The cell in which the following reactions occurs Calculate the standard Gibbs energy and the equilibrium constant of the cell reaction

Q3.6: The cell in which the following reactions occurs:

Calculate the standard Gibbs energy and the equilibrium constant of the cell reaction.

Solution:

Given that

n     = 2

T     = 298 K

E^o_cell =  0.236 V

We have the formula

∆_rG^θ = – nFE^o_cell   

Plug the values, we get

∆_rG^θ = −2 × 96487 × 0.236

∆_rG^θ = −45541.86 J mol⁻¹

Divide by 100o to convert in KJ

∆_rG^θ = −45.54 kJ mol⁻¹  

Use second formula of ∆_rG^θ

∆_rG^θ =−2.303RT log K_c

Plug the values we get

 −45541.86 J mol⁻¹ = –2.303 × 8.314 × 298  log K_c

Solve it we get

Log K_c  = 7.98

Take antilog both side, we get

K_c      = Antilog (7.98)

= 9.6 × 10⁷