Question

1. Consider the following electrochemical cell at 298.15 K: Mg(s) | MgSO4 (aq, m = 0.30) || AgNO3 (aq, m = 0.50) | Ag(s) (a) Write the half reactions and the overall reaction. (b) Calculate the standard cell potential. (c) Calculate ∆GR° and K° for the overall reaction. (d) Calculate the cell potential and ∆GR assuming activity coefficients are 1.00. (e) Calculate the cell potential and ∆GR using Table 10.3 for the mean ionic activity coefficients.

Answer 1

(a)

Anode half reaction:

Mg (s) ------------> Mg²⁺ (aq.) + 2 e

Cathode half reaction:

Ag⁺ (aq.) + e ------------> Ag (s)

Overall reaction:

Mg (s) + 2 Ag⁺ (aq.) ----------> Mg²⁺ (aq.) + 2 Ag (s)

(b)

E⁰_cell = E⁰_Ag+/Ag - E⁰_Mg2+/Mg = 0.80 - ( - 2.37 ) = + 3.17 V

(c)

deltaG⁰ = - n F E⁰_cell = - 2 * 96500 * 3.17 = - 611810 J

And

deltaG⁰ = R T lnK

- 611810 = - 8.314 * 298.15 * lnK

K = e^246.8

(d)

E_cell = E⁰_cell - (0.0591/n)Log[Mg²⁺]/[Ag⁺]²

E_cell = 3.17 - (0.0591/2)*Log(0.30)/(0.50)²

E_cell = 3.168 V