Honors General Chemistry
Honors General Chemistry CHEM 121
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CHEM121 Honors General Chemistry 1 QUANTUM NUMBERS The Schrodinger wave equation describes the energies of an electron in an atom Solutions to this equation are called wave functions and describe the location and therefore the energy of an electron The solutions are restricted due to quantum numbers Acceptable solutions are called orbitals An orbital is a region in space or a volume element where there is a high approximately 90 probability of locating an electron Each orbital is uniquely de ned by a set of three quantum numbers The quantum numbers ow directly from the solution to the Schrodinger equation and limit the number of acceptable solutions The three quantum numbers are described below 1 Principal guantum number 1n n has whole number values from 1 to in nity 11 indicates the approximate distance of the orbital from the nucleus and therefore its approximate energy For example an electron in an orbital with n 3 is located at a further distance from the nucleus than an electron in an orbital with n 2 and therefore has a higher energy The principal quantum number is essentially the principal level postulated in the Bohr theory 2 Angular momentum guantum number 1 1 may have values from 0 to nl Therefore the number of 1 values is equal to n 1 de nes the three dimensional shape of the orbital For example when l 0 the orbital is spherical and when l the orbital is shaped like a dumbbell values are generally given letter designation as follows 139 0 s f l p f 2 d 3 f 3 Magnetic guantum number ng mmay have values ranging from 0 l m describes the orientation of the orbital in space For example when 139 l m 10l These three mvalues describe three p type orbitals all of which have different orientation in space along the three coordinate axes An orbital is designated by its principal quantum number followed by its angular momentum quantum number or nl For example the orbital with n l and l 0 is called a ls orbital and when n 3 and l 2 this is a 3d orbital Orbitals with the same values for n andl but different values of m are differentiated by using subscripts x y and z for the coordinate axes along which they are oriented For example the three 2p orbitals are oriented along the x y and z coordinate axes and are therefore called 2px Zpy and 2pz Each orbital is uniquely described by a set of three quantum numbers The ls orbital is de ned by the three quantum numbers of 100 where the rst is n the second 1 and the third ml The three 2p orbital are described by 2ll 210 and 21l Adams September 28 2007 Quantum Numbers Summary Principal Angular Magnetic Quantum Quantum Quantum Orbital Number Number Number Orbitals Type Electrons n m l 0 0 l ls 2 2 0 0 1 2s 2 l l01 3 2p 6 3 0 0 1 3s 2 l l01 3 3p 6 2 2l012 5 3d 10 4 0 0 1 4s 2 l l01 3 4p 6 2 2l012 5 4d 10 3 32l0l23 7 4f 14 n nl 0 112 Zn2 total n A level is a collection of orbitals with the same value of n Thus the third principal level has 9 orbitals and 18 electrons A sublevel is a collection of orbitals with the same values of n and 1 Thus the 2p sublevel is a collection of the three 2p orbitals 2px 2py and 2pz The third level is composed of three sublevels the 3s 3p and 3d The number of sublevels for any given level is equal to the level number 11 All s sublevels contain 1 orbital and 2 electrons p sublevels contain three orbitals and 6 electrons and d sublevels contain 5 orbitals and a maximum of 10 electrons Therefore in any principal level there are n sublevels n2 orbitals and Zn2 electrons DL Adams September 28 2007 CHEM 1 21 Honors General Chemistry UMassAmherst Masses and conversion factorsquot Atomic Mass Standard 7 the atomic mass unit amu or u is de ned as 112 the mass of a C12 atom where the C12 atom has a de ned mass of 12000000 u On this relative scale the rest masses of the subatomic particles are Proton 1007276470u Neutron 1008664904 u Electron 0000548579903 u Since on the particulate level one C12 atom has an atomic mass of 120000 u and on the macroscopic mole level one mole of C12 has a mass of 12000 g then 12000u x 602x1023 atom x 10mol 602x1023 ug atom mol 12000 g or 602 1023 u 1000g and its reciprocal 1661 X 103924 g 1 u Thus the conversion factor between the particulate and molar levels microscopic and macroscopic is Avogadro s number NA 60221367 X 1023 All masses and physical quantities taken from Mills Quantities Units and symbols in Physical Chemistry Blackwell Scienti c Publications IUPAC London 1988 Adams September 14 2007 RESONANCE AND RESONANCE STRUCTURES H H A single Lewis electron dot formula often adequately represents the locations H of bonding electrons in molecules For instance ethyl alcohol is well represented by I I the Lewis formula at the right There are however molecules whose electronic distribution is inadequately represented by a single Lewis formula In these cases two or more Lewis formulas may be necessary to satisfactorily represent the molecule Resonance is a phenomenon invoked when more than one Lewis formula is needed to adequately describe the electronic distribution in a molecule Resonance is the use ofcontributing structures to represent the actual electronic distribution ofa molecule For example consider the sulfur dioxide S02 molecule Structural studies show that both SO bonds in S02 are of equal length and strength This electronic distribution is not explained by either single Lewis structure but is explained when both Lewis formulas are taken into consideration 9 e S 39 S O 39 O I e e Both Lewis structures are called resonance structures or resonance contributors Resonance contributors are separated by double headed arrows as shown The 9 actual molecule is NOT an equilibrium mixture of the imaginary resonance structures but rather a single unchanging composite structure called the S resonance hybrid Resonance hybrids are often represented by the quotpartial bondquot or combined notation The resonance hybrid for sulfur dioxide is shown 0 0 to the right 9 Fundamentally the phenomenon of resonance is invoked because of the inability of single Lewis structures to show electron delocalization over the molecule In fact resonance is often called delocalization For instance in S02 the pi electron pair is delocalized or spread over both SO bonds and not localized in a single SO bond Thus the existence of electron delocalization in a molecule means that more than a single resonance structure must be drawn to fully describe the electronic distribution within the molecule Further since electronic delocalization is stabilizing the existance of resonance implies molecular stabilization Generally the more resonance contributors the more stable the molecule DRAWING RESONANCE STRUCTURES Resonance structures differ only in the location oftheir electrons The atomic nuclei do not move and the bond angles do not change Resonance structures must all contain equal numbers of e electron pairs andor unpaired electrons One resonance W 39 A S 4 lt gt structue can be converted into another by electronic 0 0 O movements denoted by curved arrows Most of the time quot 39 39 9 9 quot these electronic shifts invlolve a lone pair becoming a pi Resonance amp Page 2 5 November 2008 Resonance Structures bonding pair or a pibonding pair becoming a lone pair Sigma bonds are generally NOT involved in drawing resonance structures For instance the two resonance structures for S02 are interconverted by the electron movements shown Of course no actual electronic movements occur this process is used as an aid in deriving additional resonance structures Another example of this relationship among resonance structures is shown with the three resonance structures of the nitrate ion NO339 90 e E gt 6N oi r eo o e O O o o e The implications of resonance are l the actual electron distribution is different than would be eXpected based on a single Lewis structure and 2 the energy of the actual molecule is lower than eXpected from a single Lewis structure This energy lowering is due to electron delocalization and is called resonance stabilization The degree of energy lowering or molecular stabilization is related to the number of resonance structures and the relative stabilities of the resonance structures CONTRIBUTION OF RESONANCE CONTRIBUTORS TO THE HYBRID Resonance structures M or may not contribute equally to the resonance hybrid Resonance structures contribute in proportion to their stability that is the more stable the resonance structure the greater its contribution to the hybrid Thus it is important to evaluate the relative energies and hence relative importance of various resonance contributors In this regard there are several situations to consider These are detailed below with examples EVALUATING THE RELATIVE ENERGY OF RESONANCE CONTRIBUTORS 1 Equivalent resonance contributors have equal energies and therefore make an equal contribution to the hybrid The larger the number of equivalent resonance structures the more stable the molecule For instance consider the allyl carbocationstabilized by the eXistence of equivalent resonance structures We previously saw the nitrate anion stabilkized by three equivalent resonance structures CH CH CHZV CH2 3H2 CH2 9 resonance contributors of equal structure and contribution to the hybrid Resonance amp Page 3 5 November 2008 Resonance Structures 2 Contributors which have no or minimum charge separation have a lower energy than structures with large charge separation In considering charge separation vs expanded octets in atoms in the 3ml period or higher minimizing charge separation has a higher priority see J Chem Educ 2001 787 981983 9 0 0 II C e major minor ll1 O lt 1 m lt 1 o 1 o p 1 1 39 1 391 major minor 3 Contributors with more complete octets have a lower energy than those with an incomplete octet 26 a OHS O CH2 4 OHS OCH2 minor contributor major contributor 4 Contributors with more bonds are more important than those with fewer bonds 9 lt gt 9 m ajor minor 5 Contributors with formal negative charges on more electronegative atoms or formal positive charge on less electronegative atoms have less energy then those with formal negative charges ofless electronegative atoms or formal positive charges on more electronegative atoms Both structures generally make a contribution to the hybrid although unequal 9 9 u C ax n C 1 C o e minor very minor major Resonance amp Page 4 5 November 2008 Resonance Structures 6 Contributors containing the following features are of suf ciently high energy so as to not contribute to the hybrid and are unimportant a contain an atom with less than on actet except Be and B b contain an expanded octet for period 2 elements c contain like formal charges on adjacent atoms D L Adams 5 November 2008 Hybridization of 25 and 2p Orbitals Atomic Orbitals Nlix Hybrid Orbitals 2p 2s2p2p2p sp3 2s 4 AO39s 4 Hybrid orbitals Tetrahedral 2p 2p 2s 2p 2p spz 2s 3 AOs 3 Hybrid orbitals Trioonal Planar 2p 2p 2s 2 sp 2s 2 AOs 2 Hybrid orbitals Linear Table 131 2 SUMMARY OF INTERMOLECULAR FORCES Principal Factors 1 Responsible for Type of Interaction Interaction Energy Dipole lon charge dipole moment Dipole Dipole including hydrogen bonding 1 Dipole moment Dipole Induced dipole Dipole moment 5 O polarizability Induced dipole induced dipole 739 Polarizability i 900 Ions in solution 039 9 9 3 quot 2 as 0 Ions being solvated was V V V soi K Q H20 Jure 63 Dissolution of ionic species The dipole of water induces a dipole in 02 by distorting the 02 electron cloud 3F 6 me A a Correlation of the TWO nonpolar atoms Momentary attractions or molecules and repulsions between electron motions between Timeaveraged nuclei and electrons in the two atoms or molecules shape is spherical neighboring molecules which are now dipolar lead to induced dipoles leads to a lower energy and stabilizes the system bp 20 K H 1000 Mall gw hp 77 K N2 CH 78 5 E bp 193 K C o C T 273 K COL gtE bp 69 R Q Q Cal4 0950 of 1 1 I 1 J 0 1 2 1 4 i P atm LV RT 39 llquefactlon 04 T 273 OK 02 0 l l l 4 J 0 100 200 300 400 500 P 211m Pressure dependence of nonideality at high pressures Redrawn from Kauzmann W Kinetic Theory ofGases New York W A Benjamin 1966 l 5 M O 01 O Compressibility ratio 2 O 3901 A SD v Ideal gas 200 400 600 Pressure atm 800 1 000 20 Compressibility z o in P 01 100 5 quotC 00 C Ideal gas 200 400 600 800 1000 Pressure atm Mr V 8R7 39 Elements united ilMeicra in fixed ratios PL751ml 39 Chemically Combine 1 w mm F39xed compos39tlon separable chemically I CannOt into to form Writ2r further puri ed N u I 7 L V J Lu Uniform composi on throughout Nonuniform 39eomposiiidn i Physically separable into Lv 751 mam 7 Cannot be sub ivide H 17 by chemicai or physica processes Anything that Occupies 39space and 39 has mass Physically separable into V7 39 Lwt v Homogeneous mixtures uniform compositions that may vary wideiy 041539 m i am CL am 146041 mi ma ViSuva NoNLANiFU m 7 We Emma 3 t W Arr 12 3quot IHSFcALl v San91mg LL 1 VMfJKLE Novena 7 MANNms i t M gm PEPPERWW 1 Ir J P 1W5 fem M H ohw ENEOHS I Saar wA39nz rL a PEWPQL Cs A1 w mat EU 8 STHN CE Cw m pLEx ny VVVM ETL m K New E SA tr A LIZ15quot ligpmm Dn WIKN MiaVJ LL PvaiLm YES Ocmowm l Lwnmzm W Iwo J MMTEIZ CMAQLG W9 891 E Eo39jLQV PoLmJ r57 omwl rny GHQMind mest l WU LECV LI a vaV u KME r N T Memf m WM ENT Q Mom 62 0x gol mm W OWL 2p x 1 A l l I l 2p 2p 2p 2p 2p 2p 2p 2p 2p 2P 2P 2P 0392 m 1 I 39139 I I w I x I I I ENERGY N A N lll N tn 03925 D 15 1 s 01 Atomic Orbitals Atomic Orbitals quot15 Atomic Orbitals I I l 1 5 Atomic Orbitals I I I 9 ll 9 tn l Molecular Orbitals Molecular Orbitals 75gt glCLCbu NL CHEM121H Honors General Chemistry 1 Dipole Moment 7 A measure of the electron distribution in a molecule or bond The dipole moment is de ned as the electronic charge at either end of the dipole times the distance between the positive and negative charges u Q x d where u dipole moment and Q is in units of Coulombs and d in units of meters Assuming that two point charges one negative and one positive are 100 pm or 1 apart then u 16x103919 C100 pmlm1012 pm 160 x10 C39m defining 1 Debye D as 334 X 103930 Cm then u 160 x 1039 C39m1D334 x 103930 Cm 479D As a rule of thumb 48 5 d where 5 fractional electronic charge and d distance in Angstroms A Thus for the carbonyl group where the measured dipole moment is 24D and the CO distance is 121 A 24 486121 or 5 041 Thus the partial charge on the oxygen atom in the polar CO double bond is 4141 and the partial charge on the carbon atom is 041 October 17 2007 Table 910 0 DIPOLE MOMENTS OF SELECTED MOLECULES Molecule AB Moment 11 D Geometry Molecule AB2 Moment u D Geometry HF 178 linear H20 185 bent HCl 107 linear H25 095 bent HBr 079 linear 802 162 bent HI 038 linear C02 0 linear H2 0 linear r Molecule AB3 Moment u D Geometry Molecule AB4 Moment 1 D Geometry NHS 147 trigonalpyramidal CH4 39 0 teLrahedral NFg 0 23 Lrigonal pyramidal CH3C1 1 92 tetrahedral BFS 0 trigonal planar CH2C12 160 tetrahedral CHC13 39 104 tetrahedral CCl4 0 tetrahedral CON H2 CHEM121H Honors General Chemistry I Vitamin B12 cobalamin There are four types of B12 with varying substituents bonded to Co Methylcobalamin cyanocobalamin hydroxycobalamin and 5 deoxyadenosylcobalamin The CCo bond found in some forms of vitamin B12 is not found anywhere else in nature this is the only biomolecule known to have a CCo chemical bond Natural forms of B12 include the methyl and deoxyadenosyl derivatives Vitamin B12 is not biologically active as a coenzyme but has 2 active derivatives Only three physiological reactions require B12 It is involved in methyl transferase and isomerization reactions Vitamin B12 is available only from animal sources plants do not manufacture it De ciency results in megaloblastic anemia pernicious anemia a condition which involves the production of large red blood cells in insuf cient numbers and a failure to produce acid in the stomach a condition especially prevalent in older people Cobalt is in the 1 oxidation state in B12 Recommended Daily Allowance RDA for adults is 24 micrograms day CI EMIZIH Honors General Chemistry Schrodinger acceptable Wave 9 w psi 9 volume element 9 orbital Equation solutions wave function around nucleus 1 e density where electron may Born Enterpretation exist De nes one Each set Only with certain restrictions 9 quantum numbers 939 n l m size shape orientation D L Rattan 899i 16200 Mass Spectrometry Allows one to determine relative atomic and molecular masses Works by taking advantage of Newton s second law ls better called Masstocharge mz Spectrometry ls colorblind spectroscopy Accelerating pms 20N9 HNB Gas inlet 0 2003 ThomsonEmoksICola We can determine carbon has a mass about 12 times that of hydrogen C has 2 stable isotopes and they differ in mass 12C 120000 13C 130034 on periodic table one finds C 12011 weighted average of isotopes 12C gt 98890 13C gt 1110 H has 2 stable isotopes and they differ in mass H 10078 2H 20014 What good is this geoscientists use 160 180 ratio to determine temperature at which rocks were formed throughout history of the earth where rocks were formed extraterrestrial or not nuclear reactors require enriched uranium gt 99 of natural uranium is 238U a higher percentage of 235U is needed for efficient reactions to be effective 235U has to be enriched from 07 to gt 5 Modern Mass Spectrometers Sam le 1390 Vacuum System Mass Detector Analyzer We need to mgke qgsphgse ions mss spectrometers gre very sensitive Signal Processing and Readout Repeller From reservoir sampling system Eleclruri bea n Ion focus plates Ions Magnet Lighter ions Direction of magnetic lield B Ion exit slit Electron multiplier detector Heavier ions Separated ion beam Harris Quantitative Chemical Analysis Instead of a magnetic field we can use electric fields Four rods O Quadrupole Ion Source C DJ f Detector rwz or a slight variation to the quadrupole mass analyzer Quadrupole Ion Trap 781 kHz Wolfgang Paul and Hans Dehmelt Nobel Prize in Physics 1989 Mass Spectrometer Vacuum System Mass Analyzer Detector Signal Processing and Readout Recent breakthroughs in MS involve the development of new ionization techniques thermal collisional ion protein solution desolvation desolvation focusing nebulizing gas N2 l l l Mass analyzer Electrospray Ionization Courtesy of Prof Igor Kaltashov John Fenn Nobel Prize in Chemistry 2002 MatrixAssisted Laser DesorptionIonization MALDI hv Q Sample 0 Matrix 0 e 0 0 H 0 H Q H o C M I ass o e39 g Analyzer e O O 0 we Koichi Tanaka Nobel Prize in Chemistry 2002 Electrospray Ionization and MALDI are major breakthroughs because we can now make gasphase ions out of almost any molecule without destroying it including DNA and proteins human genome provides blueprint for life but proteins do the work understand cellular processes by understanding what proteins are made during certain processes how these proteins are chemically modified after being made and how much of the protein is actually made Proteomics How do we identify proteins by MS 1 We start by determining the mass of the protein ionic signal au J1 O k L oi iiiiiI 10000 20000 30000 40000 50000 mz How do we identify proteins by MS 2 We then determine the order of some of its amino acids 100 80 60 40 20 Relative Abundance O 200 Relative Abundance Breakdown or digest the protein into smaller pieces 400 1000 1200 mz Tandem Mass Spectrometry mass difference between peaks identifies amino acids How do we identify proteins by MS 3 Search protein databases and match mass and information about amino acid sequence mmenm nixMm 21quot bar 7 1 Q5 Er El 9 in 53139 11quot m 1 1 31 may rszuu My ups lu39i39l vanLn we 1 51 an 1 run1 mn iFirr 2 L Iquot I u all I y l m m How do we identify protein modifications by MS Relative Abundance Relative Abundance Compare unmodified and chemically modified protein and look for mz changes ALT 39 3911394039 39 39 3911 5039 39 39 3911396039 W76 W86 39 39 3911399039 3912390039 M A ALu4ilL 1130 1140 1150 1160 1170 1180 1190 1200 mz CHEM121H Honors General Chemistry 1 Mass Terms and Units Used in Describing Atoms Atomic Mass 1mg 7 The rest mass of an atom in its electronic and nuclear ground state NonSI unit The most common unit used is the uni ed atomic mass unit amu or u defined as 112 the mass ofa carbon12 atom in its ground state1 u 11661 x 103924 g For example the atomic mass ofa 10B isotope is 1001294 u and the atomic mass ofa 11B isotope is 1100931 u Mass or Nucleon Number 1A17 The total number of protons and neutrons collectively called nucleons in the nucleus of the atom The mass number is always a whole number For example the mass number oflOB is 10 5 protons 5 neutrons Atomic Weight 0r Relative Atomic Mass Ar 7 The weighted average mass of all naturally occurring isotopes of that element For example boron has two naturally occurring isotopes 10B 199 and 11B 801 The weighted average ofthese is 10799 u Mass Defect 7 The difference between the calculated mass of an atom based on the rest masses of atomic particles and the experimentally determined atomic mass The mass defect is converted into binding energy BE upon formation of the atom Atomic 0r Proton Number 1Z17 The number of protons in the atomic nucleus Always a whole number This is the basis for element ordering in the periodic table For example Z 1 for H Z 6 for C and Z 109 for Mt Meitnerium From Mills 1 et al Quantities units and symbols in physical chemistry The Green Book IUPAC Blackwell Publications Oxford 1988 and McNaught A D Wilkinson A Compendium of chemical terminology 2e The Gold Book IUPAC Blackwell Publications Oxford 1997 D L Adams 882005 Wav A disturbance walm travels Waugh a medium aansparang energy tram ape lapaaan lts saarae a annther lapaaan Wlthnut aansparang matter Eaea lndlvldual paraele anae medlum l5 tempurarlly dlsplaced and then returns a lts arlglnal eaalllprlam pusltlun A Wave m walm partldes anae medlum mnve m a dlrecnurl perpendicular a the dream mm the Wave maves a A Wave m walm partldes anae medlum mnve m a dlrecnurl parallel a the dlrectlurl mm the Wave maves me mp www phyacalasam mumwaver am am Amplitude The maximum amount of displacement of a a particle on the medium from its rest position dashed line drawn through the center of the diagram Wavelength The length of one complete wave cycle measured as the distance from crest to crest from trough to trough or from any point on a wave to the corresponding point on the next cycle of the wave The units of wavelength are meters centimeters 10392 m nanometers 10399 m Frequency The number of times the particles of the medium vibrate when a wave passes through the medium In mathematical terms the frequency is the number of complete vibrational cycles of a medium per time The units of frequency are cyclessecond wavessecond vibrationssecond or somethingsecond Another unit for frequency is the Hertz abbreviated Hz where 1 Hz is equivalent to 1 cyclesecond Speed The distance traveled by a given point on the wave such as a crest in a given interval of time The speed of a wave is dependent upon the properties of the medium density spring constant and damping coef cient Waves travel fastest in the least dense medium The speed of a wave is not dependent on the properties of the wave amplitude wavelength frequency The units of speed are meterssecond For a given medium Speed wavelength x frequency For electromagnetic radiation the speed of light in a vacuum is given the symbol c 2998 x 108 msec Chapter 3 Lecture Worksheet 3 A De ne the term homonuclear diatomic molecule Give an example B Give an example of a heteronuclear diatomic molecule C B2 has unpaired electrons Be sure that you can sketch the correlation diagram and label the yaxis and the atomic and molecular orbitals D The bond order for B2 is PRS Answers 0 0 1 1 2 2 3 3 4 12 5 112 6 212 E You would expect the bond in B2 to be 1 Stronger 2 Weaker than the bond in B2 F Write the complete electron configuration for B2 G Using MO theory you would predict C2 to be 1 Paramagnetic 2 Diamagnetic H Draw Lewis structures for N2 and 02 1 Based on your Lewis structures you would predict 02 to be 1 Paramagnetic 2 Diamagnetic J Sketch the correlation diagram for N2 K Sketch the correlation diagram for 02 Note For oxygen to neon 02 lt mp L Based on MO Theory you would predict 02 to be 1 Paramagnetic 2 Diamagnetic M Thebond orderforOz is PRSAnswers 00 1 1223341251126212 N Does this agree with your Lewis structure 1 Yes 2 N0 Percent Composition to Formula 1 Assume 100 grams 2 composition 2 grams of each element 3 Convert to moles 4 Divide by smallest number of moles 5 If not whole numbers multiply all by 2 3 4 until they are 3 Kidney stones are composed of calcium carbon and oxygen in the ratios 313 Ca 187 C 500 0 by weight What is the empirical formula for the compound in kidney stones Formula 2 CaCZO4 Calcium oxalate