Question

Consider a cell composed of the following two half cells:

1. \[\ce{Mg_{(s)} | Mg{^{2+}_{(aq)}}}\], and
2. \[\ce{Ag_{(s)} | Ag{^{+}_{(aq)}}}\]

The EMF of the cell is 2.96 V, [Mg²⁺] = 0.130 M and [Ag⁺] = 1.0 × 10⁻⁴ M. Calculate the standard EMF of the cell. (R = 8.31 J K⁻¹ mol⁻¹, F = 96500 C mol⁻¹)

Answer 1

Given: E_cell​ = 2.96 V

[Mg²⁺] = 0.130 M

[Ag⁺] = 1.0 × 10⁻⁴ M

R = 8.31 J K⁻¹ mol⁻¹

T = 298 K

F = 96500 C/mol

The cell reaction is \[\ce{Mg_{(s)} + 2Ag{^{+}_{(aq)}} -> Mg{^{2+}_{(aq)}} + 2Ag_{(s)}}\]

here n = 2

Use the nernst equation

E_cell = `E_"cell"^circ - (RT)/(nF) log Q`

Where Q = `0.130/(1.0 xx 10^-4)^2`

= `0.130/(1.0 xx 10^-8)`

= 1.3 × 10⁷

log Q = log(1.3 × 10⁷)

= log(1.3) + log(10⁷)

= 0.262 + 16.118

= 16.38

Substitute these values in the Nernst equation

2.96 = `E_"cell"^circ - (8.31 xx 298)/(2 xx 96500) xx 16.38`

2.96 = `E_"cell"^circ - (2477.38/193000 xx 16.38)`

2.96 = `E_"cell"^circ - (0.01283 xx 16.38)`

2.96 = `E_"cell"^circ - 0.2103`

`E_"cell"^circ` = 2.96 + 0.2103

`E_"cell"^circ` = 3.17 V