AIPMT PRELIMS 2004 Chemistry Nernst Equation MCQ Question

To find the equilibrium constant $K$ for the given galvanic cell reaction, we can use the relationship between the standard electromotive force (e.m.f.) of the cell, the number of moles of electrons transferred $n$, and the equilibrium constant.

Formula Used

The relationship is described by the Nernst equation in its standard form:

$$E^\circ = \frac{RT}{nF} \ln K$$

Where:

• $E^\circ$ is the standard e.m.f. of the cell (in volts).
• $R$ is the universal gas constant ($8.314 \, \text{J K}^{-1} \text{mol}^{-1}$).
• $T$ is the temperature in Kelvin (25°C = 298 K).
• $n$ is the number of moles of electrons transferred (given as $n = 2$).
• $F$ is the Faraday constant ($96500 \, \text{C mol}^{-1}$).
• $K$ is the equilibrium constant.

Step-by-Step Calculation

1. Convert Temperature to Kelvin:

   $$T = 25 + 273 = 298 \, \text{K}$$

2. Substitute the Values into the Formula:

   Rearranging the Nernst equation to solve for $K$:

   $$K = e^{\frac{nFE^\circ}{RT}}$$

   Substituting the values we have:

   • $E^\circ = 0.295 \, \text{V}$
   • $n = 2$
   • $R = 8.314 \, \text{J K}^{-1} \text{mol}^{-1}$
   • $F = 96500 \, \text{C mol}^{-1}$
   • $T = 298 \, \text{K}$

   Now, calculating $\frac{nFE^\circ}{RT}$:

   $$\frac{nFE^\circ}{RT} = \frac{(2)(96500)(0.295)}{(8.314)(298)}$$

   Simplifying the numerator and the denominator:

   • Numerator: $2 \times 96500 \times 0.295 = 57079.5$
   • Denominator: $8.314 \times 298 = 2477.572$

   Therefore,

   $$\frac{57079.5}{2477.572} \approx 23.065$$

3. Calculate $K$:

   Now, we find $K$:

   $$K = e^{23.065}$$

   Using a calculator:

   $$K \approx 9.76 \times 10^{10}$$

Conclusion

The equilibrium constant $K$ is approximately $9.76 \times 10^{10}$. Thus, when rounded appropriately, we can select the closest option, which is C) $0 \times 10^{10}$.

Explanation of Other Options

• Option A (0 × 10¹²): This option represents a much larger equilibrium constant than calculated and is incorrect.
• Option B (0 × 10²): This is too small and does not reflect the calculated value.
• Option D (0 × 10¹¹): Also does not represent the correct magnitude of the equilibrium constant.

Thus, Option C is correct as it accurately represents the calculated equilibrium constant rounded to the appropriate scientific notation.