Question

Calculate the cell voltage for the following reaction at 25^o C:

                 

                  2 Cr³⁺ (aqueous; 0.010 M) + H₂ (gas at 1 atm)

                                    è 2 Cr²⁺ (aqueous; 0.050 M) + 2H⁺ (aqueous; pH = 2.50)

The E^o for the reaction Cr³⁺ (aq) + e^- ==è Cr²⁺ (aq) is - 0.40 V vs. the standard hydrogen half-cell.

Answer 1

When the cell is NOT under standard conditions, i.e. 1M of each reactants at T = 25°C and P = 1 atm; then we must use Nernst Equation.

The equation relates E°cell, number of electrons transferred, charge of 1 mol of electron to Faraday and finally, the Quotient retio between products/reactants

The Nernst Equation:

Ecell = E0cell - (RT/nF) x lnQ

In which:

Ecell = non-standard value

E° or E0cell or E°cell or EMF = Standard EMF: standard cell potential
R is the gas constant (8.3145 J/mol-K)
T is the absolute temperature = 298 K
n is the number of moles of electrons transferred by the cell's reaction
F is Faraday's constant = 96485.337 C/mol or typically 96500 C/mol
Q is the reaction quotient, where

Q = [C]^c * [D]^d / [A]^a*[B]^b

pure solids and pure liquids are not included. Also note that if we use partial pressure (for gases)

Q = P-A^a / (P-B)^b

substitute in Nernst Equation:

Ecell = E° - (RT/nF) x lnQ

E° = 0--0.40 = 0.40 V

n = 2e,

Q = [Cr+2][H+]^2 /([Cr+3]^2 * P-H2)

Q = (0.05)(10^-2.5)^2 / ((0.01*1)) = 0.00005

E = 0.40 - 8.314*298/(2*96500) * ln(0.00005)

E = 0.5271 V