Question

Calculate the standard cell potential at 25 ∘C for the reaction

X(s)+2Y+(aq)→X2+(aq)+2Y(s)

where ΔH∘ = -793 kJ and ΔS∘ = -143 J/K .

Answer 1

For the thermochemical change, X(s) + 2Y⁺(aq)→X2+(aq) + 2Y(s)

Given data: ΔH^∘ = -793 kJ = -793000 J and ΔS^∘ = -143 J/K and T = 25 ^∘C = 25 + 273.15 = 298.15 K

Let us calculate ΔH^∘ = ? using Gibbs equation,

ΔG^∘ = ΔH^∘ - T*ΔS^∘.

ΔG^∘ = -793000 J - 298.15 K *(-143 J/K)

ΔG^∘ =  -750365 J

Now, Standrd cell potential E^o_cell and ΔG^∘ are related as,

ΔG^∘ = - nFE^o_cell.

For given reaction as X(s) changes to X2+ (q) obviusly the # of electrons transferred = 2.

Hence n = 2 and F = Faradays constant = 96485 C

Placing all known data in aboe equation we have,

-750365 J = - 2 * 96485 C *E^o_cell.

E^o_cell = -750365 J / (- 2 * 96485 C)

E^o_cell = 3.889 J/C

E^o_cell = 3.889 V ............ (1J/1C = 1V)

Standard Cell Potential s 3.889 V.

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