Question

Calculate the EMF of a cell using the Nernst Equation.

Hint:

At 298 K, use $E = E^\circ - \frac{0.0591}{n} \log Q$ to quickly calculate EMF under non-standard conditions.

Answer 1

Concept: The Nernst Equation is used to calculate the EMF (electromotive force) of an electrochemical cell under non-standard conditions by considering ion concentrations or partial pressures.
Step 1: General form of Nernst Equation. At temperature $T$ (in Kelvin): \[ E = E^\circ - \frac{RT}{nF} \ln Q \] where $E$ = cell EMF, $E^\circ$ = standard EMF, $R$ = gas constant, $T$ = temperature, $n$ = number of electrons transferred, $F$ = Faraday constant, $Q$ = reaction quotient.
Step 2: At 298 K (room temperature). The equation simplifies to: \[ E = E^\circ - \frac{0.0591}{n} \log Q \]
Step 3: Steps to calculate EMF.

• Write the balanced cell reaction
• Determine $E^\circ$ using standard electrode potentials
• Calculate reaction quotient $Q$ using concentrations or pressures
• Substitute values into the Nernst equation

Step 4: Illustrative example. For the cell: \[ \text{Zn}|\text{Zn}^{2+} (0.01\,M) || \text{Cu}^{2+} (1\,M)|\text{Cu} \] Given $E^\circ = 1.10\,V$ and $n=2$: \[ Q = \frac{[\text{Zn}^{2+}]}{[\text{Cu}^{2+}]} = \frac{0.01}{1} = 0.01 \] \[ E = 1.10 - \frac{0.0591}{2} \log(0.01) \] \[ E = 1.10 - \frac{0.0591}{2} (-2) = 1.10 + 0.0591 = 1.1591\,V \]
Conclusion: The Nernst Equation helps calculate cell EMF under non-standard conditions by incorporating concentration or pressure effects.