Question

Consider the reaction Mg(s)+Fe2+(aq)→Mg2+(aq)+Fe(s) at 73 ∘C , where [Fe2+]= 3.70 M and [Mg2+]= 0.310 M .

What is the value for the reaction quotient, Q, for the cell?

What is the value for the temperature, T, in kelvins?

What is the value for n?

Calculate the standard cell potential for

Mg(s)+Fe2+(aq)→Mg2+(aq)+Fe(s)

Answer 1

Consider the reaction Mg(s)+Fe2+(aq)→Mg2+(aq)+Fe(s) at 73 ∘C , where [Fe2+]= 3.70 M and [Mg2+]= 0.310 M .

What is the value for the reaction quotient, Q, for the cell?

Q = [Mg2+]/[Fe2+]

Substitute values, Q = (0.310)/(3.70) = 0.08378

Q = 0.08378

What is the value for the temperature, T, in kelvins?

T = 73C = 73+273 = 346 K

What is the value for n?

n = 2 mole of e-, since Fe2+ goes from +2 to 0, n = 2

Calculate the standard cell potential for

Mg(s)+Fe2+(aq)→Mg2+(aq)+Fe(s)

Fe2+ + 2 e− ⇌ Fe(s) −0.44

Mg2+ + 2 e− ⇌ Mg(s) −2.372

Ecell = -0.44 - (-2.372) = 1.932 V

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

Ecell = 1.932 - 8.314*346/(2*96500) * ln (0.08378)

Ecell = 1.9689