For the reaction 2Co3 + (aq) + 2Cl - (aq) →2Co2 + (aq) + Cl2 (g). E∘=0.483 V what is the cell potential at 25 ∘C if the concentrations are [Co3+] = 0.765 M, [Co2+] = 0.369 M, and [Cl-] = 0.486 M, and the pressure of Cl2 is PCl2 = 9.30 atm? Express your answer with the appropriate units.

Ecell = 0.500 V

Explanation:

For a chemical cell, the cell potential (Ecell) is:

Ecell = E° - (0.0592/n) * logQ (Nernst equation)

Where n is the number of electrons involved in the redox reaction, and Q is the reaction coefficient.

Let's see a half-reaction:

2Co³⁺ (aq) → 2Co²⁺ (aq)

The charge goes from + 6 (2*3) to + 4 (2*2), so n = 6 - 4 = 2 electrons.

The reaction coefficient is the multiplication of the concentration of the products elevated by their coefficients, divided by the multiplication of the concentration of the reactants elevated by their coefficients:

Q = ([Cl₂]*[Co⁺²]²) / ([Co⁺³]²*[Cl⁻]²)

The concentration of Cl₂ is the number of moles (n) divided by the volume (V), and can be calculated by the ideal gas law:

PV = nRT

n/V = P/RT (P is the pressure, R is the gas constant, and T is the temperature)

P = 9.30 atm, R = 0.082 atm. L/mol. K, T = 25°C + 273 = 298 K

n/V = [Cl₂] = 9.30 / (0.082*298)

[Cl₂] = 0.381 M

Q = [0.381 * (0.369) ²]/[ (0.765) ² * (0.486) ²]

Q = 0.051877/0.138228

Q = 0.3753

Ecell = 0.483 - (0.0592/2) * log (0.3753)

Ecell = 0.483 - 0.0296 * (-0.4256)

Ecell = 0.500 V