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

Step-by-step solution

For the given reaction: 2 Cr(s) + 3 Fe ²⁺ (aq) 2 Cr ³⁺ (aq) + 3 Fe(s) The oxidation state of Cr changes from 0 to +3 , and for 2 moles of Cr, the total electrons transferred is 2 3 = 6 . Similarly, the reduction of 3 moles of Fe ²⁺ to Fe involves 3 2 = 6 electrons. Thus, the number of moles of electrons transferred ( n ) is 6 . The standard Gibbs energy change is given by: _ r G^ = -nFE_ cell ^ Substituting the values: _ r G^ = -6 96500 C mol ⁻¹ 0.30 V = -173700 J mol ⁻¹ = -173.7 kJ mol ⁻¹ Answer: -173.7 kJ mol ⁻¹