Question

Using the Nernst equation, calculate the cell potential (\( E_{\text{cell}} \)) under non-standard conditions. The Nernst equation is given as: \[ E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{0.0591}{n} \log k \]

• A. \( E_{\text{cell}} = 1.10 \, \text{V} \)
• B. \( E_{\text{cell}} = 1.00 \, \text{V} \)
• C. \( E_{\text{cell}} = 1.01 \, \text{V} \)
• D. \( E_{\text{cell}} = 0.90 \, \text{V} \)

Hint:

When using the Nernst equation, remember that it allows us to calculate the cell potential at any concentration, not just under standard conditions. Always ensure that the units of the equilibrium constant (\( k \)) are consistent with the equation.

Answer 1

The Correct Option is C

The Nernst equation is a key equation used to calculate the cell potential when the reaction is not under standard conditions. The equation relates the potential of an electrochemical cell to the concentration of reactants and products in the reaction. Given: - \( E^\circ_{\text{cell}} = 1.10 \, \text{V} \) (standard cell potential),
- \( n = 2 \) (number of moles of electrons transferred),
- \( k = 10^3 \) (equilibrium constant). Now, substitute these values into the Nernst equation: \[ E_{\text{cell}} = 1.10 - \frac{0.0591}{2} \log(10^3) \] \[ E_{\text{cell}} = 1.10 - \frac{0.0591}{2} \times 3 \] \[ E_{\text{cell}} = 1.10 - 0.08865 \] \[ E_{\text{cell}} = 1.01135 \, \text{V} \] Thus, the correct answer is \( E_{\text{cell}} = 1.01 \, \text{V} \).