The standard cell potential for the following galvanic cell reaction is 0.30 ~V at 298 ~K : 2 Cr ( s )+3 Fe ²⁺( aq ) 2 Cr ³⁺( aq )+3 Fe ( s ) Calculate the standard Gibbs energy change for the cell reaction. (Given 1 ~F =96500 ~C ~mol ⁻¹ )

Step-by-step solution

The given cell reaction is: 2 Cr ( s )+3 Fe ²⁺( aq ) 2 Cr ³⁺( aq )+3 Fe ( s ) The oxidation half-reaction is: 2 Cr ( s ) 2 Cr ³⁺( aq )+6 e ⁻ The reduction half-reaction is: 3 Fe ²⁺( aq )+6 e ⁻ 3 Fe ( s ) The number of moles of electrons transferred in the balanced equation is n = 6 . The standard Gibbs energy change is given by: G ^ = -n F E _ cell ^ Substituting the values: G ^ = -6 96500 ~C ~mol ⁻¹ 0.30 ~V G ^ = -173700 ~J ~mol ⁻¹ G ^ = -173.7 ~kJ ~mol ⁻¹ Using n=2 or n=3 leads to incorrect values of -57.9 ~kJ ~m