Question

What is the calculated value of the cell potential at 298K for an electrochemical cell with the following reaction, when the Hg²⁺ concentration is 1.18 M and the Mn²⁺ concentration is 8.88×10^-4 M ?

Hg²⁺(aq) + Mn(s)------>Hg(l) + Mn²⁺(aq)

Answer: ___V

The cell reaction as written above is spontaneous for the concentrations given: _______(true)(false)

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°cell = Ecathode - Eanode = EHG - EMn

Mn2+ + 2 e− ⇌ Mn(s) −1.185

Hg2+ + 2 e− ⇌ Hg(l) +0.85

E°cell = 0.85 --1.185 = 2.035 V

Ecell = E° - (RT/nF) x lnQ

n = 2, F = 96500, R = 8.314 , T = 298L,

Q = [Mn+2] / [Hg+2] = (8.88*10^-4)/(1.18) = 0.000752

ln(Q) = ln(0.000752)= -7.1927

Ecell = 2.035 -8.314*298/(2*96500) * -7.1927

Ecell = 2.1273 V

this must be spontaneous as writte, since Ecell > 0