Calculate the Gibbs free energy change at 25 °C when 2.20 g of iron is deposited

Question

A Cr(s)|Cr3 (aq)||Fe3 (aq)|Fe(s) galvanic cell has a standard cell potential of 0.700 V. Calculate the Gibbs free energy change at 25 °C when 2.20 g of iron is deposited. Assume the concentrations in the cell remain at the standard state values of 1 M through the entire deposition process.

 

delta G=? J

 

Calculate the maximum amount of work done by the cell on its surroundings.

 

wmax= ? J

Answer 1

We can use the equation deltaG = -nFE_cell to solve for the first part, where 

n = the number of moles electrons

F is the Faraday constant (96,500 C/mol e–) and 

E_cell is the standard cell potential 

 

Since E_cell is given in the problem, and F is a constant, the only variable we still need to solve for deltaG is n, which is given by the number of electrons transferred per mole in the balanced redox reaction and turns out to be 3:

Cr(s)  --> Cr³⁺ + 3e-  and Fe³⁺ + 3e- --> Fe (s)

 

Substituting all of those values into the equation we get,

deltaG = -(3 mol e-)(96,500 J/V.mol e–)(0.700V) = 202,650 J