General Chemistry Review for the MCAT
General Chemistry Review for the MCAT
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General Chemistry Review for the MCAT Dr Paul A Jelliss Monsanto Hall 114 314 9772834 je11issps1uedu The M CA T Basic Structure Verbal Reasoning 85 minutes 65 questions Physical Sciences Igt Physics amp Gen Chem 100 minutes 77 questions PC Writing Sample 30 minutes 2 essays Biological Sciences Igt Organic amp Biology 100 minutes 77 questions Jl l7 T71 The Essentials for Class A functional brain not yet tumed to mush it might after this Eyes amp Ears preferably attached to aforementioned brain Penpencil amp notepaper to Write stuff down When I suggest eg examples We ll try to make this at least a bit interactive to keep you awake whereeelesearenlgyonratherehe 7arlisHen a cold turday J K F ebrlri r What can we do in 6 hours No Way can We cover absolutely everything from two semesters of general chemistry would you really Want to relive that entire nightmare anyway We can look at key concepts from gen chem and try some examples which are MCAT releVant Most importantly RELAX but don t overdo it you will leam and test better under moderate anxiety Freaking out Won t help General Chemistry on the M CAT Intermingled With physics in a Physical Sciences section total 77 questions in 100 minutes 75 seconds per question Sorne passages some free standing questions consider doing the latter rst Immediately following the Verbal section before lunch QM7 iLWr Back to the Basics Atomic Structure Atom smallest unit of any element Subunits protons neutrons electrons protons and neutrons are neueleons Atomic number Z proton number identi es element X charge of 1 mass of1 amu 166 x 1027 kg Back to the Basics Atomic Structure Mass number A mass of the atom A Z protons N neutrons Z nucleons Neutrons same mass as protons no charge Written as superscript before the element symbol A Z X electrons Z in a neutral atom Isotopes Atomic Weight and Ions t iWhat is an isotope Two atoms of the same element that differ in their number of neutrons 74Be and Be Atomic Weight not atomic mass What s the difference Weighted average of masses of naturally occurring isotopes Ions gain or of electrons anion or I T Average Atomic Weight iE1ement X has two isotopes of atomic mass 386 and 426 in 13 relative abundance iWhat is the atomic Weight of X 426 417 406 397 Isotopes Atomic Weight and Ions Example iAn atom contains 16 protons 17 neutrons and 18 electrons Which of the following best indicates this atom 33c1 34c1 33 S2 34S2 Quantum Numbers Electron Zip Code Z i What is the purpose of quantum numbers Quantum numbers designate a unique zip code for each electron in an energy level lNo two can have same zip code HOW many quantum numbers in a zip code y i One zip code Igt four quantum numbers subshell spin The First Quantum Number What does it designate What is its symbol Principal quantum number designates the symbol is n Related to the size and energy of an orbital a three dimensional region around the nucleus in Which the electron is likely to be found What are the possible Values n l 2 3 4 5oo higher Values are higher in energy and farther from nucleus The Second Quantum Number What does it designate Symbol rSubshell number symbol is l describes shape of electron s orbital rValues 01 2n 1 Ifn 3 then l 01 or 2 s 1 cl and f subshells correspond to l Values of O 1 2 and 3 respectively Subshells have shape What are they The Second Quantum Number The Third Quantum Number What does it designate Symbol rOrbital number symbol is ml describes the three dimensional orientation of an orbital rValues r Value of m l0l inclusive IflOthenmO Ifl lthenml lOl Ifl2thenm 2 lO 12 The Fourth Quantum Number What does it designate Symbol 7 number symbol is ms designates electron s intrinsic magnetism p Values Value of ms or only Every orbital can accommodate 2 electrons If an orbital is full the electrons it holds are spinpaired 6a Assigning Quantum Numbers Rules Aufbau principle What is it N Electrons occupy the lowest energy orbitals available 2s2p3s3p 3d 55 5p6s 5d 6p7s5f6al7p Hund s Rule Basic point Electrons in same subshell occupy available orbitals singly before pairing up Pauli Exclusion Principle Think exclusion No two electrons can have same set of four quantum numbers Q M W J pVQ m 2 3 5 7 N n S Gwmw HOQw r O H HO Cw U S w u R m 3 b m N m u t n a u Q 3 m n we S S A Ground State Electron Configurations rUse previous three rules to Write r39How Would oxygen look v 1s22s22p4 Frequently shortcut designations are used instead of Writing out the entire con guration P for example Ne3s23p3 Electron Con gurations nllgaLIra i9 is HOE CF18 2Ic Laarl one stalbillty lghfilled or 1czf fZllerl subshells Ar4s23d4 K l7But What is it really 39lXC1 actual Ar 451 3075 I IIII Electron Configurations Ions Anions accommodate the gained electrons in the first available orbital with the lowest available energy F Z9 has con g ls22s22p5 While F has con g ls22s22p6 con guration exactly like Ne F and Ne are called isoelectronic iso sarne electronic con guration Electron Configurations Ions Cations lose electrons from the most unstable orbital How would Li look Li Z 3 has con g ls22s1 and Li has con g ls2 How about Ti For transition metals the Valence s electrons are always lost rst before any cl electrons Ti Z 22 expected Ar3d14s2 but Ti actually Ar3o 24s1 Electron Configurations Examples Which of the following gives the electron con guration of an aluminum atom ls22s22p1 ls22s22p2 ls22s22p63s23p1 ls22s22p63s23p2 Electron Configurations Examples 7What is the electron con guration of an atom of copper Remember Cu is an exception Expected Ar 3d94s2 P Actual Ar 3 d1 4s1 7Mora1 beware of stability in transition metals Diamagnetic and Pammagnetic Amms Diamagnetic all electrons are spin paired even number of electrons atom repelled by a magnetic eld Paramagnetic not all electrons are spin paired atom attracted by a magnetic eld lI1OW the difference these are easy points Electron Energy Levels and Spectra l Ground state de ne Lowest possible energy EXClt d state At least le in higher energy level elbsorption or energy change Incoming photon absorbed by electron jumping to higher energy level lEmission or energy change Electron dropping to lower energy level emits photon Electron Energy Levels and Spectra Formula for the energy of a photon E hr he1 define the terms Planck s constant h 663 gtltlO 34 J s Emission vs absorption spectra What s the difference Emission electrons dropping to lower energy levels emit light of specific frequencies Which are separated into bright lines by a prism speci c frequencies of White light are absorbed by gaseous element based on differences between quantized energy levels dark bands Electromagnetic Spectrum lFrorn lowest to highest energy level lRadiowaVes gt microwaves gt infrared gt Visible light gt ultraviolet gt Xrays gt gamma rays rVisible light from lowest to highest frequency lRed gt orange gt yellow gt green j 39 blue gt gt Violet ROYGB V Trends are important not Values Nuclear Structure and Decay Protons and neutrons held together by strong nuclear force which overcomes the electrical repulsion between the protons What is radioactive decay Unstable nuclei undergo a transformation by altering the number and ratio of protons and neutrons or lowering their energy What are parent and daughter nuclei Anyone done the different types in class Alpha Decay 05 lAn alpha particle denoted by 05 consists of 2 protons and 2 neutrons equivalent to a He nucleus which is ejected l llpha decay reduces the parent s atomic number by 2 and mass number by 4 210 4 MP0 gt 2 682Pb 2He AZ 2AA 4 Beta Decay 6 When unstable nucleus contains too many neutrons it may convert a neutron into a proton and an electron 6 particle which is ejected 1On gt 11p 1e Atomic number of daughter nucleus is l greater than parent but mass number same e 14 14 0 6C gt 7N 1e AZLAAO Positron Decay t When unstable nucleus contains too few neutrons it may convert a proton into a neutron and positron 8 particle which is ejected 11p 10 O1 Positron is electron s antiparticle identical to electron but charge is positive Atomic number of daughter nucleus is 1 less than parent but mass number same A 0 p O l 9F quot 80 16 AZLAA Electron Capture Conversion of a proton into a neutron by an unstable nucleus by capturing an electron e from the closest shell 11p 1e gt 1On Atomic number of daughter nucleus is 1 less than parent but mass number same just like positron emission 5 6 5 1 O 5 1 24Cr 16 23V AZ 1AAO Gamma Decay 7 Nucleus in excited state often after alpha or beta decay emits energy in form of photons of electromagnetic radiation rGamma photons 7rays have neither mass nor charge and their ejection changes neither atomic mass or number 3114Si 31151 3 quot 31151 7 AZOAAO Radioactive Decay Example Radioactive calcium47 a known 6 emitter is administered in form of 47CaC12 by IV as a diagnostic tool to study calcium metabolism What is the daughter nucleus of 47Ca2 46K 47K 47Ca2 47SC2 Radioactive Decay Example Memory device t decay starts with proton and makes it a neutron 2 decay starts with neutron and makes it a proton Radioactive Decay Half Life t What is a halflife tThe time it takes for one half of some sample of radioactive substance to decay t39Shorter half lives mean faster decay tHalf life denoted by t12 t Make a chart to solve these problems forget the formula unless you do efunctions in your head Radioactive Decay Half Life Time Amount of Sample Remaining O 100 1 halflife 39gt 12 1250 2 ha1f 1iVes 39gt Ztl2 122 14 25 ha1f 1iVes 39gt t12 12 18 125 ha1f 1iVes 39gt t12 12 116 625 Half Life Example Radiolabeled Vitamin B12 containing radioactive eoba1t 58 is administered to diagnose a defect in a patient s Vitamin B12 absorption If the half life is 72 days approximately What percentage of the radioisotope will remain in the patient a year later 3 5 8 10 f LL truce gt conmins selrrrle q crbo 2 o1s in Chemical Compounds I pure substance can be broken into 2rnore elements Molecule I smallest unit of a compound still retains properties formula unit for ionic compounds I smallest unit of an element Any compound always contains sarne composition by mass eg iron III oxide lFe 699 o 301 Empirical Formula 1Find lowest mu1tip1es of Whole atoms I 2 step process G assume 100 g compound 1 mol Fe 699 g x 125 mol 559 convert numbers to lowest Whole mu1tip1es 188 mo1O 15 mo1O 3 mol I F6203 125 mol Fe 10 mol Fe 2 mol Fe 42 Molecular Formula lFor many usually organic compounds actual molecular formula usually not empirical simplest ratio eg glucose Empirical CH2O molecular C6H12O6 molecular mass integer n I CmHnyOnZ empirical mass lFor glucose I n 6 Balanced Chemical Equations Inorganic chemistry I conservation of matter 2H2 O2 gt ZHZO Stoichiometric rganic chemistry coef cients C3H8 2 gt CD2 H20 6 C3H8 2 gt 3C2 H20 Q C3H8 2 gt 3C2 4H2 C3H8 502 gt BCO2 4H2O a Ba1ance 0 last why Chemical Reactions tStoichiometric factors 4Fes 3O2g gt 2Fe2O3s How many moles 2 required to react completely with 5 mol Fe 3 mol 2 5 mol Fe x 375 rno1O2 4 mol Fe How many moles Fe2O3 are produced When 5 mol Fe react completely 2 H101 F6203 2 50 mol F O C 4 mol Fe 2 3 45 5rno1Fegtlt Limiting Reagent F279 g Fe amp 128 g 2 are allowed to react Which is the limiting reagent 279 g Fe x x 559 g Fe 4 mol Fe 1 mol Fe2O3 400 g Fe2O3 I Fe is limiting 1 1110102 X 2 mol Fe2O3 X 160 g Fe2O3 320 g O2 3 mol 2 1 mol Fe2O3 427 g Fe2O3 I O2 is in excess l28gO2gtlt 46 Yield lTheoretical yield I maximum yield allowed by limiting reagent in grams Percentage yield actual yield x 100 percentage yield theoretical yield lMeasure of how successfully reaction proceeds in forward direction Yield l Wher1 279 g Fe amp 128 g 2 are allowed to react only 300 g of Fe2O3 are recovered What is the percentage yield 300 g 400 g x lOO750 Types of Chemical Reaction Precipitation reactions Neutralization reactions Gasforming reactions Redox reaction Precipitation Reactions Formation of insoluble product PbNO32aq 2KIaq gt PbI2s 2KNO3aq Pb2aq 2Nlt73 aq aq 21 aq gt PbI2ltsgt ltaqgt N 2 ltaqgt Spectator ions Net ionic reaction Pb2aq 2I aq gt PbI2s Neutralization Reactions Strong acid strong base gt salt Water HC1aq NaOHaq gt NaC1aq H2O1 Hltaqgt 1ltaqgt Naltaqgt oHltaqgt Nffaq aq H200 Spectator ions Net ionic reaction Haq OH aq gt H2O1 Gasforming Reactions Reaction Where one of the products is a gas Na2CO3aq 2HC1aq gt C2g H2O1 2NaC1aq 2N aq C032 aq 2Haq 261 aq gt C02g H200 N Taq aq Spectator ions Net ionic reaction C032 aq 2H aq gt 1 1 52 Redox Reactions Reactions involving transfer of electrons and changes in oxidation state gt Fe3aq e MnO4 aq Se gt Mn2aq oxidant MnO4 aq Se gt Mn2aq MnO4 aq 8Haq 4 Mn2aq 4H2O1 5Fe2aq gt 5Fe3aq 26 5Fe2aq MnO4 aq 8Haq gt 5Fe3aq Mn2aq 4H2O1 53 The Periodic Table Eh PEPIDDJC CVF LEMeE TJ Groups of the Periodic Table Periods are horizontal rows Groups families are Vertical columns Metals nonmetals and metalloids which are Which 7What are the electrons in an atom s outermost shell called rValence electrons primarily responsible for chemical behavior 3B 3 4B 4 5B 5 6B 6 2B 12 3A 13 4A 114 SA 15 6A 16 7A 17 p N 2322 Zsz pq 2s3922p5 15 P 3523355 31523354 21 S M1452 22 Ti 3a124s2 V 24 Cr 3 z 30 Z11 3d1394s2 1 1 33 As 3d 19452 433 34 139 P 410 Zr 4d25s392 b 1 48 Cd 7 1 4dm552 A 51 Sb 10552 5P3 72 0 H 3 4f145bdl1 652 83 Bi 4f l T 6526p 112 Lanthanjde XE series Achlnide SE1 1ES R111 Groups of the Periodic Table Group Name Valence Con g Group I Alkali Metals nsl Group II Alkaline Earth Metals VLS2 Group VII Halogens ns2np5 Group VIII Noble Gases ns2np6 The S block Representative Elements 11514 The a block Transition Metals n l dquotnsY The p block Representative Elements The f block Rare Earth Metals 112 f n l dYnsZ 57 Representative sblock Representative ptbl0cllt elements elements Transition metals fBlock metals Groups of the Periodic Table The Octet Rule What is an octet Great stability in ns2np6 electron con guration All noble gases have a complete octet 8 Valence electrons One exception What is it Periodic Trends Nuclear Shielding rf Outer 353 eleetmms Cemreined effieacet 1 2 Valence electrons feel a reduction in the positive 0 Pe ID s 11 L5 20 25 6 Dnlstanm from nueleeus A nucleus quot Rariia1 E1Ef39fI lI39l density Periodic Trends Atomic and Ionic Radius What properties of an atom determine radius rRadius is a function of total pull of protons on Valence electrons what does the trend look like More protons to the right Within a period means stronger pull Igt Number of shells doesn t change in a period rMore shells downward Within a group means more shielding 39gt larger radius Periodic Trends Ianization Energy What is an ionization energy Amount of energy necessary to remove the leasttightly bound electron IE n l23 What is IE related to Smaller radii means leasttightly bound electron is closer to nucleus held tighter and requires more energy to ionize Filled Valence shells have high IE reluctant to relinquish stability IE2 vs IE1 Periodic Trends Electron Affinity Anyone Want to de ne it mL i The energy associated With the addition of an electron negative and positive values How is electron af nity related to octet stability Becomes more negative the closer the atom is to an octet con guration what does this mean Positive values energy required for atoms to accept an electron anions of these are unstable 63 Periodic Trends Electronegativity De nition or description rAn atom s ability to pull electrons to itself when forming a covalent bond Greater attraction means higher electronegativity Notice a pattern z Trend follows same pattern as IE rA Hobbit mnemonic Igt FONCI BrISCH FgtOgtNClgtBrgtIgtSgtCgtH Periodic Trends Example Which of the following Will have a greater Value for phosphorus than for magnesium I Atomic radius 11 Ionization energy III Eleetronegativity 391 only 1 and 11 only 11 and III only 1 II and III Lewis Dot Structures quot Anyone remember the rules h Pay attention to Valence electrons l total Valence e count group s Valence e pairs Valence e 2 make single covalent bonds remaining pairs Igt terminal atoms Igt lone pairs octet skeleton structure Igt central atom lowest 5 rule left over e Igt central atom if still lt 8 er then turn lone pair 39gt bond pair 39gt multiple bonds C N O P S 66 Lewis Dot Structures Formal Charge Anyone know what it is Are atoms sharing Valence electrons in the best way possible formal charge O HCN or HNC Only one is right even though both satisfy the octet rule FC V 13 L V Valence electrons free atom B bonding electrons L lone pair electrons Lewis Dot Structure Examples Which is the best Lewis structure for CHZO A common question Count Valence electrons first and rule out any With the Wrong number If more than one accounts for the right number use formal charge Lewis Dot Structure Examples tWhieh is the best Lewis structure for the nitronium ion N02 Polar Covalent Bonds Covalent bonding shared electrons Polar covalent unequal sharing A bond is polar if electron density between the atoms is uneven a function of What Dipole moment u er Polar or not tX CC14HFOCSNO3 V 5 Y Coordinate Covalent Bonds Still covalent bonding shared electrons How different from covalent bond Here one atom Will donate both of the shared electrons in the bond Complex contains a Lewis base ligand and Lewis acid which is Which Good example BF3 and NH3 AB Ionic Bonds What are they One atom gives a Valence electron to the other and electrostatic interaction holds atoms together Usually between a metal and nonmetal but always between two atoms with large electronegativity difference A NaCl KCl etc VSEPR Theory Basic premise electron pairs on a central atom try to move apart as far as possible Electron group geometry vs molecular geometry Electron group geometry electron groups and nonbonding on center atom determine geometric family Molecular geometry pairs around center atom determine shape more speci c than electron groups Moral determine family then shape VSEPR Theory The Families Electron Groups Geometric Family 2 Linear Trigonal Planar Tetrahedral Trigonal Bipyramidal Oetahedral VSEPR Theory Shape amp Lone Pairs Number of E1E trnrm ElEI2 I IT Elumaixl ErnmlVing Nunbandimg Mnillelculaur Dnmaims Geometry Dnimaima D nama4ins GEHIHET 13939 E 39J I1 lp39lvE39 TA1139Lgrnal planar 0w Ii W n Number Elf E1rEt1rnn Elmitmxl ADGmaixu Enn1i11g Ehzznmain GenmEtry TZ39In main5 TertralmEdral Nnnbm1dimg l maim5 Maltacular GEmn E itry Trgnnlal pjrrami1daKl 39 1 Tina lectmm 1I3m11arin3 Elrettmninne Dman nd img I39 3i e un m eIry Wumzaijnias Mnnfhn11diing Immairn5 MmlEculaIr E139 III fIrEquot1iy39 Trig na ririInrniII7Eul Trigmnal bipyrami dal Number Elf E1rEt1mn 39E1evz tm11 ADEmain Banding Nnnb nNdimVg Maliacular Ehzlmain Enmvetry T39It1i ma1in1 5 TD maim5 GE I11l E iiIquot EJIEI139lp39lE39 SIE 8 x cta od rail uri I Sqiuare planar VSEPR Theory Examples lDetermine the geometric family and predict the shape of each of the following molecules H20 BrF3 XeOF4 NH3 NH4 BF3 VSEPR Theory Examples riDraWthink about Lewis structures rCount electron groups around center atom for family r Count bonding groups around center atom to narrow down family into molecular shape multiple bond counts as one group rDon t memorize all of this Visualize except geometry names familiar Hybridization rHoW do you determine hybridization around a central atom rEach pair needs an orbital 5 lls first x 1 thenp x 3 then d x 5 2 electron groups Sp hybridized electron groups hybridized electron groups hybridized 5 electron groups sp3d hybridized 6 electron groups sp3d2 hybridized Hybridization Example 7Determine the hybridization of the central atom in each of the following molecules H20 BrF3 XeOF4 NH3 NH4 BF3 Polar Molecules CC14 HF OCS NO I Polar or not Solids and Intermolecular Forces lDifferentiate between ionic network and metallic solids lonic electrostatic attractions NaCl CaF2 Network lattice of covalent bonds diamond quartz lMetallic covalent lattice of nuclei and inner electrons surrounded by cloud of electrons What are conduction electrons Solids and Intermolecular Forces Intermolecular forces are relatively weak interactions between neutral charged molecules Four major types what are they polar molecules attracted to ions between positive and negative end of two polar molecules permanent dipole induces dipole in nonpolar molecule instantaneous dipole induces a dipole in neighboring nonpolar molecule also Van der Waals forces 85 Solids and Intermolecular Forces Hydrogen Bonding When does it occur Only between H attached to an N O F and the lone pair of another N O or F atom This is major N O and F only not C or any other atom Why does it occur Very small hydrogen low 5 next to fairly small atom Very high 5 gt intense partial positive charge r latches onto lone pair of electrons with hlgh 86 Phase Transitions Closely related to What property of molecules Temperature measure of internal kinetic energy r39States or phases name them Solids liquids gases all differ in kinetic energy and intermolecular forces rPhase change caused by overcoming or strengthening intermolecular forces boiling point Vapor pressure etc Phase T mnsitions Summary Evaporation condensation fusion crystallization sublimation deposition de ne EVaporation liquid to gas lCondensation gas to liquid lFusion melting solid to liquid Crystallization freezing liquid to solid lSubli1nation solid to gas Deposition gas to solid Phase T mnsitions Summary rGas I liquid I solid what happens to heat KB and entropy rHeat released internal KE decreases entropy decreases r39Solid I liquid I gas What happens to heat KB and entropy r Heat absorbed internal KE increases entropy increases P Know the conceptual trends Heats of Phase Changes change of phase depends on what two things of substance and of substance tHeat of transition AH what does it represent z is amount of energy required to complete a phase transition oonst pressure Equation q mm What is n signs on terms rPOSi iV AH and q Igt heat absorbed Igt endotherrnie NegatiVe AH and q 39gt heat released 39gt Calorimetry Absorption or release of heat what are two possible consequences Temperature change or phase change but not both at same time Equation for amount of heat absorbedreleased i q mcAT 0 de ne the terms What is speci c heat Intrinsic property resistance to temperature change High c means small temperature change holds absorbed heat better Calorimetry Example Equal amounts of heat are absorbed by l0 g solid samples of four different metals aluminum lead tin and iron Of the four Which Will exhibit the smallest temp change Aluminum C 090 J g 1K 1 Lead C 013 Jg 1K 1 Tin C 023 Jg 1K 1 Iron c 045 Jg 1K 1 Phase Transition Diagrams What is plotted on one What does it show Note during a phase transition temperature of substance does not change sound familiar Pressure vs temperature shoWs how phases are determined by these properties Some terms triple point Triple point temp and pressure at which all phases exist simultaneously in equilibrium beyond this point substance has properties of gas and liquid high density low Viscosity supereritieal uid Phase Transition Diagrams CIquoti CEl1 Y PDLIFTE T T Liquid Melting F39reez4i1quot1g Sulid Vaporization GZ Pressure V h C1 39I1C139E391 lS tiQ Sub1imati0 vi T1 iP1e V C V V Defpositimi Temperature Phase Diagrams Water amp C02 rOne difference between Water and other substances What 7Let s draw and label Water and carbon dioxide phase diagrams rFor Water an increase in pressure at constant temperature can favor liquid phase not the solid as usual ice skating Phase Diagrams Water amp C02 Y arm 218 atm Pressure 1 am A 511 atm Pressure Temp ture QC Temperanture QC Gases and KineticMolecular Theory What is the purpose of the theory Sets the conditions for an ideal gas Normally real gases operate like ideal gases so these conditions can be applied to understand gas behavior A good example of this application the ideal gas law Assumptions of the Theory First assumption 4 Gas molecules take up essentially no Volume compared to the average spacing between them 4 Second as sumption Constant motion constant speeds and random collisions Pressure Igt average force exerted per unit area Elasticity Igt KEi KEf No intermolecular forces Assumptions of the Theory 5 K Third assumption Direct proportionality between average kinetic energy of gas molecules and temperature in Kelvin degrees KE oc T Note that this is average kinetic energy not average speed speed involves additional factors as We Will see Ideal Gas Law Units What are the units of Volume temperature and pressure that are used ern3 1 mL1 m3 1000 L Kelvin Celsius 273 latrn 760 torr 760 mmHg Standard temp and pressure 7 27 3 K and 1 atm Ideal Gas Law Describes behavior of gases following kineticmolecular theory i What is the equation rPV nRT de ne the terms Gas constant R 00821 Latm rno1 1K 1 Derivations of other laws from the idea1 gas law three proportionalities two have names Other P VT Gas Laws 7Volume proportional to temperature at constant pressure What law rCharles Law 39gt V1T1 V2T2 Pressure inversely proportional to Volume at constant temperature What law Boyle s Law Igt PIVI PZVZ rPressure proportional to temperature at constant Volume 39gt P1T1 P2 T 2 Other P VT Gas Laws Suppose you hold n constant 39gt PIVIT1 P2V2T2 What did he propose If two equalVolume containers hold gas at the same pressure ar1dterr1p then they contain the same number of particles regardless of identity What is the consequence of this law 224 L 273 K and 1 atm 103 IdealGas Law Example iHOW many atoms of helium are present in 112 liters of the gas at a pressure of 1 atm and temperature of 273 K 39 301 X 1023 39 602 X1023 120 X1023 Cannot be determined from information given Dalton s Law of Partial Pressures Total pressure of sample of 3 different gases is due to collisions of all types with container Wall What does this say for the pressure of each type of gas Daltor1 s Law of Partial Pressures PPaPbPC Corollary Pa XaP Where Xa is mole fraction ofgas a Dalton s Law Example 8 mixture of neon and nitrogen contains 05 mol of Ne and 2 mol of N2g If total pressure is 20 atm What is partial pressure of neon Graham s Law of Effusion What is effusion Escape of a gas molecule through a tiny hole comparable in size to the molecule into an evacuated region 4 Our concerns With Graham s Law What factors determine speed of effusion What equations will help determine relative rates of effusion for two gases Graham s Law The Conditions Temperature in container of gas molecules is a constant Average kinetic energies are equal iMolar masses of gases may be different 4 Given What We know about kinetic energy mass must play a role in average speed KE 2m2 Graham s Law Formulas C G The usable formula Rate of Gas A Molar Mass Gas B Rate of Gas B Molar Mass Gas A PM Notice the relationships lThe rate of effusion and molar mass are inverses so the faster a gas effuses the smaller its molar mass must be Graham s Law Remember Molecules of different gases at same temp have same average kinetic energy Average speed takes into account molar mass rAs temp of sample is increased the average speed will increase Cannot account for Wide range of speeds in individual molecules Graham s Law Some Examples container holds methane and sulfur dioxide at temp of 227 C Which of following best describes the relationship between their speeds Where vm represents methane and vs sulfur dioxide vs l6vm 39 vS2vm vm2vS 12111 16128 Graham s Law Some Examples l Chamber A holds a mix of four gases 1 mol of each A tiny hole is made in the side and the gases are allowed to effuse into an empty chamber When 2 mol of gas have escaped which gas will have the greatest mole fraction in Chamber A C12 12 N2 CO2 Approaching Ideal Gas Behavior Under normal conditions real gases behave like ideal gases so the assumptions of kinetic molecular theory apply molecules are so small compared with surrounding space that they essentially occupy no Volume molecules experience no intermolecular forces Approaching Ideal Gas Behavior lBut these assumptions fail under certain conditions making the real gas not ideal name them q quotHigh pressures Low temperatures Strong intermolecular forces esp Hbonds High MW and diatomic gases behave less ideally than low MW and monatomic gases Ideal Gas Behavior Example 40f the following which gas would likely deviate the most from ideal behavior at high pressure and low temperature H6 g 39 H2 8 39 O2 E 39 H20 E