Question

The free energy change for the following reaction at 25 °C, when [Cr3+] = 1.32×10-3 M and [Fe3+] = 1.14 M, is 131 kJ: Cr3+(1.32×10-3 M) + Fe2+(aq) Cr2+(aq) + Fe3+(1.14 M) ΔG = 131 kJ What is the cell potential for the reaction as written under these conditions? Answer: V Would this reaction be spontaneous in the forward or the reverse direction?

Answer 1

Answer:

E°cell = - 1.3575 V

This reaction is spontaneous in the reverse direction

Explanation:

The given cell reaction:

Cr³⁺(1.32 × 10⁻³ M) + Fe²⁺(aq) → Cr²⁺(aq) + Fe³⁺(1.14 M)

The given Gibbs free energy: ΔG = 131 kJ = 131 × 10³ J     (∵ 1 kJ = 10³ J)

As we know,

ΔG = - n F E°cell

Here, n - the number of moles of electrons transferred = 1

F - Faraday constant = 96500

E°cell - cell potential = ?

$\therefore E^{\circ }_{cell} = -\frac{\Delta G}{n \: F} = -\frac{131\times 10^{3}\, J}{1\, mol\times96500 \, C.mol^{-1}}$

$\Rightarrow E^{\circ }_{cell} = -1.3575\, V$

For a given chemical reaction if-

1. ΔG = negative and E°cell = positive

⇒ The reaction is spontaneous and proceeds spontaneously in the forward direction.

2.  ΔG = positive and E°cell = negative

⇒ The reaction is non-spontaneous and proceeds spontaneously in the reverse direction.

Since, for this chemical reaction:

Cr³⁺(1.32 × 10⁻³ M) + Fe²⁺(aq) → Cr²⁺(aq) + Fe³⁺(1.14 M)

ΔG = + 131 × 10³ J ⇒ positive

and, E°cell = - 1.3575 V ⇒ negative

Therefore, this reaction is spontaneous in the reverse direction.