第2章+分析化学中的化学平衡.doc

14第二章 分析化学中的化学平衡第二章 分析化学中的化学平衡本章平衡常数方面基本在无机接触过，须灵活掌握以供今后计算使用；分布系数在计算浓度时非常有用，注意记清质子化与配合的区别联系，较易混淆；副反应系数和条件平衡常数在滴定计算，尤其是配合滴定中，非常有用，是本章又一重点及考点。作为本书的基础章节，虽难点不多，但需要熟练牢记，后面才不会卡住。书后习题解析（for reference）*1. 离子强度及活度系数，小化只要求了解公式ai =ii(1) I = 1/2CiZi CNa+ = 0.050 mol/L CNO2- = 0.050 mol/L I = 1/2(0.0501 + 0.0501) = 0.05 mol/L (分子的离子强度为0，即HNO2的I = 0)(2) CNH4+ = 0.066 mol/L CSO4= 0.033 mol/L I = 1/2(0.0661 + 0.0332) = 0.099 mol/L(3) CHCOO = 0.100 mol/L CNa+ = 0.100 mol/L I = 1/2(0.1001 + 0.1001) = 0.100 mol/L(4) I = 1/2(0.051 + 0.051) = 0.05 mol/L2. I = 1/2CiZi2 = 1/2(0.0512 + 0.0512 ) = 0.05 mol/L a H+= 0.9 a NH+= 0.3 lgH+ = -0.51210.05/(1+3.280.90.05)= -0.069 H+ = 0.85 lgNH+ = -0.51210.05/(1+3.280.30.05)= -0.0938 NH+ = 0.81NH4+ = H+ + NH3 Ka (I=0) = a H+/ a NH+Ka (I=0) = Ka (I=0.05)H+/NH+ Ka (I=0.05) = 5.210-10 =10-9.283. Zn + 4CN = Zn(CN)2-4 4(I=0) = aZn(CN)4/(aZnaCN)= 4(I=0.1)Zn2+(CN-)4 lg4(I=0) = lg4(I=0.1) + lgZn2+ + 4lgCN- aZn= 0.9 a CN-= 0.3 lgZn2+ = -0.51220.1/(1+3.280.60.1)= -0.3991 Zn2+ = 0.399lgCN- = -0.51210.1/(1+3.280.30.1)= -0.123 CN- = 0.753lg4(I=0) = 16.7 + (-0.3991) + 4(-0.123)= 15.814(I=0) = 1015.814. Ksp(I=0) = Ksp(I=0.1)Ag + Cl- lgAg+ = -0.51210.1/(1+3.280.30.1)= -0.123 a Ag+= 0.9 Ag+ =0.75 ; a Cl-= 0.3 Cl- = 0.75 lg Ksp(I=0) = lg Ksp(I=0.1) + lgCl- + lgAg+ = -9.49 - 0.123 - 0.123 = -9.74 Ksp(I=0) = 10-9.74 = 1.810-10 5. pKa1 pKa6 : 0.9 , 1.6 , 2.07 , 2.75 , 6.24 , 10.34 (I = 0.1,书P370) K1 H = 1/Ka6 = 1010.34 , K2 H = 1/Ka5 = 106.24 , K3 H = 1/Ka4 = 102.75 ， K4 H = 1/Ka3 = 102.07 ， K5 H = 1/Ka2 = 101.6 ， K6 H = 1/Ka1 = 100.9 K1 H = 1010.34 1 = K1 H = 1010.34 K2 H = 106.24 2 = K1 HK2 H = 1016.58 K3 H = 102.75 2 = K1 HK2 HK3 H = 1019.33 K4 H = 102.07 2 = K1 HK2 HK3 HK4 H = 1021.4 K5 H = 101.6 2 = K1 HK5 H = 1023.0 K6 H = 100.9 2= K1 HK6H = 1023.96.(1) Br2 + 2e- = 2Br E1= 1.087 V I2 + 6H2O + 10e- = 2IO3+ 12H + E2= 1.20 V I2 + 5 Br2 + 6H2O = 2IO3+ 10 Br+ 12H + lgK = 10(1.087-1.20)/0.059 = -19.15 K = 10-19.15 = 7.110-20 (2) lgK = n(E1- E2)/0.059 = 2-0.91-(-0.44)/0.059 = -15.93 K = 10-15.93 = 1.1710-16 (3) lgK = 21.359-(-2.37)/0.059 = 126.4 K = 10126.4 = 2.5710126 (4) lgK = 6(1.23 - 1.695)/0.059 = -47.29 K = 10-47.29 = 5.1310-48 (5) Ag + + e- = Ag E1= 0.799 V Ag(S2O3)23- + e- = Ag + 2S2O32- E2= 0.017 V Ag + + 2S2O32- = Ag(S2O3)23-lgK = (0.799-0.017)/0.059 = 13.25 K = 10 13 = 1.7810 13 (6) lgK =(0.185-0.518)/0.059 = -5.64 K = 10-5.64 = 2.2910-6 7. C6H5OHKa = 10-9.95 Kb = 10-4.05 1H = 1/Ka1 = 10 9.95H2C2O4 Ka1 = 10-1.22 Kb2 = 10-12.78 2H = 1/(Ka1Ka2) = 10 5.41H2C2O4- Ka2 = 10-4.19 Kb1 = 10-9.81 1H = 1/Ka1 = 10 1.22CH3COOH Ka = 10-4.74 Kb = 10-9.26 1H = 10 4.74N+H3OH Ka = 10-5.96 Kb = 10-8.04 1H = 10 5.96N+H3CH2COOH Ka1 = 10-2.35 Kb2 = 10-11.65 2H = 10 11.95N+H3CH2COO- Ka2 = 10-9.60 Kb1 = 10-4.40 1H = 10 2.35 酸性：H2C2O4 N+H3CH2COOH H2C2O4- CH3COOH N+H3OH N+H3CH2COO- C6H5OH8. 5 = 1012.86 ； 2 = 1016.34 ； 1 = 1018.0 ； 2 = 108.9 ； 4 = 106.46 ； 1 = 1018.80 ； 3 = 1021.0 ； 1 = 104.4 Cu-邻二氮菲EDTA柠檬酸乙酰丙酮NH3草酸酒石酸三乙醇胺9. (1) NH3 + H + = NH4+ Kt = NH4+ /(NH3H + )= 1/Ka = 109.26 (2) OH - + H + = H2O Kt = 1/(OH - H +)= 1/Kw = 1.01014 (3) HCO3- + H + = H2CO3 Kt = H2CO3/(HCO3- H + )= 1/Ka1 = 106.38 (4) HS - + OH - = S2-+ H2O Kt = H2OS2- /(HS - OH - )= Ka2/Kw = 10 -14.15 /10-14 = 10-0.15 (5) H3BO3 + OH - = H2BO3- + H2O Kt = H2BO3- /(H3BO3 OH - )= Ka1/Kw = 10 -9.24 /10-14 = 104.76 10. HAc=HAc C = C1H H + /(1 + 1H H + ) = C(H + /Ka)/(1+H + /Ka)= CH + /(H + + Ka) = 0.1010-7.00 /(10-7.00 + 10-4.74 )= 5.510-4 Ac- =Ac - C = C /(1 + 1H H + )= CKa/(H + + Ka) = 0.110-4.74 /(10-7.00 + 10-4.74 )= 0.099511. 0 = A2- /CA = Ka1Ka2/(H + 2 + Ka1H + + Ka1Ka2)= 0.391 = HA- /CA = Ka1H + /(H + 2 + Ka1H + + Ka1Ka2)= 0.602 = H2A /CA = H + /(H + 2 + Ka1H + + Ka1Ka2)= 0.001C2O42- = CH2A0 = 0.039 mol/LHC2O4- = CH2A1 = 0.060 mol/LH2C2O4 = CH2A2 = 1.010-4 mol/L12. NH3 = Ka/(Ka + H + )= 10-9.26 /(10-9.26 + 10-9.0)= 10-0.45 = 0.355NH4+ = H + /(Ka + H + )= 10-9.0 /(10-9.26 + 10-9.0) = 10-0.19 = 0.646NH3= 0C = 0.20.355 = 0.071 mol/LNH4+ = 1C = 0.20.646 = 0.129 mol/L13. Cu(NH3)+ = 1NH3/(1 + 1NH3 + 2NH3)= 105.93-4/(1 + 105.93-4 + 1010.86-8)= 10-0.98 = 0.105Cu(NH3)2+ =2NH3/(1+1NH3+2NH3)= 102.86/102.91= 10-0.05 = 0.891Cu(NH3)+ = C1 = 0.010.105 = 1.0510-3 mol/LCu(NH3)2+ = C2 = 0.010.891 = 8.9110-3 mol/L14. Hg-Cl的lg1lg4: 6.74 ,13.22 ,14.07 ,15.071 =1Cl/(1+1Cl+4Cl4 ) = 106.74-3/(1+106.74-3 + 1013.22-6 + 1014.07-9+ 1015.07-12 )= 103.74/(1+ 103.74 + 107.22 + 105.07 + 103.07) = 10-3.48 2 = 107.22/107.223 = 0.993 3 = 105.07/107.22 = 10-2.51 4 = 103.07/107.22 = 10-4.52 主要以HgCl2型体存在HgCl2= C2 =1.010-3 0.993 = 9.9310-4 mol/L15. Al3+ CF = 1.05/(42.000.05)= 0.5 mol/LOH - F- H F(H) pKa = 3.18 pH = 5.0 Al(OH) Al(F) F- =0CF = KaCF/(Ka + H+ ) = 10-3.18 0.5/(10-3.18 + 10-5 ) = 10-0.31 = 0.49Al(F) = 1+1F+6F6 = 1018.27 Al = 1018.27 +100.4 1 = 1018.27 Al3+ = CAl/Al = 0.01/ 1018.27 = 10-20.27 = 5.3710-21 mol/L16. MgNH4PO4 Mg2+ + NH4+ +PO43- Mg2+ = 5.610-4 mol/LNH4+ = CNH4+ = 5.610-4 10-9.7/(10-9.7 +1014-4.74 )= 10-3.82 PO43- = CPO43- = 5.610-4 10-12.36/(10-9.7 +10-12.36 )= 10-5.91 Ksp =Mg2+ NH4+ PO43- = 5.610-4 10-3.8210-5.91 = 10-12.88 = 1.010-13 17. AgI = Ag+ + I- I- = 0.0021000/100 = 0.02mol/L Ag+ = Ksp/I- = 10-16.03/0.02= 10-14.33 Ag(NH3) = CAg+/Ag+ = 0.02/10-14.33 = 1012.63 又Ag(NH3) = 1+1NH3+2NH3 = 1+103.24 NH3+107.05 NH3NH3= 102.79 mol/L18. 1.00/Al(OH)30.01= 1.00/7810 = 0.1282mol/L = Al(OH)4- Al(OH)4- /OH - = 10 OH - = 0.1282/10 = 0.01282mol/L1.0V = 0.01282(100 + V) + 0.1282(100 + V)V = 16.42 mL19. Ksp-PbI2 =10-8.15 Ksp-AgI = 10-16.03 PbI2 沉淀时，I- = (Ksp/Pb2+ ) = (10-8.15/0.20) = 10-3.73 AgI 沉淀时，I- = Ksp/Ag+ = (10-16.03/0.01) = 10-14.03 AgI 先沉淀Ag+ = Ksp/I- = 10-16.03/10-3.73 = 10-12.30 = 5.010-13 20. 提示： (1) Ag+ + Cl- = AgCl Cl 0.1+ss = Ag+ + AgCl + AgCl2- + AgCl32- + AgCl43- = Ag+ (1 + 1Cl- + 2Cl- 2 + 3Cl- 3 + 4Cl- 4 ) = Ksp(1/Cl- + 1 + 2Cl- + 3Cl- 2 + 4Cl- 3 )(2) s(0.1 + s)= Ksp21. (1) AgI Ag+ + I- Ag(NH3) = 1 + 1NH3 + 2NH32 Ag(NH3) = 1 + 103.24 1 + 107.05 1 = 107.05 Ag+ I- = Ksp= KspAg(NH3) = 10-16.03 107.05 = 10-8.98S 2 = Ksp= 10-8.98 S = 10-4.49 = 3.2410-5 mol/L(2) AgI Ag+ + I- Ag(S2O3) 的 lg1 - lg3 :I- S2O32- 8.82 ,13.46 ,14.15Ag(I) Ag(S2O3) Ag(I) = 1 + 106.58-2 + 1011.74-4 + 1013.68-6 = 108.01 Ag(S2O3) = 1 + 108.82-2 + 1013.46-4 + 1014.15-6 = 109.48 Ag = Ag(I) + Ag(S2O3)1 = 108.01 + 109.481 = 109.48 Ag+ I- +0.01= Ksp= KspAg = 10-16.03 109.48 = 10-6.55S (S + 0.01) = Ksp = KspAg = 10-16.03 109.48 = 10-6.55 S = 10-4.55 = 2.8210-5 mol/L22. PbSO4 Pb2+ + SO42- Ksp = 1.610-8 ; HSO4- : Ka = 10-2 Pb(Cl) = 1 + 1Cl- + 2Cl- 2 + 3Cl- 3= 1 + 101.21.0 + 100.61.0 2 + 101.21.0 3 = 101.56 SO4(H) = 1 + H+ /Ka = 1 + 1/10-2 = 102 Pb2+ SO42- = S= Ksp = KspPb(Cl)SO4(H)S = (1.610-8 101.56102 ) = 10-2.12 = 7.610-3 mol/L23. Ag2S 2Ag+ + S2- S(H)= 1 + 1H + 2H2 = 1019.03 S 2S S+0.1 Ksp = 10-48.7 Ksp=2S2 (S+0.1)= KspS(H)S =(210-48.7 1019.03 /0.4) = 10-14.64 = 2.3110-15 24.(1) CuS Cu2+ + S2- S(H)= 1 + 1H + 2H2 S S S = 1 + 1014.15-7 + 1014.15 + 6.88-14 = 107.40 Ksp= S2 = KspS(H) S = (KspS(H) =(10-35.2 + 7.40 ) = 10-13.90 = 1.310-14 mol/L (2) Cu2S 2Cu+ + S2- Ksp = 10-47.7 由(1) 知，S(H)= 107.40 Cu+ 2S2- =(2S)2S = Ksp= KspS(H) = 10-47.7+7.4 = 10-40.3 S = 10-13.63 = 2.310-14 mol/L (3) (Ksp)1/3 和水电离相近，故不可忽略水的电离，改用无机算法。 Tl2S + H2O 2Tl+ + HS- + OH S 2S S S S2- + H+ = HS- 1/Ka2 ; H2O H + + OH Kw ; Tl2S 2Tl+ + S2- Ksp (2S)2 SS = K总 = KspKw/Ka2 4S4 = 10-20.310-14.0/10-14.15 = 10-20.15 S = 6.510-6 mol/L = 10-5.19 25. Y(H) = 1 + 1H + + + 6H + 6 = 1 + H + /Ka6 + H + 2/(Ka6Ka5) + + H + 6/(Ka6 Ka1)= 1+1010.34H+ +1016.58H+ 2 +1019.33H+ 3 +1021.4H+ 4 +1023.0H+ 5 +1023.9H+ 6 pH = 4.5 Y(H) = 1+105.84 +107.58+105.83+103.40+100.5+10-3.1 = 107.59 pH = 5.5 Y(H) = 1+104.9 +105.58+102.83+10-0.6+10-4.5+10-9.1 = 105.66 pH = 4.5 Y/CY =0 =1/107.59 = 10-7.59 = 10-5.59 % = 2.5710-6 %pH = 5.5 0 =1/105.66 = 10-5.66 = 10-3.66 % = 2.1910-4 %26.(1) Co2+ + Y4- = CoY NH3= 10-1.30 Co(NH3) = 1+100.81 +101.14 +100.89 +100.35 +10-0.77 +10-2.69 = 31.43 = 101.50 lgY(H) = 2.27 lgK = 16.31 K= 1016.31/(31.43102.27 )= 1012.54 = 3.51012 (2) lgY(H) = 0.45 lgK= lgK - lgY(H) -lgCo(NH3) = 16.31 - 0.45 - 1.50 = 14.36 (3) NH3= 10-0.30 Co(NH3) = 1 + 101.81 + 103.14 + 103.89 + 104.35 + 104.23 + 103.31 = 104.71 lgK= 16.31 2.27 4.71 = 9.33 (4) lgK= 16.31 0.45 4.71 = 11.1527.(1) lgKCdY = 16.46 pH = 5.0 lgY(H) = 6.45 Cd(I) = 1 + 1I- + + 4I- 4 = 1+102.10-1 +103.43-2 +104.49-3 +105.41-4 =1+101.10 +101.43 +101.49 +101.41 = 101.99 lgKCdY=lgKCdY - lgY(H) - lgCd(I) = 16.46 - 6.45 - 1.99 = 8.02 KCdY= 108.02 (2) pH = 7.0 lgY(H) = 3.32 lgKCdY= 16.46 - 3.32 - 1.99 = 11.15 KCdY= 1011.15 (3) Cd(I) = 1 + 102.10-2 + 103.43-4 + 104.49-6 + 105.41-8 = 1 + 100.1 + 10-0.57 + 10-1.51 + 10-2.59 = 100.41 lgKCdY= 16.466.450.41 = 9.60 KCdY= 109.60 (4) lgKCdY= 16.463.320.41 = 12.73 KCdY= 1012.73 28.(1) Al3+ + Y4- = AlY Y(Ca) = 1+1Ca2+ = 1+1010.69 = 108.69OH H Ca2+ Y = Y(Ca) + Y(H) - 1 = 108.69 lgKAlY= lgKAlY lgY lgAl(OH) = 16.3 - 8.69 - 0.4 = 7.21 (2) Fe3+ + Y4- = FeY KFe3+Y = 1025.1 ; KFe2+Y = 1014.32 OH Fe2+ H Y(H) = 1010.60 ; Fe3+(OH) = 100.4 Y(Fe2+ ) = 1 + Fe2+ = 1 + 1014.32 0.01 = 1012.32Y = Y(H) + Y(Fe2+ )1 = 1010.60 + 1012.32 1 = 1012.32 lgKFeY= lgKFeY lgY lgFe(OH) = 25.1 - 0.412.32 = 12.38KFeY= 1012.38 (3) Zn2+ + Y4- = ZnY2- Y(Mg) = 1+1Mg= 1+108.7 0.01 = 106.7 H Mg Y = 106.45 + 106.71 = 106.89 lgKZnY= lgKZnY lgY = 16.56.89 = 9.61(4) Bi + Y = BiY Y(H) = 1018.01 ; lgKBiY = 27.94 OH Pb H lgKPbY = 18.04 ; lgBi(OH) = 0.1 Y(Pb) = 1+Pb= 1+ 1018.04 0.01 = 1016.04 Y = 1016.04 +1018.01 1 = 1018.01lgKBiY= lgKBiY - lgBi(OH) - lgY = 27.94 - 0.1 - 18.01 = 9.83K= 109.83 29. Ni2+ + Y4- = NiY2- lgNi(OH) = 0.1 ; lgY(H) = 1.28 OH NH3 H NH3 = 1/(1+1H H)=1/(1+109.26-9 )=0.355 NH3= CNH3NH3 = 0.200.355 = 10-1.15 = 0.07Ni(NH3) = 1 + 1NH3 + + 6NH36 = 1 + 101.65 + 102.74 + 103.32 + 103.36 + 102.96 + 101.84 = 103.77 Ni = 100.1 + 103.77 - 1 = 103.77 lgKNiY= lgKNiY - lgNi - lgY(H) = 18.62 - 3.77 - 1.28 = 13.5730. Ag2SO4 2Ag + SO42- E(Ag+/Ag)= E(Ag+/Ag)+0.059lgAg+ =E(Ag+/Ag)+0.059/2lgAg+ 2 E(Ag2SO4/Ag)= E(Ag2SO4/Ag) + 0.059/2lg(1/SO42- ) 当 = 时，E(Ag2SO4/Ag) = E(Ag+/Ag) + 0.059/2lgAg+ 2 - 0.059/2lg(1/SO42- ) = E(Ag+/Ag) + 0.059/2lg(Ag+ 2SO42- )= E(Ag+/Ag) + 0.059/2lgKsp= 0.799 + 0.059/2lg(1.510-11 ) = 0.799 - 0.319 = 0.48V31. E = E(Zn2+/Zn) + 0.059/2lgZn2+ E = E(ZnS/Zn) + 0.059/2lg(1/S 2- ) - ,E(Zn2+/Zn) - E(ZnS/Zn)= 0.059/2lg1/(Zn2+ S2- )= 0.059/2lg(1/Ksp)-0.763-(-1.44)2/0.059 = lg(1/Ksp)= 1022.95 Ksp = 10-22.95 = 1.1210-2332. E = E(Zn2+/Zn) + 0.059/2lgZn2+ E = E(ZnY/Zn) + 0.059/2lg(ZnY/Y) - ,E(ZnY/Zn) - E(Zn2+/Zn)= 0.059/2lg(Zn2+ Y/ZnY) = 0.059/2lg(1/KZnY) = 0.059/2lg(1/1016.5 )E(ZnY/Zn) =E(Zn2+/Zn) +0.059/2lg(1/1016.5 )= -0.763+(-0.487)= -1.25V33.(1) E = E+ 0.059lgH+ 2 = 1.00 - 0.0592 = 0.882 V (2) E = E+ 0.059lg0.012 = 0.764 V34. Fe3+ + e Fe2+ Fe3 = 1/(1+1Y) Y OH Y = 1/Fe3(Y) = 10-13.50 Y = CY /Y(H) = 0.1/1010.60 = 10-11.60Fe3(Y) = 1+1025.1-11.6 = 1013.50 Fe2(Y) = 1+1014.32 -11.60 = 102.72 E = E+ 0.059lg(Fe2(Y)/ F