Question

calculate the Electromotive Force (E) at 298 K for

Zn(s) + Sn4+(aq) <-> Zn2+(aq) + Sn2+(aq)

If

[Sn4+] = 0.21

[Zn2+] = 0.44

[Sn2+] = 0.21

Assume that γ±γ± = 0.82 for all species. Give your answer in volts to three decimal places (X.XXX).

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

Sn4+ + 2 e− ⇌ Sn2+ +0.15

Zn2+ + 2 e− ⇌ Zn(s) −0.7618

E° = Ered - Eox = 0.15--0.7618 = 0.9118 V

Q = γ[Sn+2]γ [ Zn+2 ]/γ[Sn+4]

Q = 0.82*[Sn+2] [ Zn+2 ]/[Sn+4] = 0.82*0.21 * 0.44 / 0.21 = 0.3608

Ecell = E° - (RT/nF) x lnQ

Ecell = 0.9118 - (8.314*298)/(2*96500) * ln(0.3608)

Ecell = 0.924886V