 gtgt p due to shape There are 5 sets of hybrid orbitals Sp linear 2 sp3d trigonal bipyriamidal 5 Sp2 trigonal 3 sp3aa octahedral 6 SP3 tetrahedral 4 All except sp3d yield a set of equivalent orbitals sp3d can be thought of a combination of 3 Sp2 and 2 dp hybrids Finally like atomic orbital subshells overlaying all of the orbitals of a given hybrid set generates a spherical distribution of electron density See the Orbitron link on the class webpage Read the rest of this section on your own Molecular Orbital 1M0 Theog There is a major conceptual difference between VB and MO theory In VB theory we talk of overlapping orbitals to form a bond and this seems to be intuitively reasonable In contrast while MO theory uses the atomic orbitals of its constituent atoms the product MOs are thought of as completely new entities although the MOs frequently resemble the atomic orbitals This is reasonable since core electrons are not involved in bonding and even valence electrons are not going to be completely separated from the parent atomic orbital One thing to remember is that each atomic orbital will give rise to one MO The Orbitron website has nice images of both atomic and molecular orbitals It is linked on the 448 webpage The linear combination of atomic orbitals method of generating MO will be discussed now It is one of many methods We will use H2 as an example with WA and WE representing the electrons on the respective hydrogen atoms There are two possible linear combinations Wb WA M Wb bonding M0 wa WA WE wa antibonding MO For Hf l electron system WHZ wb WA WE For H2 2 electron system WHZ wa WA WB2 WA1WA2 WA1WB2 WA2WB1 WB1WB2 Note how similar this is to the VB equation Here the ionic contribution is weighted too heavily but this can be corrected for WA and WE can be represented pictorially p155 by 444 4 T44 41 WA WB WA 39 WB At the center points the values of 412 can be easily calculated WA W132 WA2 2WAWB W132 4WA2 Since WA WB for H2 WA 39 W132 WA2 39 2WAWB WE2 0 Molecular orbitals can be diVided into three categories bonding MOs the signs of the interacting wave lnctions are the same the interaction is a net attraction antibonding MOs the signs of interacting wave lnctions are opposed so the interaction is repulsive That is the atoms are pushed apart This is because electron density is forced from between the nuclei and the nuclear charges are not screened from each other nonbonding MOS occurs for lone pairs and when half of interacting wave functions have the same sign and half are opposed eg GB GD 7 vs GB 7 7 Ifthe signs ofthe end functions are xed and opposed the middle is irrelevant Nonbonding is no net interaction or overlap Skip normalization through end of section pp 156157 top smmet and Overlap Read on your own Smmet of MOS Sigma 6 bonds possess no nodes that include the intemuclear axis Pi 11 bonds possess 1 node that includes the internuclear axis Delta 5 bonds possess 2 nodes that include the internuclear axis Antibonding orbitals are designated with an asterisk Note the symmetry of the MO is the same as the atomic orbital of analogous designation ie on s gerade nu p ungerade MOs in Homonuclear Diatomics These are the simplest molecules and will be discussed before heteronuclear diatomic molecules and polyatomic molecules There are two criteria for formation of a bond 1 There must be net positive interaction between the orbitals of interacting atoms ie the signs of the wave functions must be the same 2 The orbitals must have roughly equal energies ie ls interacts with ls ZS with 23 2p with 2p etc We shall soon see that if necessary any two valence atomic orbitals with the proper symmetry will combine A bonding interaction is expressed as 615 wlsA WISE or 615 ISA 133 where A amp B are labels used to designate the atoms of a homonuclear diatomic molecule An antibonding interaction is expressed as 615 wlsA WISE or 615 ISA 13B These expressions are very similar in presentation to those in H2 and are identical mathematically 7 The level of bonding interaction between 2 atoms is described by bond order which is similar to the number of bonds in a molecule BO 12 number of bonding electrons number of antibonding electrons Examples of some diatomic molecules include H2 6152 B0 12201 He2 6152 6152 B0 122 2 0 This molecule does not exist B2 KK 6252 6252 n2p2 BO 124 2 1 C2 KK 6252 6252 n2p4 BO 126 2 2 N2 KK 6252 6252 62p2 n2p4 BO 128 2 3 02 KK 6252 6252 62p2 n2p4 n2p2 BO 128 4 2 There are several points worthy of note 1 Fractional bond orders are possible eg Lif 6252 6251 B0 12 2 1 12 This ion actually exists with a longer bond length than Liz Valence bond theory does not have any formal way of dealing with fractional bonds 2 You would expect the B2 molecule would begin by lling a 62p before the 112p but the reverse is observed This is because the energy gap between 23 and 2p is not large and for the 62p bond the 23 can mix in This has the effect of raising the energy of the 62p orbital Note on Fig 513 p 165 mixing with the 625 also occurs 3 When lling MOs the same rules apply as for atomic orbitals Thus for a pair of orbitals the rst electron goes in either orbital the second in the other orbital This suggests that C2 and 02 should be paramagnetic which is experimentally observed Bond Lengths and Ionization Energies As was mentioned for Liz experimental evidence for the MO model of molecules comes from bond lengths Ionization energy also provides further supporting evidence An example from the book Bond Length 02 25 112 pm 02 2 121 pm 02 15 126 pm 02239 1 149 pm The book shows you that the ionization energy of NO 894 ldmol is much smaller than that of either an isolated nitrogen atom 1402 ldmol or an oxygen atom 1314 ldmol On rst consideration one would expect the ionization energy of NO to be slightly less than average of these values This is because the ionization of an electron from the molecule would spread the charge over two centers The ionization energies of the component atoms are comparable so the charge would be shared roughly equally and so the ionization of the molecule would be a little lower than the average of the ionization energies Yet it is about 35 less Why The electron is taken out of a high energy antibonding orbital An aside based on electronegativities one would expect oxygen to have a higher ionization energy than nitrogen Why are the values reversed Electron Density in Liz F2 Read this section on your own MOs in Heteronuclear Diatomic Molecules The most important difference between heteronuclear and homonuclear diatomic molecules is that the bonding atoms in the former have dilTerent electron affmities and ionization energies Hence they have di ering tendencies to gain or lose electrons The component atoms in homonuclear diatomic molecules are the same so their IEs and EAs are the identical A result is the equal sharing of electron density In heteronuclear bonds the electron density is shared unequally and is measured in terms of electronegativi Greater electronegativity is a greater tendency for an atom to attract electrons from an atom to which it is bound This is represented in equation form by vb mm wa and w bwA awB where a b in a homonuclear diatomic molecule and b gt a if B is more electronegative than A Note that atom B contributes more to the bonding MO than A but the converse is true for the antibonding MO The result is that the greater the difference in electronegativity between two 9 atoms the more the product MO will be like the parent atomic orbital of the more electronegative atom The logical extreme is a 0 and b l in a hypothetical purely ionic bond This last point relates the relative covalencyionicity of a bond to M0 theory If a b the bond is completely covalent As the difference increases ionicity increases At small dilTerences a bond is polar covalent at large differences a bond is ionic This can be seen pictorially as follows 139 6 Ilr 6 i x 6 L x x I x I x i r I 2 I I I 39IT A 6 B A 6 B A 6 B pure covalent polar covalent a b ionic b gt a b gtgt a One more thing needs to be considered What about orbitals not used in bonding These These are one of the two major types of nonbonding orbitals and correspond to lone pairs in valence bond theory nun orbitals particularly if they are in a region of space away form bonding remain largely unchanged 39 Orbitals in Triatomic 39 39 and Ions We ll use the two triatomic species used by the book BeH2 and NOf The valence shell of beryllium consists of the ZS and 2p orbitals Recall from earlier that their energies are similar Thus if conditions are right both may be involved in bonding can t n bond First assume a linear geometry its least crowded with HBeH along the zaXis Then px and py cannot participate in bonding because they are perpendicular to the bonding axis and s orbitals There are two approaches to how the MOs can be constructed One is an intuitive method generally used which you would probably use at this point That is select an orbital on beryllium and match it with an appropriate hydrogen orbital This turns out to be quite dif cult with larger molecules and is not 10 A second approach is to treat all atoms bound to the central atom as a group The difference will seem trivial for BeH2 however it is important for larger molecules In this approach the hydrogens can be in phase le wHZ or out of phase le wHZ The inphase combination interacts constructively with 23 The outofphase with 2p Antibonding orbitals are obtained by reversing the signs on the hydrogen atoms Thus Wg aW2s bWH1 WH2 Wu cW2p dWH1 39 WH2 Wg bW2s 39 aWH1 WH2 111 dW2p 39 cWH1 39 WH2 The N0239 ion contains 2 types of bonding 6 and 11 The sigma bonds will require the s and l p orbital on the nitrogen Since the nitrogen will have a lone pair a second p orbital is needed The net effect is a set of orbitals which is essentially equivalent to spz The 11 system can be treated similarly to the 6 system in BeH2 That is the oxygen p orbitals can be treated as a group WOI H1102 or WOI 14102 wb axpN b04101 1102 W Wb bWN aW01 W02 The third orbital is a little dilTerent because the same result is obtained whether W is added or subtracted WK 8 8 Wn WN W0139 W02 Wn WN 39W0139 W02 Wn W01 39 W02 or wn WOI 14102 i WN as your book puts it This is the second type of nonbonding orbital Skip the symmetry discussion from the middle of p 178 182 top Electronegativitx This is the ability of an atom in a molecule to attract electron density to itself The Pauling 1 1 scale is by far and away the most common scale and for general purposes works as well as the others On page 187190 ve different scales are shown The Pauling scale is based on a comparison of the bond energy of an AB bond vs the average of AA and B B bond energies Mulliken 7 J a e Electronegativity Scale This method has the advantage of taking into account the number of things bound the atom ie oxidation state and which orbitals are involved in bonding The values are relatively easy to calculate x 12IE EA Therefore the scale is based both on how well on atom adds an electron w how well it holds onto its own electrons Read through the end of paragraph 2 on p 185 then skip through the text on p 191 Variations in Electronegativity As you can see in Table 56 the electronegativity of an atom depends on its hybidization Why A relatively simple way to address this question involves examining hydrocarbon reactivity The pKa of CH4 is about 60 For ethylene pKa m 44 and acetylene pKa m 25 Since carbon and hydrogen have similar electronegativities this property cannot give rise to the acidity difference Go back to Table 56 Look at the various hybrids and you will see that as s orbital character increases so does electronegativity The reason is the same as for the acidity difference First one will have to know what they have in common EN As 3 character increases the atom is better able to remove electron density from a neighboring atom acidity As 3 character increases the carbon is better able to stabilize a product negative charge or better it causes a larger charge separation polarization in the CH bond The s orbital causes this because it penetrates closer to the nucleus than do p orbitals Thus electrons in s orbitals experience greater nuclear attraction Read the rest of this section on own Pauling s Electronegativity 7 Read this section on your own Other Methods of Estimating Electronegativity 7 Skip from here to the end of the chapter October 20 2004 Chapter 2 The Structure of the Atom Since the book assumes you have a background in quantum chemistry we will go over some of what you will need to begin Chapter 2 At this point it would behoove you to go back and read your general chemistry text on topics concerning atomic structure A prime mission of inorganic chemistry is to understand the bonding in molecules To understand bonding is in large measure to understand reactivity Now for a quick review of general chemistry By the late 19th century it was known that the atom contained electrons The discovery of the nucleus and protons in the early 20th century required a model of the atom classical physics could not provide The rst real model to describe the atom with some accuracy was proposed by Neils Bohr and is the familiar electron traveling around the nucleus in circular orbits This model employed several assumptions including energy quantization Unfortunately it had two signi cant problems 1 it only worked for one electron atoms and 2 there were no good justi cations for the assumptions beyond that they seemed to work A better description of the atom was developed when it was realized that electrons behaved both as particles and as waves This is called particlewave duality What we will now do is discuss how this dual nature of the electron affects the structure of the atom An early contribution to the study of wave mechanics the study of electrons in atoms as waves was made by Louis de Broglie He proposed that the electron wave obeyed the relationship p7 h p momentum That is to say the higher the momentum of an electron the shorter is its wavelength As p2 is directly proportional to kinetic energy this means long 7 electrons have low kinetic energy and short 7 electrons have high kinetic energy A second major contribution was made by Werner Heisenberg who realized that it is impossible to know both the position and momentum of a particle precisely He proposed that ApAX Z lzhZTE That is the more accurately you determine the momentum of a particle the less precisely you know its position and viceversa This is reasonable because in order to determine the position or momentum of a particle you must have an interaction with the particle The interaction will cause the energy of the particle to change and this will cause some uncertainty in the result In other words in order for the particle to reveal information about itself its energy must change Now what can we say about the electron wave In 1926 Erwin Schrodinger proposed an equation to describe the electron wave H 1 E 1 where 1 is the wave function H is called a Hamiltonian and performs a transformation on 1 such that it is regenerated and multiplied by a constant E that equals the energy of the system Remember that 1 is simply an amplitude it has Q physical reality In the case of an atom in 3dimensions 22 E V PO This equation is very difficult to solve for an atom eg V changes with distance from the nucleus and doing so isn t really necessary for this course However a hypothetical example that can be solved by hand is the particleina box We will solve this problem in ldimension See separate handout Now the major differences between the particlein a box and an atom are a The potential energy in the box is limited to 2 values eliminating a gradient b The total distance of the box is fixed Conceptually however the problems are the same and as a result their solutions are related The Hydrogen Atom Solving the Schrodinger equation for the hydrogen atom is very similar to doing so for the particleina box In addition to the 3 requirements placed on the particleinabox a 4th one is required for the hydrogen atom The total probability must equal 1 ie There is a 100 probability of nding the electron on the atom The results for the hydrogen atom can be summarized as follows a 3 quantum numbers are generated n principle angular momentum m magnetic since the equation is solved in three dimensions b Instead of solving it in Cartesian coordinates x y 2 it is easier to solve and interpret in polar coordinates cl 9 r Thus the solutions have the form w Rr 9 Generally the latter two functions are grouped together w R The Radial Wave Function We will now look at the two parts separately taking the radial part rst This is the distance function Radial wave equations are shown for the ls ZS and 2p orbitals on page 11 of your book The exact equations are not important to this course but the general forms shown below are where e g K15 is a constant st K1se39ZIa0 R2s K2s2 39 Zraoe39Zr2a0 R2 K2pre39Zr2a0 For the ls orbital we nd that the wave function and hence the probability 12 of nding the electron drops off as the electron moves further from the nucleus Since exponential functions tend to change much more rapidly than do linear ones the trend of lower electron density with increasing distance is always true at large distances At small distances variations occur A second important point should be noted in the R2S equation When Zrao 2 R2S 0 This is a place where the wave function goes to zero That is the electron cannot exist there This point is called a radial node While it may seem odd that the electron may exist on either side of the node but not at it remember the electron is just as much a wave as it is a particle Recall from the particleinabox handout the solution was a cosine function which naturally has a value of zero at 72 and 37172 Since the wave function describing the electron is similar the existence of a node is reasonable It is essentially impossible to think of an electron as a standing wave and it is still relatively difficult to treat each point along the wave A conceptually easier way of looking at the atom is in terms of thin shells centered on the nucleus Since all atoms are spherically distributed the probability of nding an electron at any point distance r from the nucleus is given by P 411r2R2 where 411r2 is the surface area of a sphere Thus for a ls orbital R R2 41tr2R2 f j r r r The volume element solves an apparent problem earlier it appeared as if the electron spent most of the time in the nucleus which we know is not true On page 13 the radial probability functions for the Is 3d orbitals are shown As you see a 33 orbital has two radial nodes 3p has 1 node and 361 has 0 nodes Therefore in general there are n Z l radial nodes per orbital Angglar Wave Functions The angular wave function yields the shape of the orbital s p d f and its orientation in space eg px py pl Unlike R Ed is independent of n As n increases the sizes of the orbitals change but not the shapes The angular wave functions for 3 orbitals 3 pl and dzl are shown on p15 Note for the s orbital Ed is a constant This means there is no angular dependence and a sphere is generated The p orbital takes the form Acost9 If the function is plotted on polar graph paper one obtains a gure that looks something like the 2lobe form you are used to seeing It also gives rise to the plus and minus signs you have seen placed in orbitals earlier Squaring this function yields a diagram shown below that shows the probability of nding the electron and is the shape of the orbital you are familiar with seeing Kory There are two things worth mentioning here The rst has to do with the signs or the whiteblue shading in the gure These signs refer to the amplitude of the wave function not the charge on the electron Electrons are M negatively charged When a cosine function is drawn on Cartesian graph paper the wave undulates above and below the zero line When the wave is above the line the amplitude is positive when it is below the line the amplitude is negative If you look at the plot of a cosine function on polar graph paper you will see how the two lobes have either fully positive or negative amplitudes The second point has to do with the various pictorial representations of orbitals shown in the book in particular on p 16 The simplest drawings eg Figure 29a c give you a very qualitative view of the orbital perhaps including the sign of the wave function They are the easiest to draw Electron density diagrams eg Figure 27a have the advantage of showing either from a particle perspective where the electron spends relatively more of the time or in the wave view where the amplitude is greatest Contour diagrams e g Figure 27b 28 have the advantage of providing all of the information provided by the other types of figures and the location of the nodes as well The wave function for a d orbital AB cos29l yields 4 lobes Each type of orbital has a fixed number of angular nodes associated with it Number angular nodes One feature of d orbitals that everyone notices is the odd shape of the dzz orbital relative to the other 4 orbitals Why is it that the dxy dxz d yz and dXLyz orbitals all have 4 lobes while the dzz orbital consists of a double lobe with a torus about the center The answer lies in a mathematical curiosity When the Schrodinger equation for Z 2 is solved one obtains siX solutions not five Physical reality allows only five orbitals so the dzz orbital is a result of the averaging of two of the solutions Notice how on moving from any position x y z on an s orbital to a position on the other side of the nucleus x y z the sign of the wave lnction remains the same positive In contrast the sign changes in the p orbital Orbitals that do not change signs on opposite sides of the nucleus have gm even symmetry Those whose wave lnction changes signs are ungerade S and d orbitals are gerade while p and f orbitals are ungerade This feature will become important when we discuss bonding Energies of Orbitals The energies of the hydrogen atom orbitals are determined solely by the principle quantum number n which may have any integral value 1 2 3 When n co the electron is lost and the atom is ionized The angular momentum gn X represents the shape of the orbital and may have integral values of 0 to n l Commonly letters are used to represent this quantum number 0 s lp2d3f4g The magnetic gn mg gives the number of each type of orbital and its orientation in space There are 2 l of each type of orbital and the orientations are designated by m Z In the absence of an external magnetic eld or other perturbing force the orbitals with the same n and Z are equal in energy or degenerate In the presence of a magnetic eld the orbitals differ in energy hence the name magnetic qn It turns out that when all of the my orbitals are combined for any X value the product orbital has spherical symmetry just like an s orbital That is at any distance r from the nucleus 412 is the same regardless of the angle There is a summary of the rules just discussed on the top of p 20 The Polyelectronic Atom Now what happens when atoms possessing more than 1 electron are considered The wave functions for such atoms cannot be determined exactly This is because 3 or more interactions occur simultaneously For helium the nucleus is attracted to each electron and the electrons repel one another The problem is that the wave equation that describes the motion of each particle must include terms for interactions with the other two particles both of which move independently Hence there is no exact solution The most common approximation is done by rst assigning reasonable wave functions to each of the electrons One is re ned while the others are held constant This is done sequentially and repeatedly until the energy of the system changes by an insigni cant amount Of course insigni can is a relative term and different people will select different values to terminate the calculation Nonetheless over a very broad range of cutoff values the appearance of orbitals does not change appreciably It has been found the orbitals in multielectron atoms are very similar to those in the hydrogen atom and are thus called hydrogenlike orbitals Unlike for hydrogen in multielectron atoms different orbital types differ in energy if they are occupied For any principle qn s lt p lt d lt f We ll get to why later The general energy ordering of orbitals is shown in the middle of p 21 and in the diagram at the top of p 22 For the most part the order follows increasing n then Z That is Is lt 23 lt 2p lt 3s the two exceptions being nd is always higher that n ls and nf always follows n ld1 Electron Spin and the Pauli Principle When a magnet is rotated an electric eld is established This is how hand crank generators operate The opposite is also true a spinning charged particle generates a magnetic eld It was known that some atoms interacted with a magnetic eld suggesting the electrons were spinning When the Schrodinger equation is solved with time included a new quantum number is produced It can have only two values ilz Classically clockwisecounterclockwise spins This quantum number was assigned to spin because the electron behaves as if it were spinning In reality the nature of this qn is more complicated because waves don t spin at least not in the classical sense Atoms with all electrons spin paired equal number of each are diamagyetic Those with one or more unpaired electrons are paramagnetic The Pauli exclusion principle tells us that no two electrons may have the same 4 quantum numbers The Aufbau Principle and Hund s Rule The aufbau principle provides a method for lling atomic orbitals The atomic orbitals are lled according to the list on p 21 that is Is 23 2p 3s 3p 43 3d Within subshells with multiple orbitals eg p d f electrons are placed singly in each orbital until all contain 1 electron then the electrons are paired This is because the electrons repel each other and each orbital is directed towards a dilTerent region of space so the electrons can get away from each other Be able to write out the electron con guration of y element using the ordering on p 21 Do not worry about the exceptions just treat them as if they were normal We won t deal with term symbols in this course Hund s rule states that ground state electronic con gurations have maximum spin multiplicity once the aufbau principle has been applied What this says is that unpaired electrons in degenerate orbitals will have the same spin alignment For example consider 2 electrons in 2p orbitals The aufbau principles tells us the electrons will go in different orbitals while Hund s rule tells us they will both be either spin up or spin down Periodicity 0f the Elements As the book points out the development of the periodic table is an interesting story The same information that lead to the discovery of the periodic table is part of what makes it very useful to the practicing chemist Telling me the position of an element tells me its most stable oxidation states and the types of bonds it forms and their strength among other things A knowledge of atomic structure makes it even more valuable Eg the alkali metals oxidation state 1 for all and ionic bonds for all elements in the group All transition metals have a stable 2 oxidation state except group IIIB We will look at this in greater detail in the lab part of the course Semantics Histo and Other uestions Read on your own I will address one point here Why do some chemists myself included not think of Zn as atransition metal Because of its reactivity It behaves just like Mg What about Cuf Cu2 meets the general criteria as does Hg22 and some Cd compounds I would argue solely on the basis of chemical reactivity Shielding Now we begin to apply some of these more abstract concepts to the physical and chemical properties of atoms With each successive electron added to an atom a proton is also added In a one electron atom or ion the energy of attraction of an electron to a nucleus is given by Z2 n2 where Z is the nuclear charge Since Z increases faster than n this would suggest that as one moves through the periodic table electrons are pulled increasingly closer to the nucleus and it would be more difficult to pull off an electron Of course this is wrong Alkali metals are a case in point So why does the energy of an electron behave differently from what the equation predicts Begin by noting that hydrogen is the only one electron element Two factors must then be considered First as n increases the energy of the electron increases and this forces it away from the nucleus The increase in distance reduces the electron nuclear attraction but there is more to it than this An electron with a smaller n will spend a substantial portion of the time between the nucleus and an electron with a higher n ee The outer electron experiences less electrostatic attraction l proton is partially to completely canceled to the nucleus and is repelled by the inner electron Thus this electron experiences a lower effective nuclear charge than the electron closer to the nucleus As larger numbers of electrons are added the lowering of Z can be substantial This process is called shielding The second factor that affects Z is the shape of the orbital There are four orbital types 3 p d and f The s orbital is spherical with the electron density concentrated near the nucleus In contrast the p orbital has a nodal plane passing through the nucleus This has the effect of forcing electron density away from the nucleus For d orbitals 2 nodal planes and forbitals 3 nodal planes the effect is more pronounced Orbitals that allow electron density to concentrate closer to the nucleus are said to be more penetrating Electrons in more penetrating orbitals shield other electrons better than electrons in less penetrating orbitals Some general trends 1 Orbitals within the same subshell do not shield each other 2 Orbitals with the same n shield each other poorly 3 Orbitals in the preVious shell shield well 4 Orbitals 2 or more shells lower shield completely eg ZeffforAr ls 175 2p 140 3p 68 2s l22 3s 78 Skip Slater39s Rules and Modi cations The Sizes of Atoms As the book points out the size of an atom depends on how and where the measurement takes place The specifics will be covered later but two general trends are known 1 Atomic size increases down a group The principal qn increases and the electrons are placed in successively less penetrating better shielded orbitals The result is the nuclear valence electron attraction is reduced and the electron moves away The book lists Zeff for Group IA on p 35 2 Within a period the size of atoms decreases left to right Here n remains constant From the rules given in the shielding section we know that electrons in orbitals of the same shell and subshell shield each other poorly Therefore as one moves from left to right each time an electron is added so is a proton Each proton adds 1 to Z but since the new electron is not well shielded by the last electron it experiences most of the electrostatic attraction of the new proton and is pulled closer Data for Group IIA are provided on p 35 Ionization Ener This is the energy required to remove an electron from an isolated gas phase atom or ion It is M positive endothermic IE tends to decrease down a group because the principal qn increases ie the size increases and the valence electrons are well shielded IE tends to increase right across a period In this case n is constant Protons and electrons are both being added and the new electrons are poorly shielded so they are held more tightly The increase is not smooth however On moving from Group IIA to IIIA or B the newest electron is placed in a diiTerent type of orbital p or d vs s Since the s shields a little better than the others the increase should be a little smaller than expected Finally the IE of elements with half lled subshells see nitrogen on p 36 is slightly higher than expected This is because in a half lled shell there is a uniform distribution of electrons with the same spin This Pauli stabilization is maximized in halffilled subshells Ionization This section begins by stating the obvious For the most part electrons are removed from an atom ionization in reverse order of addition That is last in rst out The major exceptions to this rule are the transition metals Here the us electrons are added before the nld electrons 1 are removed rst Why The book gives one general explanation Here is a plausible extension Turn to p 13 and look at the 3s and 3d orbitals The 43 will have a very similar diagram to the 33 with 4 humps with largest being a little further from the nucleus I39ll use the 3s for my arguments since you have the picture The line between 400 and 600 pm is the 361 maximum The area under the curve to le of this line is larger for 361 than for 33 however the 3s puts some electron density closer to the nucleus Now consider an argon atom When a proton and an electron are added where does the electron go The space around the nucleus has 18 electrons so e39e39 repulsions are signi cant Since the 361 electron has a higher probability of being in this region its repulsions and hence its energy are raised relative to 43 When electrons are removed from transition metals two things come into play 1 Reduced e39e39 repulsions lower the energy of 361 more than 43 and 2 higher Zeff will lower the energy on the electrons that spend the greatest time near the nucleus Thus residual electrons wind up in 3d This is explained it greater detail in one of the handouts I d like to emphasis a point the books makes It is the total energy of the system that matters Therefore you must consider the aggregate effect of principal qn and orbital shape angular momentum qn on both the initial and nal states e g pre and postionization when considering into which orbital an electron goes or from which it is removed Electron Affmity The energy released when an electron is added to the valence shell of a gas phase atom or ion is electron af nity This is a great de nition intuitively the problem is its sign convention is opposite to the standard practice We will get around this by using AH eg Fg e39 gt Fg39 EA 328 ldmol AH 328 kJmol Some general notes 1 The second EA of all atoms is M endothermic 2 The rst EA of open subshell atoms is exothermic 3 The rst EA of closed subshell atoms is zero 4 First EA generally become more exothermic left to right across a period The point made by Figure 213 p 41 is worth remembering October 13 2004 Chapter 8 Chemical Forces Understanding the relative meltingboiling points of two substances requires an understanding of the forces acting between molecules of those substances These intermolecular forces are important for many additional reasons For example solubility and vapor pressure are governed by intermolecular forces The same factors that give rise to intermolecular forces eg bond polarity can also have a profound impact on chemical reactivity Chemical Forces Internuclear Distances and Atomic Radii There are four general methods of discussing interatomic distances van der Waal s ionic covalent and metallic radii We will discuss the first three in this section Each has a unique perspective of the nature of the interaction between interacting atomsions Van der Waal39s Radii half the distance between two nuclei of the same element in the solid state not chemically bonded together eg solid noble gases In general the distance of separation between adjacent atoms not bound together in the solid state should be the sum of their van der Waal s radii a d W 139 di39 van er aa sra 1 a J Ionic Radii 7 Ionic radii were discussed in Chapter 4 and you should go back and review that now One further thing is worth mentioning here Evidence that bonding really exists and is attractive can be seen in ionic radii For all simple ionic compounds the ions attain noble gas configurations eg in NaCl the Na ion is isoelectronic to neon and the Clquot ion is isoelectronic to argon For the sodium chloride example just given van der Waal s radii would predict Table 81 p 292 a distance of separation of 350 A while the actual distance is 281 A vs 285 A predicted by adding ionic radii This shortening ca 20 is evidence for a strong attractive force Covalent Radii half of the distance between two nuclei of the same element singly bonded together A similar argument for covalent bonding to be net attractive can be made as was done for ionic bonding For all homonuclear diatomic molecules the atoms are separated by less than predicted by doubling the van der Waal s radius For example chlorine atoms in C12 lie 199 A apart while van der Waal s radii predict a separation of ca 360 A a 45 shortening Read through the bottom of p 294 actually ending on the first line of p 295 but don t worry about the details of how the covalent radii can be estimated covalent radius x 2 Types of Chemical Forces Covalent Bonding and lonic Bonding Read these sections on your own They are largely a review of Chapters 5 and 6 One thing that is worth reiterating is that on average ionic bonds and covalent bonds are equally strong It is the nature of the attraction not the magnitude that differs Ion Dipole Forces This is the strongest of the non bonded interactions It typically occurs when ionic compounds are dissolved in polar solvents This is usually a salt dissolved in water but can include organic salts dissolved in polar organic compounds eg Et4NBr in acetone The negative end of the dipole will be attracted to positive ions and vice versa Thus the polar molecules will align 0 Na 3139 themselves with the ions to which they are attracted 3 The magnitude of the interaction depends on the ionic charge and the size of the dipole The Z e size of the interaction is given by E 7 2 47rsor where u dipole moment and r 2 distance of separation between the ion and the molecular center of the dipole Note that ion dipole forces 1 1 vary as 1r2 E cgtlt 7 whereas ion ion forces vary as 1r E cgtlt 7 Thus they act over much shorter r r distances than do ionic bonds Dipole dipole Interactions Dipoles tend to align with oppositely charged ends directed at each other These are the next strongest intermolecular force C 3 Q Q QQD solid The first graphic would most accurately portray a solid ln room temperature liquids there is plenty of energy to disrupt these forces so while the molecules will attempt to align significant disorder will exist in the liquid phase and frequently the ends of the dipoles with like charges will approach 215112 4 3 Thus this force starts out weaker ireOr one another The force of attraction is given by E than ion dipole 112 is smaller than Z in the numerator and weakens even more rapidly as distance increases Dipole dipole interactions occur in polar molecular compounds eg acetone and dichloromethane lnduced Dipole Interactions lnduced dipole interactions occur when nonpolar molecules are mixed with ions or polar molecules eg dissolving benzene in acetone The way to think about this interaction is to imagine the nonpolar molecule as a sphere whose electron cloud is distorted by a nearby charge The electrons on the nonpolar molecule are attracted to the positive end of the dipole see figure below and repelled by the negative end of the dipole The interaction lasts as long as the polar molecule is in close proximity to the nonpolar molecule E polar nonpolar polar molecule w molecule molecule 11101601116 induced dipole Z 2a e 2 and for a The energy of attraction for an ion to nonpolar molecules is given by E 2a 6 r polar molecule to a nonpolar molecule by E where X is the tendency of the electron cloud on the nonpolar molecules to be distorted In both cases the forces are quite weak and operate over very short distances Of the two the latter interaction is more common e g solvent mixtures Dipole Induced Dipole Tnteractinn These are sometimes called London dispersion forces and are the forces that act between nonpolar molecules and allow them to be liquefied London dispersion forces occur when a momentary imbalance in the electron density on an atom or molecule causes a dipole to be established for an instant The attraction then occurs just like in a dipole induced dipole interaction This dipole may then induce a dipole in a neighboring molecule and this can propagate for some 210 I6 distance The energy of attraction is E They operate over the shortest distance of all forces and are usually the weakest The strength of the interaction also depends on the polarizability of the nonpolar molecule Other things being roughly equal the polarizability of a molecule increases with size that is it is easier to distort a large electron cloud than a small one because the electrons in the former are held less tightly Thus in large nonpolar molecules eg paraffin London dispersion forces can become substantial In general chemistry you were probably told that London dispersion forces increase with molecular weight This is not really true It is true that larger masses will frequently affect physical properties in the same way as do intermolecular forces but not for the same reason London dispersion forces are affected by molecular volume much less so by molecular mass One example of this is the boiling points of hydrogen isotopes Mass 2 20K 4 23 K T 6 25 K As you can see a 3 fold increase in mass results in only a 5 degree 25 increase in boiling point Similarly for the series of 182 C 164 C 150 C 130 C 23 C 76 C CF4 which is only slightly larger than CH4 but is 55 times heavier has melting and boiling points very similar to methane but far different from CCl4 which is only 175 times heavier than C134 Repulsive Forces These are the forces that keep two molecules from collapsing to a point They are nuclear nuclear and core electron repulsions The repulsive energy is given by E krn n 12 frequently Hydrogen Bonding This is a special bonding case that lies somewhere between dipole dipole interactions and covalent bonding It occurs when hydrogen is bound to some very electronegative small element F O N although it does extend in weakened fashion to a couple of second row elements Cl and S Physical evidence for hydrogen bonding comes from crystallography You would expect that one element H bond would be of standard length while the other would roughly equal the sum of their van der Waal39s radii ie a standard nonbonded interaction In molecules where hydrogen bonding occurs the latter bond will be considerably shorter than expected In some extreme cases where the hydrogen atom binds to two atoms of the same element the bonds may be of equal lengths Hydrogen bonds in nonionic situations can have energies on the order of 50 kJmol compare the C H single bond 2 400 kJmol One way they are manifested is in higher melting points eg H20 2 0 C HZS 85 C HZSe 60 C HZTe 49 C Hydrates and Clathrates We ll brie y discuss one aspect of this section Beginning ie first year students are frequently confused by the existence of hydrates The compounds are usually written as Mny39ZHZO and little to no information is provided about what role the waters play in its composition Towards the end of general chemistry one learns about coordination compounds and that explains the role of much of the water in these compounds but not all As you learned earlier simple crystal lattice packing patterns involve packing anions in a closest packed array and filling in the tetrahedral and octahedral holes with cations p 8 amp 9 of Chapter 4 notes If the cations aren t small enough for the holes the lattice has to expand to accommodate them and this may create gaps in the lattice Solvent molecules in this case water can fill in the empty space and these molecules are lattice solvates or hydrates for the case of water Effects of Chemical Forces Melting and Boiling Points The forces we have just discussed are responsible for many of the bulk properties of a material How strongly molecules are held together may be inferred from their melting points and boiling points Molecular substances tend to have low melting and boiling points Note that both rise as the molecules get larger This is predicted by the description of London dispersion forces Also larger molecules with polar bonds may have higher than expected mpbp High symmetry also raises melting point has a smaller effect on boiling point because more stable lattices are generated For example neopentane CMe4 melts at 16 C vs 130 C for n pentane Other things being equal more symmetrical molecules Will have higher melting points because they pack more efficiently meaning they have higher lattice energies High symmetry helps to explain a curious feature in chemistry sublimation That a material should go from solid to liquid to gas as the temperature increases is intuitive That it skips directly from the solid to gas phases surprises most people and not Without good reason We think of a solid as a collection of molecules locked into fixed positions largely unable to move except for bond vibrations The addition of heat causes molecules to Wiggle in place until they break out of their lattice slot and begin to slide past one another This is melting Eventually enough energy is added that intermolecular forces are completely overcome and the molecule breaks into the gas phase So Why does sublimation occur High symmetry allows more efficient packing that in turn raises melting points greater lattice energy relative to similar less symmetrical substances Also highly symmetrical molecules Will generally have a much greater ability to rotate in the solid phase Without disturbing their neighbors than Will low symmetry molecules Thus molecules are able to effectively store thermal energy by spinning in place until they can break directly into the gas phase Consider C02 Which is linear and highly symmetrical Dmh Unlike less symmetrical molecules of comparable size eg H20 thermal energy can cause CO2 to rotate around its Cm axis Without disrupting the lattice Even at high rates of rotation the lattice remains reasonably undisturbed until individual CO2 molecules go directly into the gas phase As was discussed brie y earlier in the notes uoro compounds have unusually low mpbps because the electron clouds on uorine are difficult to polarize MP SE 90 P135 83 SF6 50 In general the melting points and boiling points will increase as the strengths of the intermolecular forces increase The highest temperatures are required for ionic and covalent network lattices A word of caution here A common misconception is that if a molecule possesses covalent bonds it will have a high melting point This is not true if the bonds are internal to the molecule That is hexane has a low melting point because the only attraction to an adjacent hexane molecule is London dispersion forces In contrast diamond has a very high melting point because there is a lattice in which each C atom is connected to four other C atoms in the lattice To melt it these C C bonds must be broken Quartz has a structure as shown in the figure below each oxygen atom is bound to two silicon atoms On melting the giant lattice is broken into smaller sublattices each containing many of the units shown in the figure For this reason the melting point exceeds 1700 C ultimately when the quartz boils SiOZ forms The high temperature is required because strong Si O o bonds are replaced by weak SiO Tc bonds and that requires a great deal of energy o OSi Agt OSiO o O lonic compounds exhibit a wide range of melting points We already talked about this when discussing Fajan39s rules in Chapter 4 page 131 As cations become more polarizing smallermore positive and anions become more polarizable largermore negative melting points and boiling points decrease This is because strong lattices have uniform charge distribution As ions are polarized bonding becomes directional That is some interactions strengthen while others weaken These weakened interactions are easier to disrupt or melt Remember the polarization is an instantaneous disruption that has only a eeting existence Look at Table 86 and 87 on pp 309 310 See how halide salt melting points and boiling points decrease as anions gets larger Silver compounds are lower than potassium because silver is comparably good at polarizing anions The sodium values are anomalously high showing that other factors are present Table 87 shows cation effects Solubility You should be familiar with the adage quotlike dissolves like We will now examine why this is true The simpler case is the dissolving of nonpolar substrates in nonpolar solvents In both cases London dispersion forces operate so the interactions are likely to be small for each and about equal in magnitude Therefore AH lx z 0 Thus the mixing of nonpolar solvents is entropy driven TAS z 112 kJmol This term is fairly small but is enough to allow mixing to occur Why don39t nonpolar and very polar substances mix Let s assume London dispersion forces in each are comparable The dipole dipole interaction in the polar molecule will be much stronger than the London dispersion forces Thus the energy released from a polar polar interaction will be much more negative favorable than the nonpolar polar induced dipole interaction Therefore more energy is released by having the polar molecules aggregate and exclude the nonpolar molecules into a second layer than by allowing complete mixing What about dissolving salts in a polar liquid From the previous two examples either solvent salt interactions will be equal in energy to solvent solvent and ion ion interactions and dissolution will be entropy driven or the ion solvent interactions will be stronger than the solvent solvention ion interactions and the process will be enthalpy driven As it happens entropy is usually not a major factor in determining if a salt dissolves For a salt to dissolve solvation energy must be more negative favorable than lattice energy This can happen because each ion will be solvated by several solvent molecules Although ion dipole forces are weaker than ion ion forces they are stronger than the dipole dipole forces in the solvent Each ion is solvated by several solvent molecules and this may override the strength of the lattice For salts with highly charged anions or cations the lattice energy will increase more rapidly 10 than solvation energy which is Why salts with highly charged ions frequently have lower solubilities In rare cases the lattice energy is ever so slightly more stable than the solvation energy In these cases dissolution is entropy driven and the salts form cold solutions when they dissolve Finally salts composed of ions of very different sizes tend to have much higher solubilities than those of similar sizes lons of similar sizes pack more efficiently and minimize anion anion repulsions This generates more stable crystals higher lattice energies and correspondingly lower solubilities December 2 2003
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