Question

Calculate E_cell and ΔG for the following at 28°C :

Mg_(s) + Sn²⁺( 0.04M ) → Mg²⁺( 0.06M ) + Sn_(s)

E°_cell = 2.23V. Is the reaction spontaneous ?

Answer 1

`Mg_(s) + Sn_(aq)^(2+) -> Mg_(aq)^(2+) + Sn_(s)`

`[Sn^(2+)] = 0.04M[Mg^(2+)] = 0.06M`

Q = `[Mg^(2+)]/[Sn^(2+)] = [0.06]/[0.04] = 1.5`

`E_(cell)^(°) = 2.23V`

R = 8.314 JK^-1 mol^-1
T = 28°C = 28 + 273 = 301K
n = 2
F = 96500 C/mol e^-

∴ `E_(cell) = E_(cell)^(°) - [2.303 RT]/[nF] log_10 Q`

= `2.23 - [2.303 xx 8.314 xx 301]/[2 xx 96500] log_10 (1.5)`

= `2.23 - [2.303 xx 8.314 xx 301]/[2 xx 96500] xx (0.1760)`

= 2.23 - 0.005255

`E_(cell)` = -2.2247 V
ΔG = `nFE_(cell)`

ΔG = `-2 xx 96500 xx 2.2247`

ΔG = - 429367 J
∵ ΔG is negative therefore reaction is spontaneous.