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 6.28×10^-4 M and the Al³⁺ concentration is 1.43 M ?

3Hg²⁺(aq) + 2Al(s)------>3Hg(l) + 2Al³⁺(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 = Ered - Eox = EHg - EAl

Hg2+ + 2 e− ⇌ Hg(l) +0.85; Al3+ + 3 e− ⇌ Al(s) −1.662

E°cell = 0.85 - -1.662 = 2.512 V

n = 2*3 = 6 e-,

Q = [Al+3]^2 /[Hg+2]^3 = (1.43)^3/ ((6.28*10^-4)^2) = 7414618.74

Ecell = E° - (RT/nF) x lnQ

Ecell = 2.512 - (8.314*298/(6*96500))*ln(7414618.74)

Ecell = 2.44 V

this is spontaneous, since Ecell > 0