4. ELETROHEMISTRY - II Molar coductace, Equivalet coductace, cell cetat ad Kohlraush Law :. Give : l 0.98 cm a.3 cm cell cost. cell cost. a l cell cost. a l 0.98.3 0.7538 cm As : ell costat for the cell is 0.7538 cm. Give : K.05 0 4 Ω cm 0.005 M Λ Λ K 000 Λ K 000.05 0 4 000 0.005.05 0.005 0.3 Ω cm mol As : Molar coductivity of the solutio is.3 Ω cm mol 3. Give : Λ 407. Ω cm mol 0.0 M K K Λ K 000 Λ K 000 000 407. 0.0 000 8.44 0 3 Ω cm As : oductivity of the solutio is 8.44 0 3 Ω cm 4. Give : 0.0005 M R 370 Ω l 0.7 cm a 0.8 cm Λ Λ K 000 K cell cost. G 0.7 0.8 0.7.4. 370. 0 5 Ω cm
50 Mahesh Tutorials Sciece Λ K 000. 0 5 000 0.0005 Λ 4. Ω cm mol As : Molar coductivity of the solutio is 4. Ω cm mol 5. Give : 0.0 M R 44 Ω Λ 4.8 Ω cm mol cell cost. Λ Nal Λ K 000 For Kl : K cell cost. R cell cost. For Nal : K R 0.004 484 0.84 cm K cell cost. G K cell cost. R Λ K 000 4.8 K 000 0 K 4.8 0 0 3 4.8 0 5 Ω cm K cell cost. G cell cost. K R 4.8 0 5 44.79.8 cm As : ell costat of the cell is.8 cm. Give : For Kl 0.0 M R 484 Ω K 0.004 Ω cm For Nal 0.00 M R 5490 Ω 0.84 5490 K.4 0 4 Ω cm Λ K 000.4 0 4 000 0 3.4 0 As : Molar coductivity of solutio is 4. Ω cm mol 7. Give : For 0. M Kl R 00 Ω K.9 Sm.9 0 Scm K ad Λ for Kl (0.0 M) K cell cost. G Λ K 000 For 0.0 M Kl R 50 Ω
Mahesh Tutorials Sciece 5 For Kl (0. M Kl) : K cell cost. R cell cost. K R.9 0 00.9 cm For Kl (0.0 M) : K cell cost. R.9 50.48 0 3 Ω cm Λ K 000.48 0 3 000 0 48 Λ 4 Ω cm mol As : K.9 cm Λ 4 Ω cm mol 8. Give : Λ 0 H 3 OOK 4.4 Ω cm mol Λ 0 48. Ω HBr cm mol Λ 0 5.9 Ω KBr cm mol Λ 0 H 3 OOH 9. Give : Λ. Ω cm mol α, K a Λ 0 390.7 Ω cm mol 0.0 M α 0, K α a α 0 K a α. 390.7 (0.04) 0.0 0 4 0. 0 5 As : α 0.04 K a. 0 5 0.Give : Λ 0 NH 4 l Λ 0 NaOH Λ 0 Nal Λ (NH4 OH) 0.04 9.8 Scm mol 7.4 Scm mol 08.9 Scm mol 9.33 Scm mol 0.0 N Λ 0 H 3 OOH Λ0 H 3 OOK + Λ0 HBr Λ0 KBr 4.4 + 48. 5.9 54. 5.9 390.7 Ω cm mol As : Molar coductivity is 390.7 Ω cm mol % dissociatio ad K a α 0, K a α
5 Mahesh Tutorials Sciece Λ 0 NH 4 OH Λ0 NH 4 l + Λ0 NaOH α 0 Λ0 Nal 9.8 + 7.4 08.9 38.3 Ω cm mol 9.33 38.3 α 3.9 0 % α 3.9 0 00 3.9 % K a α (3.9 0 ) 0 5. 0 4 0 5. 0.5 0 5 As : % dissociatio 3.9% K a.5 0 5 Problems based o Nerst Equatio. i) Mg (s) Mg + (aq) (0.00M) u + (aq) (0.000M) u (S) E 0 Mg E 0 u.37 V 0.34 V E 0 log cell 0 E 0 oxid + E0 red E 0 Mg + E0 u.37 + 0.34.7 V E 0 log cell 0 Mg u Mg u + + + + 3. alculatio of ph : i) Give : ph 0 T 98 K P atm E oxid.7 0 0.7 0.095 0.7 0.095 ().8 V ell reactios are spotaeous because is positive. ii) Fe (s) Fe + (0.00M) H+ (M) H (g) ( Bar) Pt E 0 Fe E 0 H 0.440 V 0 V E 0 oxid + E0 red 0.440 + 0 0.440 V E 0 log cell 0 3 4 Fe + H 0.440 log 0 0 3 0.440 log 0 (3) 0.440 + 0.088 0.58 V
Mahesh Tutorials Sciece 53 E oxid E 0 oxid H P H () ( [H + ]) ph 0 0 V H (g) H + (aq) + e iii) Give : V E oxid E 0 oxid H P H ph E oxid 0 H H Ni [H + ]. [H + ] [H + ] () ( [H + ]) ph 0 As : E oxid 0.59V ii) H + (aq) + e H (g) E red E 0 log red 0 0 +. H ph H. log0 [H + ] [H + ] Pt H H + Ni + (M) Ni H (g) H+ (aq) + e...oxidatio Ni + (aq) + e Ni (s)...reductio H (g) Ni+ -- (aq) H+ + Ni (aq) (s). [H + ] [H + ] [H + ] As : ph iv)give : E red 0.43V H Ni H
54 Mahesh Tutorials Sciece ph 4. Determiatio of equilibrium costat : i) Give : E 0 u 0.34 V E 0 S 0.54 V E red E 0 red u + (aq) S+ (aq) S4+ (aq) (s) H + (aq) + e H (g) E red E 0 red 0.43 0 0.43 + Reductio H P H H +. [H + ] H 0.43 ( ) ( [H + ]) 0.43 ph ph.98 As : ph 7 0.43 E 0 + oxid E0 red E 0 + s E0 cu 0.54 + 0.34 + 0.8 V At equilibrium 0 0 0.8 0.8 0.8 0.37 370 59. AL [3.5705.775] AL (0.799).950.950 AL (.950).97 0 ii) Give : E 0 S + /S 0.4 V E 0 u + /u+ 0.5 V S (s) S + + (aq) e... Oxid u + + (aq) e u +... Red (aq) S (s) + u + (aq) S+ + (aq) u+ (aq)
Mahesh Tutorials Sciece 55 E 0 + oxid E0 red E 0 + S E0 u + 0.4 + 0.5 0.9 V 5. Determiatio of : Give : E red 0.877 V E H 0 V (Ioic product of water) At equilibrium. 0 0 0.9. 0.9 0.9 0.58 5 8 0 0 5 9.. AL (3.734.775) AL (0.999) 9.85 AL (9.85) As :.53 0 9 ell reactios : H (g) H + (aq) + e...oxidatio H O (l) + e H (g) + OH (aq)...reductio H O (l) H + (aq) + OH (aq) [H + ] [OH ] 0 (At equilibrium) 0 [H + ] [OH ] E0 oxidatio + E0 reductio 0 0.877 0.877 V 0.877 0.877 877 59 877 59 3.978 AL.775.43 4.0055 4.0055 AL [4.0055] AL [ 5.9945] 9.87 0 5 As : 0.98 0 4 0 4
5 Mahesh Tutorials Sciece. Determiatio of : i) Give : E 0 +/Ag 0.80 V Ag E 0 /AgI, Ag 0.59 V I of AgI I the give cell, Ag Ag+ I AgI, Ag Ksp Reductio half cell is saturated with AgI ad whe i cotact with Ag Ag + half cell, equilibrium costat is i terms of Ksp ad at this stage 0. ell reactios : Ag (s) Ag + (aq) + e...oxidatio AgI (s) + e Ag (s) + I...reductio AgI (s) Ag + (aq) + I (aq) K + [Ag ][I ] [AgI] K.[AgI] [Ag+][I ] [Ag+][I ] At equilibrium, 0 [Ag + ][I ] 0 E 0. log cell 0 E 0 cell E0 oxidatio + E0 reductio 0.80 + (0.59) 0.959 V E 0. log K cell 0 sp 0.959 0.959 959 59 3.9785 Al.775.07.04 Al [.04] Al [.0000 0.04 + ] Al[ 7.893] As : 7.87 0 7 ii) Give : E 0 + 0.34 V u /u ph 4 of u(oh) 0 9 E reductio E reductio E 0 reductio ph 4 poh 0 poh [OH ] 0 [OH ] [OH ] Al (0) [OH ] M of u(oh) 0 9 [u + ][OH ] 0 9 [u + ] 0 9 + [u ]
Mahesh Tutorials Sciece 57 [u + ] 0 9 Reductio of u + u + (aq) + e u (s) E reductio E 0 reductio E reductio 0.34 0.34 + 0.34 + + [u ] 0 9 0 9. (9) 0.34 9.5 0.34 0.5 As : E reductio 0. V. Problems based o G 0. Mg (s) + S + (aq) Mg + (aq) + S (s) i) ell formula : e Mg (s) Mg + (aq) S + + (aq) S (s) ( M) ( M) i ii) [Mg + ] 0.035 M [S + ] 0.05 M E 0 Mg.37 V ; E 0 S 0.3 V Mg S + + E 0 oxid + E 0 red E 0 + Mg E0 S.37 0.3.34 V.34.34.34 0.035 0.05 35 5 7 5.34 0.095.4.34 0.095 0.4.34 0.0043.97 V.3 V iii) G F 9500.3 430390 J G 430.39 kj. r (s) r 3+ o + o (s) (0.005 M) (0.0M) Give : E 0 o 0.80 V E 0 r 0.74 V ell reactio G G F ell reactio : Aode : r (s) r 3+ (aq) + e (Oxid.) athode : 3o + (aq) + e 3o (s) (Red.)
58 Mahesh Tutorials Sciece Net cell reactio : r (s) + 3o + (aq) r 3+ (aq) + 3o (s) E 0 E 0 + cell oxid E0 red E 0 + E 0 r o 0.74 + ( 0.80) E 0 0.4 V cell 0.4 0.4 0.4 0.4 0.4 0.4 r o 3+ + ( 0.005 ) 3 ( 0.0) 45 0 78 0 450 78 3 8 9 (4.58 3.375) (.3883) 0.080 0.4 0.037 0.444 V G F Ecell 9500 0.444 5845. J G 58.4 kj 3. Give : E 0 Mg.37 V P H 0 atm,, G0 E 0 + oxid E0 red G 0 F Mg (s) Mg + (aq) + e (Oxid.) H + (aq) + e H (g) (Red.) Mg (s) + H + (aq) Mg + (aq.) + H (g) 4. Give : E 0 u + u 0.5 V E 0 u + u + 0. V, G0, Keq. E 0 + oxid E0 red G 0 F E 0 oxid + E0 red E 0 Mg + E0 H.37 + 0.37 V.37.37.37 0.095 ().34 V Ms + p H log 0 0 0 G 0 F 9500.37 45740 J G 0 457.40 kj H
Mahesh Tutorials Sciece 59 Keq u + (aq) u + (aq) + e (Oxid.) u + (aq) + e u (s) (Red.) Z (s) Z + (aq) H+ (aq) H (g) Pt (0. M) (.M) Z (s) Z + (aq) + e (Oxid.) H + (aq) + e H (g) (Red.) u + (aq) u + (aq) + u (s) E 0 + oxid E0 red E 0 u + u + + E0 u + u 0. + 0.5 0.3 V G 0 F 9500 0.3 34740 J G 0 34.74 kj Z (s) + H + (aq) Z + (aq) + H (g) E 0 oxid + E0 red E 0 Z + E 0 H 0.73 + 0 0.73 V 0.73 Z ++ H ph 0. (.) Keq 5. Give : E 0 Z 0.73 V Keq 0.3 300 59 AL [ 3.553.775] AL (0.7848) Keq.095 Keq AL (.095) Keq. 0 Z + H 0.73 + 0.73 + 0.73 +.44 0..4. 0.380 0.73 + 0.90 0.73 + 0.0 0.774 V. i) I (s) + e I (aq) E 0 I 0.535 V [I ] 0.03 M E red E 0 log red 0 I I (s) 0.535 log 0 (0.03)
0 Mahesh Tutorials Sciece 7. Give : E 0 Ni 0.5 V Keq E 0 Ag 0.799 V Keq Ni (s) + Ag + (aq) Ni + (aq) + Ag (g) E 0 + oxid E0 red E 0 Ni + E 0 Ag + 0.5 + 0.799.049 V E red 0.535 0.03 0.535 (.477) 0.535 + 0.43 0.83 V ii) Fe 3+ (aq) e Fe + (aq) [Fe + ] 0. M [Fe 3+ ] 0.0 M E 0 Fe + Fe 3+ 0.77 V E red E 0 log red 0 E red Fe Fe + 3+ 0.77 0 0 0.77 0 0.830 V Keq 0 (At equilibrium).049 Keq Keq Keq Keq.049 0980 59 AL (4.38.775) Keq AL (.5503) Keq 35.5058 Keq AL (35.5058) Keq.754 0 35.098 8. i) The Nerst equatio for electrode potetial is 0.059(V.mol e ) [ produce] [ reactats] E Br Br E 0 Br 0.059(V.mol e ) Br [Br ] E 0 Br.08 V, Br mol e ad [Br ] 0.0 M Hece, E 0 Br.08 Br 0.059( m ol ( ) m ol e e ) [0.0].08 0.09 0 4.08 + 4 0.09.98 V
Mahesh Tutorials Sciece ii) u + (aq) + e u + (aq) E u +,u + E 0 u +,u + 0.059(V. mol e ) u ( mole log ) 0 u E 0 u +,u + 0.53 V, [u + ] 0. M, [u + ] 0.05 M Hece, E u +,u + 0.53 0.059 + + 0. 0.05 0.53 0.059 0.53 0.059 (0.300) 0.53 0.078 0.35V. 9. The half cell reactios ad overall cell reactio are as follows : 3 Z (s) Z + (0.008M) + e (oxid. at aode) r 3+ (0.0M) + 3e r (s) (red. at cathode) 3Z (s) + r 3+ (0.0M) 3Z + (0.008M) + r (s) (overall cell reactio) Nerst equatio for the cell potetial is E 0 0.059(V.mol e ) cell Z r mol e, [Z + ] 0.008M, [r 3+ ] 0.0M E 0 E 0 cell r E0 Z 0.74V ( 0.73V) 0.03V + 3+ 3 Hece, 0.03 0. Give : E calomel 0.8 V [H + ] 0.5 M P H atm [l ] M ell reactio 0.059(V. mol e ) 0.03 0.059 0.03 0.059 0.03 + 0.0 0.045V ( ) mol e E oxid + E red ell reactio : Aode : H (g) H + (aq) + e (Oxid.) athode : Hg l (s) + e Hg (l) + l (aq) (Red.) Net cell reactio : H (s) + Hg l (s) Hg (l) + H + + (aq) l (aq) E calomel 0.8 V We ca fid E H usig Nerst equatio H (g) H + + e (Oxid.) 0.005 (.907) [ 0.008] [ 0.0] 3
Mahesh Tutorials Sciece E H E 0 H H ph 0 E H 0.078 V. log ( 0.5) 0. (0.5). ( 0.300) E oxid + E red E H + E calomel 0.078 + 0.8 0.978 V