Nernst Equation Chemistry Tutorial - AUS-e-TUTE

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Nernst Equation Chemistry Tutorial

Key Concepts

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

  E = Eo -(RT/nF)lnQ

  Eo = 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 = Eo -(0.0592/n)log10Q

  Eo = 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:

  Eo = (0.0592/n)log10K

  Eo = 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 = Eo -0.0592/n × log10Q
2. Calculate Eo 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 = Eo -0.0592/n × log10([Sn2+]/[Ag+]2)
5. Substitute the values: Eo = +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 > Eo, and positive, so the cell reaction has a greater tendency to take place at these concentrations.

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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 = Eo -(0.0592/n)log10Q

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

   Eo = (0.0592/n)log10K

3. Calculate Eo for the equation (as above) = +0.94 V
4. Calculate n (moles of electrons transferred) = 2
5. Substitute values for Eo 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 = 1031.76 = 5.71 × 1031

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

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