Test 2 Study Guide
Test 2 Study Guide CHEM 345
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This 8 page Study Guide was uploaded by Kayli Antos on Monday October 19, 2015. The Study Guide belongs to CHEM 345 at Towson University taught by Dr. Ma in Summer 2015. Since its upload, it has received 58 views. For similar materials see Physical Chemistry in Chemistry at Towson University.
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Date Created: 10/19/15
P Chem Test 2 The First Law of Thermodynamics ltgt Derivative Problems x 1 x 1 For when n 1fx 2xquot dx xquot x E x quot1 1 n1 n1 1 X 2 x 1 x For when n1f 2 dx 1n x1 x x1 0 IhermgshemiguanaBeastign nthaley Heat of Formation 69 This is the change in enthalpy during the formation of one mole of a pure substance in its standard state from components that are also in their standard states 69 Afm Standard Enthalpy of Combustion 69 This is the change in standard enthalpy for each mole of a combustible substance 69 AC The Second Law of Thermodynamics ltgt Ther9h hiity9fagate Molecules in a system ca have different arrangements Many more disordered microstates than ordered microstates ltgt Entrgpy State function Extensive property Measured in JK ltgt Entr92ychange ExpansionCompression For expansion entropy change is positive For compression entropy change is negative Wrev Wmax and are both along with Wirrev are all negative values This leads to ASuniV being positive because the absolute value of Wrev is greater than Wirrev ASuniv is zero for a reversible reaction and positive for an irreversible spontaneous reaction 69696969 69 Absolute Entropy and the Third Law of Thermodynamics ltgt T1eI1irdLawQtlhermgdvnamics At absolute zero the entropy of a pure element or compound is zero because it can only form one microstate Gibbs and Helmholtz Energies and their Application 0 ihbsEI19rgy State function Extensive property Measured in J f AG lt O the reaction is exergonic work producing and spontaneous f AG O the reaction is reversible and at equilibrium f AG gt O the reaction is endergonic work consuming and not spontaneous ltgt emh9tzEn9rgy f AA lt O the reaction is spontaneous f AAOthe system is at equilibrium f AA gt O the reaction is non spontaneous Measured in J State function Extensive property 0 SIandardMelaQibbs nergyet grmatiqn The change in Gibbs energy during the formation of one mole of any compound at one bar from its elements in their standard state Af o 0 Dependence 9f ihh ED913199 Iemneratu 9 Where the molar Gibbs energy of two states is equal AGO and the reaction is at equilibrium and reversible 0 Normal BP indicates a pressure of 1 atm Equations To Know 0 AH Z Afm products Z uAme39eactants where u is the stoichiometric coefficient 0000 0 0000000 AH AU APV if pressure is constant AH AU PAV if condensed states don t contribute volume and assuming ideal gas behavior AH AU AngasRT if temperature is constant AH AU RTAngas at constant pressure qp AHO AH qp nffz EPdT 1 T T a pure substance HT2 HT1 n lez CPdT or HT2 HT1 lez CPdT substance i in a mixture H HT 2 fpiidT or 0 T HTi HT1i l39 ITO CPidT reaction enthalpy AHT c m dHTID aHTIA bHTIB T T T c Hm fTo Cde d Hm fTo CPID dT a HTOIA fTo CPIAdT T b HTOIB fTo CPIBdT cHTO dHTOID aHTOA bHTOIB T T T T c fTO Cde d fTO CRDdT a fTO CRAdT b fTO CPBdT AHTO T fT0CCPC l39 dCPD aCPA l39 bCPBdT Kirchoff s LawEquation AHTO ACPdT AHT if EP is constant 0 AHT AHTO To Clrev d when temperature Isn t constant AS f T when temperature IS Clrev constant AS ideal gas isothermal conditions AS nR 1n or A5 71R 1 g 1 2 temperature of the system and the surroundings is the same Clsurr qsys Mm T T q reverSIble ASSyS m q q reverSIble ASSWT Sf quot 2 779quot reversible ASunw ASSyS ASSW 0 T I u q IrreverSIble ASSyS 2 Te CI Q39 W39 w Assurr surr erev erev 117817 T T T T I u q W39 W W IrreverSIble ASuniv ASSyS Assn 717 quotgel 2 7rev 1317 nA V 1 VA V n VA 96A 00000 0000000 000000000 T2 when n is constant T1 T when volume is constant AS T Cquot dT T A5 nfTZV when Cv IS constant AS nCVlnT 2 1 1 T n5 dT when pressure IS constant AS T2when n IS constant 1 T Cquot dT T A5 n fTZP when Cp IS constant AS nCP lnT 2 1 1 CIrev CIP AH at constant temperature and pressure AS T S kB nW T2 CTp T2 6p constant pressure AS nfT dT or A5 L dT 1 1 If T1298K T2T AST A5298 f A aw 298 T ASaba 555983 l39 d5 980 SabaA l39 b5 983 AH at constant pressure qSyS qp 2 AH so ASSWT T same temperature and pressure in initial and final states Gibbs AG AH TAS Helmholtz constant temperature and volume A U TS dAdU TdS dAdU dqrev mixing of 2 ideal gases AA RTn1nX1 m lnX2 AG 0 Z uAfCO products Z uAfCO reactants for an infinitesimal change dG dH dTS or dG dq dw PdVVdP TdS SdT d3 dCIrev T for a reversible path dqrev TdS dA ClWrev max work dWrev dWPVrev deonPVrev expansion nonexpansion ClWPVrev PdV d6 oIqrev onrev PdV VdP TdS SdT dwnonpvrev VdP SdT constant temperature and pressure AG wnonpvrev only expansion work dG VdP SdT constant pressure dG SdT or d6 S39dT integrate L d6 ff SdT or 62 61 ff SdT assume molar 1 1 1 entropy is constant A5 S39AT constant temperature dG VdP or d6 VdP ltgtltgtltgtltgt integrate A6 fl VdP 1 condensed states A5 VAP ideal gas behavior A6 fligz dp or A6 RTlnE 1 P 131 P AG 2 nRT lnP 2 like the equation for work at constant temperature 1 w nRT1nE V1 since Ca 2 CB VadP fadT VBdP SBdT or AVdP Ade or dP LS dT AV AH dP d T 2 TN Clapeyron Equation CIrev qP T T since A5 dP AH for a change involvmg a condensed phase and gas d T F assuming 9 dP AHP ideal gas behaVIor dT RTZ differential form of ClausiusClapeyron Equation dP E P21 TZE separate variables P RTZ dTintegratefP1 PdP le RTZ dT assume P A17 1 1 change in molar enthalpy is constant ln 2 1 P1 R T2 T1 integrated form of ClausiusClapeyron Equation phase transitions involving gas assuming ideal gas behavior assuming change in molar enthalpy is constant constant pressure and temperature two sets of equilibrium AS 52 51 kBan1 q V ideal gas isothermal rever5ible nR an 2 1 entropy of mixing 2 isothermal gas expansions AmixS ASA ASB VAVB nBR 1n VAVB VB nAR 1n RnA 1n xA nB 1n x3 A H constant pressure AquS M and AMPS Tf Tb Ideal Gas Equation PV 2 nRT Virial Equation for real gases Z 1 g 32 33 or P 1 11 2 V V V V coefficients van der Waals Equation for ideal gases V nbP nRT B C D are second third fourth virial RT 2 van der Waals Equation for real gases P n a 11 or V nb V2 2 P a V nb nRT a and b are van der Waals parameters V with units of Pa m6 mol2 and m3 molquotl respectively Using molar volume a P V b RT N Pressure of a gas With N moles 172 IS the mean veIOCIty squared found by squaring the velocity of every molecule and dividing by number of molecules For an ideal gas PV 2 Etmns 2 nRT or 3 3 RT Etnms EKBT 2 EN one moleculeone mOleltEtransgt IS the average transitional kinetic energy of one molecule For real gasses dN Ms2 The Maxwell Distribution Law 47T M 2 26 2RT d5 dNN is the N 27IRT fraction of molecules moving between speeds s and sds 2RT Most probable speed 8RT Average speed ROOt mean square speed Urms 3 3RT M 2 Collision Frequency Zl ndzg 2 nd SNAP Number Mean Free Path xi 2 NA is Avogadro s 1 V RT ndZN ndZPNA Z q CTZ T1 qheat Cheat capacity constant T1 intial temperature Tzfinal temperature When C is not constant and is dependent on T dq CdT or or qufTZCdTqnfTTZEdT T T Usmg molar heat capaCIty at constant pressure q 11sz deT 1 T Usmg molar heat capaCIty at constant volume q 71sz CVdT ltgt ltgt ltgt 0 ltgtltgtltgt ltgtltgtltgtltgtltgt ltgt PressureVolume PV WorkExpansion Work or or since Pex A dw Pex A dx or w JzPexgtde Irreversible expansion w ff Pede P2 V2 Reversible expansion w ff Pede nRT1n 1 V 1 V2 E fVl PdV nRTan Reversible expansioncompression of ideal gas at constant temperature Irreversible Reaction is external pressure is constant w PexV2 P Infinitesimal change in energy dU dq dw and for PV work AU 2 q V V12 196de Energy change at constant volume bomb calorimetry AU qv O Enthalpy H U PV Partial pressures P1 quot1 PTx1PTP2 n2 111 n2 n1n 2 PT 2 szT where X is the mole fraction of the gas The mole fractions will always add up to 1 PV CompreSSIon factor nRT NRT Z lt AH AU APV at constant pressure AH AU PAV qp w PAV AU qV nffz qp nffz 1 1 Ideal gases H U nRT AH AU nRAT dU TLC VdT dH 2 TLC PdT H dUanT 716 13 nCVnR C CVnR V R P1V1 P2V2 0 PV 2 nRT ERT m mass M molar mass p density 0 w nRTln 2 reversible isothermal can sub P1P2 1 EnRT 2 ltgt isothermal AHO AUO Constants To Know 0 R 8314 Jmol K or 008206 L atmmol K 0 KB Boltzman constant 1381 X 1026 J 0 NA Avogadoro s Number 6022 X 1023
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