上海交通大学：《材料热力学》教学资源_2010课件_lecture 9 electrochemistry I

Contents of Today S.J.T.U. Phase Transformation and Applications Review previous On Gibbs free energy Electrochemical Nomenclature Calculation of Cell voltage Direction of Reaction etc. SJTU Thermodynamics of Materials Spring2008©X.J.Jin Lecture 9 electrochemistry I

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2008 © X. J. Jin Lecture 9 electrochemistry I Contents of Today Review previous On Gibbs free energy Electrochemical Nomenclature Calculation of Cell Voltage Direction of Reaction etc

饱和蒸气压 S.J.T.U. Phase Transformation and Applications 饱和蒸气压概念 将一杯纯溶液置于密闭的钟 罩内，一定时间后液面将有 液相 气相 所下降，直到罩内气体压力 达到一定数值为止。此时的 A G(A) P1 气体压力称为该液体的饱和 蒸气压，简称蒸气压。分子 B G(B) P2 运动学，蒸发与凝聚的速度 相等时，气液两相达到动态 平衡条件 平衡。 G(A,liquid )=G(gas,P1) 。 饱和蒸气压的应用 G(B,liquid)=G(gas,P2) 一凝聚态某组元的化学势 4G(A-→B,liquid)=4G(gas,P1→P2) 一化学反应气相的化学势 4G(gas,P1→P2)=P7dG ·例子 SJTU Thermodynamics of Materials Spring2008©X.J.Jin Lecture 9 electrochemistry I

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2008 © X. J. Jin Lecture 9 electrochemistry I 饱和蒸气压 • 饱和蒸气压概念 – 将一杯纯溶液置于密闭的钟 罩内，一定时间后液面将有 所下降，直到罩内气体压力 达到一定数值为止。此时的 气体压力称为该液体的饱和 蒸气压，简称蒸气压。分子 运动学，蒸发与凝聚的速度 相等时，气液两相达到动态 平衡。 • 饱和蒸气压的应用 – 凝聚态某组元的化学势 – 化学反应气相的化学势 • 例子 液相 气相 A G(A) P1 B G(B) P2 G( A,liquid ) G( = gas,P1 ) G( B,liquid ) G( = gas,P2 ) 平衡条件 ΔG( A B,liquid ) G( →= → Δ gas,P1 P2 ) P2 P1 ΔG( gas,P1 P2 ) dG → = ∫

Question 6 S.J.T.U. Phase Transformation and Applications At-5 C,the vapor pressure of ice is 3.012 mmHg and that of supercooled liquid water is 3.163 mmHg.Tha latent heat of fusion of ice is 5.85 kJ/mol at-5C.Calculate AG and AS per mole for the transition from water to ice at-5°C. AG-5C 3.163 mmHg 3.012 mmHg Vapor pressure 1AG-0 △G-0 Ice Water △Gand△Sat-5C SJTU Thermodynamics of Materials Spring2008©X.J.Jin Lecture 9 electrochemistry I

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2008 © X. J. Jin Lecture 9 electrochemistry I Question 6 At -5 °C, the vapor pressure of ice is 3.012 mmHg and that of supercooled liquid water is 3.163 mmHg. Tha latent heat of fusion of ice is 5.85 kJ/mol at -5 °C. Calculate ΔG and ΔS per mole for the transition from water to ice at -5°C. Ice Water ΔG and ΔS at -5 °C ΔG1 -5 °C ΔG=0 ΔG=0 Vapor pressure 3.163 mmHg 3.012 mmHg

5.1 THERMODYNAMIC ACTIVITY (2) S.J.T.U. Phase Transformation and Applications i No Units 三 Reference state:temperature,pressure and physical form Standard state:pressure and physical form Gas:pure gas at one atmosphere Condensed mater:pure liquid or solid under one atmosphere CdG,-G,-G=RTn人-RTna dG,-G,-G;=RTIn P=RTIna, Ideal gas P The fugacity of a condensed phase is equal to the fugacity of the vapor in equilibrium with it. The value of thermodynamic activity changes not only with pressure but also with composition. SJTU Thermodynamics of Materials Spring2008©X.J.Jin Lecture 9 electrochemistry I

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2008 © X. J. Jin Lecture 9 electrochemistry I 5.1 THERMODYNAMIC ACTIVITY (2) o i i i f f α ≡ i i i i i G G i RT ff =−= RTGGdG ln = lnα ∫ o o o i i i i i G G i RT PP =−= RTGGdG ln = lnα ∫ o o o Ideal gas No Units Reference state: temperature, pressure and physical form Standard state: pressure and physical form Gas: pure gas at one atmosphere Condensed mater: pure liquid or solid under one atmosphere The fugacity of a condensed phase is equal to the fugacity of the vapor in equilibrium with it. The value of thermodynamic activity changes not only with pressure but also with composition

5.2 CHEMICAL EQUILIBRIUM S.J.T.U. Phase Transformation and Applications bB+cC=dD+eE Expression for a chemical reaction OWron=AG=dGD+eGE-bGB-cGc GB =G&+RTInag AG=d(Go+RT Inap)+e(Gi RT Inde)-b(GB+RT InaB)-c(Gc+RTInac) △G=△G°+RTIn J G=0 △G°=dG)+eGE-bGB-cG& Equilibrium constant d。 e J b △G°=-RTInm）)=-RTIn K SJTU Thermodynamics of Materials Spring2008©X.J.Jin Lecture 9 electrochemistry I

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2008 © X. J. Jin Lecture 9 electrochemistry I 5.2 CHEMICAL EQUILIBRIUM + = + eEdDcCbB δ rev D E B −−+=Δ= GcGbGeGdGW C )ln()ln()ln()ln( D +=Δ RTGdG α D E ++ RTGe α E B +− RTGb α B C +− RTGc α C o o o o α +Δ=Δ ln JRTGG o o o o o o D E B C −−+=Δ cGbGeGdGG c C b B e E d D J αα αα α = B BB += RTGG lnα o α KRT α JRTG mequilibriu −=Δ ln ( ) −= ln o Equilibrium constant Expression for a chemical reaction ΔG 0 =

Question 8 S.J.T.U. Phase Transformation and Applications 298K时，已知甲醇蒸气的标准摩尔Gibbs生成自由能( CH3OH,g)为一161.92Jmol-1,试求甲醇液体的标准摩尔 Gibbs2生成自由能(CH3OH,I)。己知该温度下甲醇液体的 饱和蒸气压为16.343kPa。假定气体为理想气体。 △G=△G°+RTInJ 4G=0 16.343kPa AG=-RT In J (equlbrum)=-RT'In Ke Gas △G=0 △G°=dG)+eGE-bGg-cG& Liquid Ka b 01 aBQC SJTU Thermodynamics of Materials Spring 2008 ©X.J.Jin Lecture 9 electrochemistry I

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2008 © X. J. Jin Lecture 9 electrochemistry I Question 8 c C b B e E d D K αα αα α = o o o o o D E B C −−+=Δ cGbGeGdGG 298K时，已知甲醇蒸气的标准摩尔Gibbs生成自由能（ CH3OH，g）为－161.92kJ·mol-1，试求甲醇液体的标准摩尔 Gibbs生成自由能（CH3OH，l）。已知该温度下甲醇液体的 饱和蒸气压为16.343kPa。假定气体为理想气体。 α +Δ=Δ ln JRTGG o α KRT α JRTG mequilibriu −=Δ ln ( ) −= ln o ΔG 0 = o i i i f f α ≡ Liquid ΔG=0 16.343kPa Gas

5.6 ELLINGHAM DIAGRAMS (4) S.J.T.U. Phase Transformation and Applications 101-3106 1010-1:04104 1. 直线位置越低，元素与氧 化合的能力越大，相应的 氧化物越稳定； 2. 位置在下的金属或元素可 以把较上面的金属从氧化 物中还原出来； 3.炼铁过程，铁以下进入炉 渣，铁以上进入铁液，决 定何时加入配料。 材一子，0 局限 2+92…20 平衡的热力学讨论 200 10-10o 1000 110-0 10- 凝聚相都是纯物质 Figure 5.7 Ellingham diagram for some oxides SJ I U Ihermodynamics ot Materials Spring 2UU8 ©X.J.Jin Lecture 9 electrochemistry I

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2008 © X. J. Jin Lecture 9 electrochemistry I 5.6 ELLINGHAM DIAGRAMS (4) 1. 直线位置越低，元素与氧 化合的能力越大，相应的 氧化物越稳定； 2. 位置在下的金属或元素可 以把较上面的金属从氧化 物中 还原出来； 3. 炼铁过程，铁以下进入炉 渣，铁以上进入铁液，决 定何时加入配料。 局限 平衡的热力学讨论 凝聚相都是纯物质

5,7 VARIATION OF EQUILIBRIUM CONSTANT WITH TEMPERATURE S.J.T.U. Phase Transformation and Applications d(△G)=-△SdT △G°=△H°-T△S dAG)=Car- H°dr T T Multiplying by 1/T,we obtain: T aag）)=a-RInK。）)=AHrd宁） SJTU Thermodynamics of Materials Spring2008©X.J.Jin Lecture 9 electrochemistry I

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2008 © X. J. Jin Lecture 9 electrochemistry I 5.7 VARIATION OF EQUILIBRIUM CONSTANT WITH TEMPERATURE Multiplying by 1/T , we obtain: dTSGd o o )( Δ−=Δ o o o Δ−Δ=Δ STHG dT T H dT T G Gd o o o Δ − Δ )( =Δ dT T H dT T G T Gd 2 2 )( o o o Δ −= Δ − Δ ) 1()ln()( T dHKRd TG d o o Δ=−= Δ α ) 1 )(ln (T d RH Kd o Δ α −= G 1 d( ) H d( ) T T Δ = Δ o o

5.8 GASES DISSOLVED IN METALS (SIEVERT'S LAW) S.J.T.U. Phase Transformation and Applications H2(g)=2H (in copper solution) 0H,(g) an [H] 1.0 ap 1 cm3(STP)/100 gCu [H](concentration of H)-> Figure 5.10 Plot of activity of dissolved hydrogen versus [I]=K&2P2 concentration. SJTU Thermodynamics of Materials Spring 2008 ©X.J.Jin Lecture 9 electrochemistry I

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2008 © X. J. Jin Lecture 9 electrochemistry I 5.8 GASES DISSOLVED IN METALS (SIEVERT’S LAW) 2)( HgH (in copper solution) 2 = )( 2 2 gH H K α α α = α H = [ ] H [ ] 2 2 PH H Kα = [ ] 2/12/1 H2 = α PKH

5.9 CHEMICAL EQUILIBRIUM AND ADLABATIC S.J.T.U. FLAME TEMPERATURES Phase Transformation and Applications Not completion First law Chemical equilibrium Chemical equilibrium Egs 5.36a and 5.36b First law (Chemical equilibrium) 0.8 Eq.5.37(AFT) 0.6 人 0.4 0.2 0 2,000 4,000 6,000r·8,000 10,000-12,00014.000 Tempperature(→ Figure 5.11 The extent of the reaction 2H-H,as a function of temperature for the AFT and chemical equilibrium calculations (Egs.5.37 and 5.36a, respectively). SJTU Thermodynamics of Materials Spring2o08©X.J.Jin Lecture 9 electrochemistry I

Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2008 © X. J. Jin Lecture 9 electrochemistry I 5.9 CHEMICAL EQUILIBRIUM AND ADLABATIC FLAME TEMPERATURES (1) Not completion First law Chemical equilibrium First law Chemical equilibrium