### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# Test 3 Study Guide/Cheat Sheet CHEM 345

Towson

GPA 3.37

### View Full Document

## 62

## 0

## Popular in Physical Chemistry

## Popular in Chemistry

This page Study Guide was uploaded by Kayli Antos on Tuesday November 17, 2015. The Study Guide belongs to CHEM 345 at Towson University taught by Dr. Ma in Summer 2015. Since its upload, it has received 62 views. For similar materials see Physical Chemistry in Chemistry at Towson University.

## Popular in Chemistry

## Reviews for Test 3 Study Guide/Cheat Sheet

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 11/17/15

G G G G P Chem Test 3 Gibbs And H lmholtz Energies And Their AEElications 31 Phase Diagram 0 Pressure vs temperature 0 Only real gases because only they can be condensed to liquid 0 Curves are phase boundaries represented by the Clapeyron Equation 0 Triple point is where all phases exist at equilibrium Except for water this is the lowest temperature where liquid can exist 0 Critical point is where supercritical fluid exists gas and liquids together C02 0 Under normal conditions does not exist as a liquid Nonelectrolzte Solutions 31 31 Raoult s Law 0 The partial vapor pressure of a substance in a liquid is equal to the product of its mole fraction and the vapor pressure of the pure liquid 0 An ideal solution all components obey Raoult s law Henry s Law 0 The vapor pressure of a volatile solute is proportional to its mole fraction of a solution 0 For dilute solutions 0 Ideal Dilute Solution the solvent obeys Raoult s Law and the solute obeys Henry s Law Chemical Eggilibrium 31313131 31 AG0 If Kgtl the products dominate If Kltl the reactants dominate If QgtK AG is positive and the reverse reaction is and K are temperature dependent spontaneous If QltK AG is negative and the forward reaction is spontaneous van t Hoff Equation is of a line ymxb The plot of ln K vs lT gives a straight line and the slope has the opposite sign of AHO Need at least 4 experimental points Electrolzte Solutions 1 1 Debye Huckel Theory 0 Complete dissociation of a dilute solution and ions ae surrounded by ions with the opposite charge 0 Kis the solubility product constant 0 S is solubility Salting ln Effect solubility increasing with ionic strength 3 Electrochemistrz 1 1 Components Of An Electrochemical Cell 0 2 electrodes 0 electrolyte solution 0 salt bridge 0 wire The Cell Diagram ZnSO4a q Salmon ICWS 0 H salt bridge I 0 The left side is the anode and the right side is the cathode 0 If there s no electrode electrode 2 phase boundary add Pt or Cwamuun as an inert 0 Electrons flow from high electrode potential anode to low electrode potential cathode Electrode Potential Enm 0 Intensive property 0 The higher reduction potential acts as a cathode 0 Reduction potentials relative to SHE Cell Potential Ea 1Electromotive Force emf 0 Reversible electrical work 0 Ebdi measured in volts 0 CV J 0 AG measured in Jmol If Ecdllt0 then AGltO and the reaction is not spontaneous 3 Chemical Kinetics 1 1 The study of the rates and mechanisms of chemical reactions Reaction Rate v 0 The change in concentration per unit time 3 Reaction Orders 1 Zero Order Reactions 1 0 Plotting R with slope ko 0 Plotting P vs time gives a graph of a straight line with slope k0 vs time gives a graph of a straight line First Order Reactions 0 Plotting A curve 0 Plotting ln A line where slope vs time gives a graph with an exponential vs time gives a graph with a straight k1 D Eggations 1 It 6 a artial molar volumes dV dn dn p I a TPn2 a TPn1 2 li lzmz 66 partial molar Gibbs energy at constant T and P Gi wai TPnj G 11161 62 chemical potential mi2 G 11 22 ideal gas at constant T A5Rlln ideal gas at constant T if P1PQl bar P2P and 6 oR1n P0 single component of ideal gas mixture at constant T Rlln ideal gas at constant T and P AmiXS R lnIA B ln 393 AmiXH AHB O AmixG AmixH Amixs Rlt A lnIA B lnIB P Pl is the vapor pressure of the pure substance PI at constant T and vapor pressure iu Ej4gand uiu Rlln if pi is in bar lem or RI1nRI1nI if M 113 RTlnli ui is the chemical potential of substance 1 in a liquid mixture potential of the pure liquid 1 UiW M is the chemical 31 3131313131 31313131 EB KBIB fraction in solution of solute B K is Henry s Law Constant X3 is the mole P amp K must have the same units EB KB B K for an ideal dilute solution of solvent A and solute B RIlnxA 12391nt 12391an3 C 1M RI1nKBRI1nCO R lncO chem potential of solute in real solution Rl lnli for realnonioleal solvent molA B for realnonioleal solute 3 0 A 6 dmp 61 b 60548 Rlln dQIH Rlln9 a Rlln b RllnN A M60 Rlln Amo Rlln 0 and AE RIin in units of pressure unitM at equilibrium AG Pi for a gas Ii Pi activity of a solvent Ii c d s ab p for an ideal dilute solution ll 2 c d K CCDCl KC 0 a b 32 2 A B A Rlln Af Rlln A IA 2 RI 1n P5P ifPin bar ab 13 PAP B for a gas lt CO o o A IA van t Hoff equation AH and AS are constant ln i R W1 AW 1n ii R I R K1 R I I 1 for a salt represented by Mqu Pq Debye Huckel limiting law 10g AIZZI 1 2E 222i C IA ICl Esp g lAglcr Agiicz Cl D Eredcathode Eredanode for a cell reaction A Ecell A A RIlnE dt rate law k mm 13 C mq step k1 A B elementary step k1 A B k1 P reaction rate law Rh kot Ro P kot Po first order reaction rate law A Abe kit AH ZuAfmproducts ZuAfmreactcmts where u is the stoichiometric coefficient AH AU APV AU PAV if condensed states don t contribute volume and assuming ideal gas behavior AH AU AngasRT if temperature is AU RTAngas at constant pressure qp T AH qp Tlsz deT 1 elementary reversible zero order if pressure is constant AH constant AH AHO a pure substance HT2 HT1 nfT2 deT or HTZ HTl I jpdT substance i in a mixture Hm H7 2 Cp idT or T HniHnj39F chdT reaction enthalpy AHfCHiC4dHD aHiA4b i3 T T T c Hm fTo Cde d Hm fTo CPID dT a HTOIA fTo CPIAdT T b HTO B ITO Cp BdT CHTO C dHTO D aHTO A bHTO B T T T T c fTO Cp dT d fTO CRDdT a fTO CPIAdT b fTO CPBdT AHTO T fTOCCPC dCPD aCPA bCPBdT Kirchoff s LawEquation AHLACdTAHf if C is constant AHT AHTO ACPT To 31 3131313131 31 dCIrev when temperature isn t constant ASf when temperature T is constant AS V ideal gas isothermal conditions AS nR ln or A5 1 P nR ln 1 13972 temperature of the system and the surroundings is the cIsurr qsys same AS S LLT39T39 T T reversibleirreversible ASSyS q CI 61 reverSible ASsurr 2 CI 61 39 CI 61quot W w Assurr SUTT39 lT39T39e U Irrev Irrev T T T T 39 61 w W w VA 11A V 1 xA V Tl VA XA I T 11539 dT when volume is constant AS T2 when n is constant 1 T C dT T AS nfTZV when CV is constant AS nCVlnT 2 1 1 I T 11539 dT when pressure is constant ASIZL when n is constant T1 T T c dT T A5 nfTZP when Cp is constant AS nCplnT 2 1 1 at constant temperature and pressure reversible AS 1PAH T T S k3 lI1W T c T C constant pressure AS nlezde or A5 f7de A If T12298K TZZT AST A5298 A52098 C52098C d52098D a52098A 19520983 AH at constant pressure qSyS qp AH so ASsurr same temperature and pressure in initial and final states Gibbs AG AH TAS Helmholtz constant temperature and volume A U TS dA dU TdS dA dU dqmw dA dew max work mixing of 2 ideal gases AA RTn1 lnx1 n2 lnx2 AG 0 Z uAfGO products Z uAfGO reactants for an infinitesimal change dG dq dw PdV VdP TdS SdT 31313131 31313131 31313131 31 for a reversible path dqmw TdS dWrev dWPVrev deonPVrev dWPVrev PdV dG dqrev dWrev PdV VdP TdS SdT deonPVrev VdP SdT constant temperature and pressure AG wmmmqmv only expansion work dG VdP SdT SdT or d dT integrate fG G d5 f72539dT or 52 51 f72539dT assume molar expansion nonexpansion constant pressure dG entropy is constant AG AT constant temperature dG VdP or dGVdP integrate A5 I VdP condensed states AGVAP QRT P dP or AGRTln 1 P P 1 ideal gas behavior AG P AGnRTln ilike the equation for work at constant 1 w nRT lnE V1 temperature since Ga GB VadP fadT VBdP BdT or AVdP A dT or d P dT AS AV Clrev c1P AH dP AH since AS Cla e ron E uation 7 T T dT TAV E y q dP AH for a change involVing a condensed phase and gas E g dP AHP assuming ideal gas behaVior EERT2 differential form of Clausius Clapeyron Equation dP AH P 1 T AH separate variables dT integratehdPjA dT 1 P 39 RT2 1 RT2 P AH assume change in molar enthalpy is constant hy 7 1 1 1 1 integrated form of ClauSius Clapeyron 2 1 Equation phase transitions involving gas assuming ideal gas behavior assuming change in molar enthalpy is constant pressure and temperature two sets of equilibrium AS 2 1 k3 lnwl constant V ideal gas isothermal reverSible g annag 1 entropy of mixing 2 isothermal gas expansions AmmS VAVB VA VAVB ASA A53 2 quotAR In VB nBR ln RnA ln xA 113 ln x3 31 313131313131 A H M and AvapS constant pressure A 55 Tf Tb y 1 E 2 adiabatic reversible expansion v CpCv 53 6 1 for a monoatomic gas wy5 E m T P E 2 2 Y T1 p1 CVT2 T1 2 AU PexV2 V1 adiabatic w nRT lni 2 AUCMH DV AH at constant isothermal ideal gas EAT adiabatic volume dqmw Cm f at constant pressure qur qaw AH 800 at absolute zero for a pure Ideal Gas Equation PVnRT crystalline solid C Virial Equation for real gases Z1F 4 or 1mT B C D I j71F73 B C D are second third fourth virial coefficients V nbP nRT nRT n2 a or V nb V2 van der Waals Equation for ideal gases van der Waals Equation for real gasesI 2 ltPan 2gt V nb nRT a and b are van der Waals V parameters with units of Pa m5 mol2 and m3 mol l a respectively Using molar volume P4m9V bRT NmEE 3V found by squaring the velocity of every v2 is the mean Pressure of a gas with N moles P velocity squared molecule and dividing by number of molecules For an ideal gas PV Etmns nRT or Eme KBT EZ one moleculeone moleltEuEmgt is the A 2N average transitional kinetic energy of one molecule For real gasses ERKBT dN M quot 13f The Maxwell Distribution Law RF4HZEEy ezRTdS dNN is the fraction of molecules moving between speeds s and sds 2RT Most probable speed gm M 8RT Average speed 3 11M 3RT Root mean square speed mmw 7T 2N nd2 NAP I Collision Frequency Zi Vind SV 757 NA is Avogadro s Number 1 V RT Mean Free Path 1 ndzN ndzPNA qXjTQ geheat C heat capacity constant Tl intial temperature Tz final temperature When C is not constant and is dependent on T dqCdT or dq T2 T2 C dT or qu leCdT q nszch Using molar heat capacity at constant pressure q 5 nledeT T Using molar heat capacity at constant volume q1yh2CydT 1 V Irreversible expanSion W fV12Pede P2V2 V1 V V ReverSible expanSioncompreSSion W fvz Pede nRTan2 1 1 Irreversible Reaction if external pressure is constant nRT nRT 1 1 W PexV2 V1 Pex P z P l eanT P P l lnfinitesimal change in energy dU dq dw and for P V V work AU q fV Pede Energy change at constant volume bomb calorimetry AU qv 0 Enthalpy H U PV quot1 Partial pressures R1 quot2 UZZxJU P2 quot1 quot2 quot1 quot2 XiiS the mole fraction of the gas The mole fractions PT X39sz Where will always add up to l PV CompreSSion factor Z 1mT NRT AMV AH AU APV at constant pressure AH AU PAV qP w PAV AU qV 11f CVdT CVT2 T1 AH qp 11f UPdT Ideal gases H U nRT AH AU nRAT AUnCVAT AH nCpAT nCp nCV nR to get Cp CV nR and Cp CV R P1V1 Psz n T1 T2 RT RT 11 PVnRTRT Mp7 m mass M molar mass p dens1ty V n MI nRThmfrevers1ble isothermal can sub P1P2 1 3 31 U n qmsAT Constants Tb Know A 0509 for aqueous solutions with water at 298K F 96485 Cmol R 83l4 Jmol K or 008206 L atmmol K KB Boltzman constant 1381 X l0 26 JK NAAvogadro s Number 6022 X 10Q3 3131313131 Conversions JPa m3 1013JL atm 1ca4184J 1atm101325Pa 1m31000L N mJ 31 h 31 h 31 h G G G G P Chem Test 3 Gibbs And H lmholtz Energies And Their AEElications 31 Phase Diagram 0 Pressure vs temperature 0 Only real gases because only they can be condensed to liquid 0 Curves are phase boundaries represented by the Clapeyron Equation 0 Triple point is where all phases exist at equilibrium Except for water this is the lowest temperature where liquid can exist 0 Critical point is where supercritical fluid exists gas and liquids together C02 0 Under normal conditions does not exist as a liquid Nonelectrolzte Solutions 31 31 Raoult s Law 0 The partial vapor pressure of a substance in a liquid is equal to the product of its mole fraction and the vapor pressure of the pure liquid 0 An ideal solution all components obey Raoult s law Henry s Law 0 The vapor pressure of a volatile solute is proportional to its mole fraction of a solution 0 For dilute solutions 0 Ideal Dilute Solution the solvent obeys Raoult s Law and the solute obeys Henry s Law Chemical Eggilibrium 31313131 31 AG0 If Kgtl the products dominate If Kltl the reactants dominate If QgtK AG is positive and the reverse reaction is and K are temperature dependent spontaneous If QltK AG is negative and the forward reaction is spontaneous van t Hoff Equation is of a line ymxb The plot of ln K vs lT gives a straight line and the slope has the opposite sign of AHO Need at least 4 experimental points Electrolzte Solutions 1 1 Debye Huckel Theory 0 Complete dissociation of a dilute solution and ions ae surrounded by ions with the opposite charge 0 Kis the solubility product constant 0 S is solubility Salting ln Effect solubility increasing with ionic strength 3 Electrochemistrz 1 1 Components Of An Electrochemical Cell 0 2 electrodes 0 electrolyte solution 0 salt bridge 0 wire The Cell Diagram ZnSO4a q Salmon ICWS 0 H salt bridge I 0 The left side is the anode and the right side is the cathode 0 If there s no electrode electrode 2 phase boundary add Pt or Cwamuun as an inert 0 Electrons flow from high electrode potential anode to low electrode potential cathode Electrode Potential Enm 0 Intensive property 0 The higher reduction potential acts as a cathode 0 Reduction potentials relative to SHE Cell Potential Ea 1Electromotive Force emf 0 Reversible electrical work 0 Ebdi measured in volts 0 CV J 0 AG measured in Jmol If Ecdllt0 then AGltO and the reaction is not spontaneous 3 Chemical Kinetics 1 1 The study of the rates and mechanisms of chemical reactions Reaction Rate v 0 The change in concentration per unit time 3 Reaction Orders 1 Zero Order Reactions 1 0 Plotting R with slope ko 0 Plotting P vs time gives a graph of a straight line with slope k0 vs time gives a graph of a straight line First Order Reactions 0 Plotting A curve 0 Plotting ln A line where slope vs time gives a graph with an exponential vs time gives a graph with a straight k1 D Eggations 1 It 6 a artial molar volumes dV dn dn p I a TPn2 a TPn1 2 li lzmz 66 partial molar Gibbs energy at constant T and P Gi wai TPnj G 11161 62 chemical potential mi2 G 11 22 ideal gas at constant T A5Rlln ideal gas at constant T if P1PQl bar P2P and 6 oR1n P0 single component of ideal gas mixture at constant T Rlln ideal gas at constant T and P AmiXS R lnIA B ln 393 AmiXH AHB O AmixG AmixH Amixs Rlt A lnIA B lnIB P Pl is the vapor pressure of the pure substance PI at constant T and vapor pressure iu Ej4gand uiu Rlln if pi is in bar lem or RI1nRI1nI if M 113 RTlnli ui is the chemical potential of substance 1 in a liquid mixture potential of the pure liquid 1 UiW M is the chemical 31 3131313131 31313131 EB KBIB fraction in solution of solute B K is Henry s Law Constant X3 is the mole P amp K must have the same units EB KB B K for an ideal dilute solution of solvent A and solute B RIlnxA 12391nt 12391an3 C 1M RI1nKBRI1nCO R lncO chem potential of solute in real solution Rl lnli for realnonioleal solvent molA B for realnonioleal solute 3 0 A 6 dmp 61 b 60548 Rlln dQIH Rlln9 a Rlln b RllnN A M60 Rlln Amo Rlln 0 and AE RIin in units of pressure unitM at equilibrium AG Pi for a gas Ii Pi activity of a solvent Ii c d s ab p for an ideal dilute solution ll 2 c d K CCDCl KC 0 a b 32 2 A B A Rlln Af Rlln A IA 2 RI 1n P5P ifPin bar ab 13 PAP B for a gas lt CO o o A IA van t Hoff equation AH and AS are constant ln i R W1 AW 1n ii R I R K1 R I I 1 for a salt represented by Mqu Pq Debye Huckel limiting law 10g AIZZI 1 2E 222i C IA ICl Esp g lAglcr Agiicz Cl D Eredcathode Eredanode for a cell reaction A Ecell A A RIlnE dt rate law k mm 13 C mq step k1 A B elementary step k1 A B k1 P reaction rate law Rh kot Ro P kot Po first order reaction rate law A Abe kit AH ZuAfmproducts ZuAfmreactcmts where u is the stoichiometric coefficient AH AU APV AU PAV if condensed states don t contribute volume and assuming ideal gas behavior AH AU AngasRT if temperature is AU RTAngas at constant pressure qp T AH qp Tlsz deT 1 elementary reversible zero order if pressure is constant AH constant AH AHO a pure substance HT2 HT1 nfT2 deT or HTZ HTl I jpdT substance i in a mixture Hm H7 2 Cp idT or T HniHnj39F chdT reaction enthalpy AHfCHiC4dHD aHiA4b i3 T T T c Hm fTo Cde d Hm fTo CPID dT a HTOIA fTo CPIAdT T b HTO B ITO Cp BdT CHTO C dHTO D aHTO A bHTO B T T T T c fTO Cp dT d fTO CRDdT a fTO CPIAdT b fTO CPBdT AHTO T fTOCCPC dCPD aCPA bCPBdT Kirchoff s LawEquation AHLACdTAHf if C is constant AHT AHTO ACPT To 31 3131313131 31 dCIrev when temperature isn t constant ASf when temperature T is constant AS V ideal gas isothermal conditions AS nR ln or A5 1 P nR ln 1 13972 temperature of the system and the surroundings is the cIsurr qsys same AS S LLT39T39 T T reversibleirreversible ASSyS q CI 61 reverSible ASsurr 2 CI 61 39 CI 61quot W w Assurr SUTT39 lT39T39e U Irrev Irrev T T T T 39 61 w W w VA 11A V 1 xA V Tl VA XA I T 11539 dT when volume is constant AS T2 when n is constant 1 T C dT T AS nfTZV when CV is constant AS nCVlnT 2 1 1 I T 11539 dT when pressure is constant ASIZL when n is constant T1 T T c dT T A5 nfTZP when Cp is constant AS nCplnT 2 1 1 at constant temperature and pressure reversible AS 1PAH T T S k3 lI1W T c T C constant pressure AS nlezde or A5 f7de A If T12298K TZZT AST A5298 A52098 C52098C d52098D a52098A 19520983 AH at constant pressure qSyS qp AH so ASsurr same temperature and pressure in initial and final states Gibbs AG AH TAS Helmholtz constant temperature and volume A U TS dA dU TdS dA dU dqmw dA dew max work mixing of 2 ideal gases AA RTn1 lnx1 n2 lnx2 AG 0 Z uAfGO products Z uAfGO reactants for an infinitesimal change dG dq dw PdV VdP TdS SdT 31313131 31313131 31313131 31 for a reversible path dqmw TdS dWrev dWPVrev deonPVrev dWPVrev PdV dG dqrev dWrev PdV VdP TdS SdT deonPVrev VdP SdT constant temperature and pressure AG wmmmqmv only expansion work dG VdP SdT SdT or d dT integrate fG G d5 f72539dT or 52 51 f72539dT assume molar expansion nonexpansion constant pressure dG entropy is constant AG AT constant temperature dG VdP or dGVdP integrate A5 I VdP condensed states AGVAP QRT P dP or AGRTln 1 P P 1 ideal gas behavior AG P AGnRTln ilike the equation for work at constant 1 w nRT lnE V1 temperature since Ga GB VadP fadT VBdP BdT or AVdP A dT or d P dT AS AV Clrev c1P AH dP AH since AS Cla e ron E uation 7 T T dT TAV E y q dP AH for a change involVing a condensed phase and gas E g dP AHP assuming ideal gas behaVior EERT2 differential form of Clausius Clapeyron Equation dP AH P 1 T AH separate variables dT integratehdPjA dT 1 P 39 RT2 1 RT2 P AH assume change in molar enthalpy is constant hy 7 1 1 1 1 integrated form of ClauSius Clapeyron 2 1 Equation phase transitions involving gas assuming ideal gas behavior assuming change in molar enthalpy is constant pressure and temperature two sets of equilibrium AS 2 1 k3 lnwl constant V ideal gas isothermal reverSible g annag 1 entropy of mixing 2 isothermal gas expansions AmmS VAVB VA VAVB ASA A53 2 quotAR In VB nBR ln RnA ln xA 113 ln x3 31 313131313131 A H M and AvapS constant pressure A 55 Tf Tb y 1 E 2 adiabatic reversible expansion v CpCv 53 6 1 for a monoatomic gas wy5 E m T P E 2 2 Y T1 p1 CVT2 T1 2 AU PexV2 V1 adiabatic w nRT lni 2 AUCMH DV AH at constant isothermal ideal gas EAT adiabatic volume dqmw Cm f at constant pressure qur qaw AH 800 at absolute zero for a pure Ideal Gas Equation PVnRT crystalline solid C Virial Equation for real gases Z1F 4 or 1mT B C D I j71F73 B C D are second third fourth virial coefficients V nbP nRT nRT n2 a or V nb V2 van der Waals Equation for ideal gases van der Waals Equation for real gasesI 2 ltPan 2gt V nb nRT a and b are van der Waals V parameters with units of Pa m5 mol2 and m3 mol l a respectively Using molar volume P4m9V bRT NmEE 3V found by squaring the velocity of every v2 is the mean Pressure of a gas with N moles P velocity squared molecule and dividing by number of molecules For an ideal gas PV Etmns nRT or Eme KBT EZ one moleculeone moleltEuEmgt is the A 2N average transitional kinetic energy of one molecule For real gasses ERKBT dN M quot 13f The Maxwell Distribution Law RF4HZEEy ezRTdS dNN is the fraction of molecules moving between speeds s and sds 2RT Most probable speed gm M 8RT Average speed 3 11M 3RT Root mean square speed mmw 7T 2N nd2 NAP I Collision Frequency Zi Vind SV 757 NA is Avogadro s Number 1 V RT Mean Free Path 1 ndzN ndzPNA qXjTQ geheat C heat capacity constant Tl intial temperature Tz final temperature When C is not constant and is dependent on T dqCdT or dq T2 T2 C dT or qu leCdT q nszch Using molar heat capacity at constant pressure q 5 nledeT T Using molar heat capacity at constant volume q1yh2CydT 1 V Irreversible expanSion W fV12Pede P2V2 V1 V V ReverSible expanSioncompreSSion W fvz Pede nRTan2 1 1 Irreversible Reaction if external pressure is constant nRT nRT 1 1 W PexV2 V1 Pex P z P l eanT P P l lnfinitesimal change in energy dU dq dw and for P V V work AU q fV Pede Energy change at constant volume bomb calorimetry AU qv 0 Enthalpy H U PV quot1 Partial pressures R1 quot2 UZZxJU P2 quot1 quot2 quot1 quot2 XiiS the mole fraction of the gas The mole fractions PT X39sz Where will always add up to l PV CompreSSion factor Z 1mT NRT AMV AH AU APV at constant pressure AH AU PAV qP w PAV AU qV 11f CVdT CVT2 T1 AH qp 11f UPdT Ideal gases H U nRT AH AU nRAT AUnCVAT AH nCpAT nCp nCV nR to get Cp CV nR and Cp CV R P1V1 Psz n T1 T2 RT RT 11 PVnRTRT Mp7 m mass M molar mass p dens1ty V n MI nRThmfrevers1ble isothermal can sub P1P2 1 3 31 U n qmsAT Constants Tb Know A 0509 for aqueous solutions with water at 298K F 96485 Cmol R 83l4 Jmol K or 008206 L atmmol K KB Boltzman constant 1381 X l0 26 JK NAAvogadro s Number 6022 X 10Q3 3131313131 Conversions JPa m3 1013JL atm 1ca4184J 1atm101325Pa 1m31000L N mJ 31 h 31 h 31 h G G G G P Chem Test 3 Gibbs And H lmholtz Energies And Their AEElications 31 Phase Diagram 0 Pressure vs temperature 0 Only real gases because only they can be condensed to liquid 0 Curves are phase boundaries represented by the Clapeyron Equation 0 Triple point is where all phases exist at equilibrium Except for water this is the lowest temperature where liquid can exist 0 Critical point is where supercritical fluid exists gas and liquids together C02 0 Under normal conditions does not exist as a liquid Nonelectrolzte Solutions 31 31 Raoult s Law 0 The partial vapor pressure of a substance in a liquid is equal to the product of its mole fraction and the vapor pressure of the pure liquid 0 An ideal solution all components obey Raoult s law Henry s Law 0 The vapor pressure of a volatile solute is proportional to its mole fraction of a solution 0 For dilute solutions 0 Ideal Dilute Solution the solvent obeys Raoult s Law and the solute obeys Henry s Law Chemical Eggilibrium 31313131 31 AG0 If Kgtl the products dominate If Kltl the reactants dominate If QgtK AG is positive and the reverse reaction is and K are temperature dependent spontaneous If QltK AG is negative and the forward reaction is spontaneous van t Hoff Equation is of a line ymxb The plot of ln K vs lT gives a straight line and the slope has the opposite sign of AHO Need at least 4 experimental points Electrolzte Solutions 1 1 Debye Huckel Theory 0 Complete dissociation of a dilute solution and ions ae surrounded by ions with the opposite charge 0 Kis the solubility product constant 0 S is solubility Salting ln Effect solubility increasing with ionic strength 3 Electrochemistrz 1 1 Components Of An Electrochemical Cell 0 2 electrodes 0 electrolyte solution 0 salt bridge 0 wire The Cell Diagram ZnSO4a q Salmon ICWS 0 H salt bridge I 0 The left side is the anode and the right side is the cathode 0 If there s no electrode electrode 2 phase boundary add Pt or Cwamuun as an inert 0 Electrons flow from high electrode potential anode to low electrode potential cathode Electrode Potential Enm 0 Intensive property 0 The higher reduction potential acts as a cathode 0 Reduction potentials relative to SHE Cell Potential Ea 1Electromotive Force emf 0 Reversible electrical work 0 Ebdi measured in volts 0 CV J 0 AG measured in Jmol If Ecdllt0 then AGltO and the reaction is not spontaneous 3 Chemical Kinetics 1 1 The study of the rates and mechanisms of chemical reactions Reaction Rate v 0 The change in concentration per unit time 3 Reaction Orders 1 Zero Order Reactions 1 0 Plotting R with slope ko 0 Plotting P vs time gives a graph of a straight line with slope k0 vs time gives a graph of a straight line First Order Reactions 0 Plotting A curve 0 Plotting ln A line where slope vs time gives a graph with an exponential vs time gives a graph with a straight k1 D Eggations 1 It 6 a artial molar volumes dV dn dn p I a TPn2 a TPn1 2 li lzmz 66 partial molar Gibbs energy at constant T and P Gi wai TPnj G 11161 62 chemical potential mi2 G 11 22 ideal gas at constant T A5Rlln ideal gas at constant T if P1PQl bar P2P and 6 oR1n P0 single component of ideal gas mixture at constant T Rlln ideal gas at constant T and P AmiXS R lnIA B ln 393 AmiXH AHB O AmixG AmixH Amixs Rlt A lnIA B lnIB P Pl is the vapor pressure of the pure substance PI at constant T and vapor pressure iu Ej4gand uiu Rlln if pi is in bar lem or RI1nRI1nI if M 113 RTlnli ui is the chemical potential of substance 1 in a liquid mixture potential of the pure liquid 1 UiW M is the chemical 31 3131313131 31313131 EB KBIB fraction in solution of solute B K is Henry s Law Constant X3 is the mole P amp K must have the same units EB KB B K for an ideal dilute solution of solvent A and solute B RIlnxA 12391nt 12391an3 C 1M RI1nKBRI1nCO R lncO chem potential of solute in real solution Rl lnli for realnonioleal solvent molA B for realnonioleal solute 3 0 A 6 dmp 61 b 60548 Rlln dQIH Rlln9 a Rlln b RllnN A M60 Rlln Amo Rlln 0 and AE RIin in units of pressure unitM at equilibrium AG Pi for a gas Ii Pi activity of a solvent Ii c d s ab p for an ideal dilute solution ll 2 c d K CCDCl KC 0 a b 32 2 A B A Rlln Af Rlln A IA 2 RI 1n P5P ifPin bar ab 13 PAP B for a gas lt CO o o A IA van t Hoff equation AH and AS are constant ln i R W1 AW 1n ii R I R K1 R I I 1 for a salt represented by Mqu Pq Debye Huckel limiting law 10g AIZZI 1 2E 222i C IA ICl Esp g lAglcr Agiicz Cl D Eredcathode Eredanode for a cell reaction A Ecell A A RIlnE dt rate law k mm 13 C mq step k1 A B elementary step k1 A B k1 P reaction rate law Rh kot Ro P kot Po first order reaction rate law A Abe kit AH ZuAfmproducts ZuAfmreactcmts where u is the stoichiometric coefficient AH AU APV AU PAV if condensed states don t contribute volume and assuming ideal gas behavior AH AU AngasRT if temperature is AU RTAngas at constant pressure qp T AH qp Tlsz deT 1 elementary reversible zero order if pressure is constant AH constant AH AHO a pure substance HT2 HT1 nfT2 deT or HTZ HTl I jpdT substance i in a mixture Hm H7 2 Cp idT or T HniHnj39F chdT reaction enthalpy AHfCHiC4dHD aHiA4b i3 T T T c Hm fTo Cde d Hm fTo CPID dT a HTOIA fTo CPIAdT T b HTO B ITO Cp BdT CHTO C dHTO D aHTO A bHTO B T T T T c fTO Cp dT d fTO CRDdT a fTO CPIAdT b fTO CPBdT AHTO T fTOCCPC dCPD aCPA bCPBdT Kirchoff s LawEquation AHLACdTAHf if C is constant AHT AHTO ACPT To 31 3131313131 31 dCIrev when temperature isn t constant ASf when temperature T is constant AS V ideal gas isothermal conditions AS nR ln or A5 1 P nR ln 1 13972 temperature of the system and the surroundings is the cIsurr qsys same AS S LLT39T39 T T reversibleirreversible ASSyS q CI 61 reverSible ASsurr 2 CI 61 39 CI 61quot W w Assurr SUTT39 lT39T39e U Irrev Irrev T T T T 39 61 w W w VA 11A V 1 xA V Tl VA XA I T 11539 dT when volume is constant AS T2 when n is constant 1 T C dT T AS nfTZV when CV is constant AS nCVlnT 2 1 1 I T 11539 dT when pressure is constant ASIZL when n is constant T1 T T c dT T A5 nfTZP when Cp is constant AS nCplnT 2 1 1 at constant temperature and pressure reversible AS 1PAH T T S k3 lI1W T c T C constant pressure AS nlezde or A5 f7de A If T12298K TZZT AST A5298 A52098 C52098C d52098D a52098A 19520983 AH at constant pressure qSyS qp AH so ASsurr same temperature and pressure in initial and final states Gibbs AG AH TAS Helmholtz constant temperature and volume A U TS dA dU TdS dA dU dqmw dA dew max work mixing of 2 ideal gases AA RTn1 lnx1 n2 lnx2 AG 0 Z uAfGO products Z uAfGO reactants for an infinitesimal change dG dq dw PdV VdP TdS SdT 31313131 31313131 31313131 31 for a reversible path dqmw TdS dWrev dWPVrev deonPVrev dWPVrev PdV dG dqrev dWrev PdV VdP TdS SdT deonPVrev VdP SdT constant temperature and pressure AG wmmmqmv only expansion work dG VdP SdT SdT or d dT integrate fG G d5 f72539dT or 52 51 f72539dT assume molar expansion nonexpansion constant pressure dG entropy is constant AG AT constant temperature dG VdP or dGVdP integrate A5 I VdP condensed states AGVAP QRT P dP or AGRTln 1 P P 1 ideal gas behavior AG P AGnRTln ilike the equation for work at constant 1 w nRT lnE V1 temperature since Ga GB VadP fadT VBdP BdT or AVdP A dT or d P dT AS AV Clrev c1P AH dP AH since AS Cla e ron E uation 7 T T dT TAV E y q dP AH for a change involVing a condensed phase and gas E g dP AHP assuming ideal gas behaVior EERT2 differential form of Clausius Clapeyron Equation dP AH P 1 T AH separate variables dT integratehdPjA dT 1 P 39 RT2 1 RT2 P AH assume change in molar enthalpy is constant hy 7 1 1 1 1 integrated form of ClauSius Clapeyron 2 1 Equation phase transitions involving gas assuming ideal gas behavior assuming change in molar enthalpy is constant pressure and temperature two sets of equilibrium AS 2 1 k3 lnwl constant V ideal gas isothermal reverSible g annag 1 entropy of mixing 2 isothermal gas expansions AmmS VAVB VA VAVB ASA A53 2 quotAR In VB nBR ln RnA ln xA 113 ln x3 31 313131313131 A H M and AvapS constant pressure A 55 Tf Tb y 1 E 2 adiabatic reversible expansion v CpCv 53 6 1 for a monoatomic gas wy5 E m T P E 2 2 Y T1 p1 CVT2 T1 2 AU PexV2 V1 adiabatic w nRT lni 2 AUCMH DV AH at constant isothermal ideal gas EAT adiabatic volume dqmw Cm f at constant pressure qur qaw AH 800 at absolute zero for a pure Ideal Gas Equation PVnRT crystalline solid C Virial Equation for real gases Z1F 4 or 1mT B C D I j71F73 B C D are second third fourth virial coefficients V nbP nRT nRT n2 a or V nb V2 van der Waals Equation for ideal gases van der Waals Equation for real gasesI 2 ltPan 2gt V nb nRT a and b are van der Waals V parameters with units of Pa m5 mol2 and m3 mol l a respectively Using molar volume P4m9V bRT NmEE 3V found by squaring the velocity of every v2 is the mean Pressure of a gas with N moles P velocity squared molecule and dividing by number of molecules For an ideal gas PV Etmns nRT or Eme KBT EZ one moleculeone moleltEuEmgt is the A 2N average transitional kinetic energy of one molecule For real gasses ERKBT dN M quot 13f The Maxwell Distribution Law RF4HZEEy ezRTdS dNN is the fraction of molecules moving between speeds s and sds 2RT Most probable speed gm M 8RT Average speed 3 11M 3RT Root mean square speed mmw 7T 2N nd2 NAP I Collision Frequency Zi Vind SV 757 NA is Avogadro s Number 1 V RT Mean Free Path 1 ndzN ndzPNA qXjTQ geheat C heat capacity constant Tl intial temperature Tz final temperature When C is not constant and is dependent on T dqCdT or dq T2 T2 C dT or qu leCdT q nszch Using molar heat capacity at constant pressure q 5 nledeT T Using molar heat capacity at constant volume q1yh2CydT 1 V Irreversible expanSion W fV12Pede P2V2 V1 V V ReverSible expanSioncompreSSion W fvz Pede nRTan2 1 1 Irreversible Reaction if external pressure is constant nRT nRT 1 1 W PexV2 V1 Pex P z P l eanT P P l lnfinitesimal change in energy dU dq dw and for P V V work AU q fV Pede Energy change at constant volume bomb calorimetry AU qv 0 Enthalpy H U PV quot1 Partial pressures R1 quot2 UZZxJU P2 quot1 quot2 quot1 quot2 XiiS the mole fraction of the gas The mole fractions PT X39sz Where will always add up to l PV CompreSSion factor Z 1mT NRT AMV AH AU APV at constant pressure AH AU PAV qP w PAV AU qV 11f CVdT CVT2 T1 AH qp 11f UPdT Ideal gases H U nRT AH AU nRAT AUnCVAT AH nCpAT nCp nCV nR to get Cp CV nR and Cp CV R P1V1 Psz n T1 T2 RT RT 11 PVnRTRT Mp7 m mass M molar mass p dens1ty V n MI nRThmfrevers1ble isothermal can sub P1P2 1 3 31 U n qmsAT Constants Tb Know A 0509 for aqueous solutions with water at 298K F 96485 Cmol R 83l4 Jmol K or 008206 L atmmol K KB Boltzman constant 1381 X l0 26 JK NAAvogadro s Number 6022 X 10Q3 3131313131 Conversions JPa m3 1013JL atm 1ca4184J 1atm101325Pa 1m31000L N mJ 31 h 31 h 31 h

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

#### "I made $350 in just two days after posting my first study guide."

#### "Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

#### "Their 'Elite Notetakers' are making over $1,200/month in sales by creating high quality content that helps their classmates in a time of need."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.