Question

The reaction of cr2+(aq) with cr2o2−7(aq) in acid solution to form cr3+(aq). calculate δg∘rxn.

Answer 1

The correct answer is -1059.45 kJ.

Step-by-step explanation:

The balanced equation is:

6Cr₂⁺ + Cr₂O₇²⁻ + 14H⁺ ⇒ 8Cr₃⁺ + 7H₂O

In the mentioned reaction 6 electrons are transferred

By calculating Ecell with the use of reduction potential of each cell:

Ecell = Eox + Ered

Ered = 0.50V

Eox = -Ered = -(-0.50V) = 0.50V

Ered = 1.33V

Ecell = 0.50V + 1.33V

Ecell = 1.83V

Now in order to calculate ΔG

n = 6, Faraday constant (f) = 9.68470 × 10⁴ = 96847 C mol⁻¹

ΔG = -nFE

ΔG = -6 × 96487 C mol-1 × 1.83V

ΔG = -1059.42 KJ

The relation between ΔG and ΔG°rxn

ΔG = ΔG° + RTlnQ

Under the standard condition Q = 1 and ΔG = ΔG°

Thus,

ΔG°rxn = ΔG = -1059.42 KJ

Answer 2

The reaction is:
6 Cr²⁺ + Cr₂O₇²⁻ + 14 H⁺ → 8 Cr³⁺ + 7 H₂O

E₀ = 1.33 - (-0.5) = 1.83 V

ΔG = - n f E₀
= - 6 * 96485 * 1.83
= - 1059405.3 J / mol
= - 1059.4 kJ / mol