Nernst Equation Chemistry Tutorial

Key Concepts

• The Nernst Equation allows us to calculate the voltage produced by any electrochemical cell given E^o values for its electrodes and the concentrations of reactants and products.
• The general Nernst Equation:

  E = E^o -(RT/nF)lnQ

  E^o = standard electrochemical cell potential (voltage)
  R = ideal gas constant
  T = temperature
  n = moles of electrons
  F = Faraday constant = 96,485 C mol^-1
  Q = mass-action expression (approximated by the equilibrium expression)

• At 25°C the Nernst Equation is simplified to:

  E = E^o -(0.0592/n)log₁₀Q

  E^o = standard electrochemical cell potential (voltage)
  n = moles of electrons
  Q = mass-action expression (approximated by the equilibrium expression)

• For a system at equilibrium at 25°C, E = 0 and the Nernst Equation is simplified to:

  E^o = (0.0592/n)log₁₀K

  
  E^o = standard electrochemical cell potential (voltage)
  n = moles of electrons
  K = equilibrium expression

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Worked Example of E Calculation

Question:

Calculate the voltage produced by the cell Sn_(s)|Sn²⁺||Ag⁺|Ag_(s) at 25°C given:
[Sn²⁺] = 0.15 mol L^-1
[Ag⁺] = 1.7 mol L^-1

Solution:

1. Write the Nernst Equation for 25°C:
   E = E^o -0.0592/n × log₁₀Q
2. Calculate E^o for the cell:
   

   anode:	Sn(s)	→	Sn2+ + 2e	Eo = +0.14 V
   cathode:	2 × [e- + Ag+	→	Ag(s)]	Eo = +0.80 V
   cell:	Sn(s) + 2Ag+	→	Sn2+ + 2Ag(s)	Eo = +0.94 V

3. Wite the expression for Q:
   Q = [Sn²⁺]/[Ag⁺]²
   (concentrations of solids is constant and incorporated in the value of Q)
4. Write the Nernst Equation for this example:
   E = E^o -0.0592/n × log₁₀([Sn²⁺]/[Ag⁺]²)
5. Substitute the values:
   E^o = +0.94 V
   n = 2 (2 moles of electrons transferred during the redox reaction)
   [Sn²⁺] = 0.15 mol L^-1
   [Ag⁺] = 1.7 mol L^-1

   E = +0.94 -0.0592/2 × log([0.15]/[1.7]²)

6. Calculate Q:
   E = +0.94 -0.0592/2 × log₁₀[0.0519]
7. Calculate logQ:
   E = +0.94 -0.0592/2 × -1.285
8. Calculate E:
   E = +0.94 -0.0592/2 × -1.285
   E = +0.98 V

Note: E > E^o, and positive, so the cell reaction has a greater tendency to take place at these concentrations.

Worked Example of K Calculation

Question:

Calculate the equilibrium constant, K, for the reaction Sn_(s)|Sn²⁺||Ag⁺|Ag_(s) at 25°C.

Solution:

1. Write the Nernst Equation:

   E = E^o -(0.0592/n)log₁₀Q

2. Write the Nernst Equation for the equilibrium expression:
   At equilibrium Q = K and E = 0

   E^o = (0.0592/n)log₁₀K

3. Calculate E^o for the equation (as above) = +0.94 V
4. Calculate n (moles of electrons transferred) = 2
5. Substitute values for E^o and n into the equation:
   +0.94 = (0.0592/2)log₁₀K
6. Calculate log₁₀K:
   +0.94 = 0.0296log₁₀K
   log₁₀K = 31.76
7. Calculate K:
   K = 10^31.76 = 5.71 × 10³¹

Note: K is very large so the forward reaction is favoured and the equilibrium position lies very far to the right.