For a cell reaction involving a two-electron change, the standard EMF of the cell is found to be 0.2 — Electrochemistry Chemistry Question

💡 Solution & Explanation

Step 1 - Understand the Relationship between Standard EMF ($E^\circ_{\text{cell}}$) and the Equilibrium Constant ($K_c$) For any electrochemical cell, when the cell reaction reaches a state of dynamic chemical equilibrium, the actual cell potential ($E_{\text{cell}}$) becomes zero ($E_{\text{cell}} = 0\text{ V}$). Consider a general redox equilibrium involving the transfer of $n$ electrons: $$\ce{A_{ox} + n e^- <=> A_{red}}$$ At chemical equilibrium, the Nernst equation simplifies to relate the standard electromotive force ($E^\circ_{\text{cell}}$) directly with the equilibrium constant ($K_c$): $$E^\circ_{\text{cell}} = \frac{2.303 RT}{nF} \log_{10} K_c$$ At the standard temperature of $25^\circ\text{C}$ ($298.15\text{ K}$), the term $\frac{2.303 RT}{F}$ is constant and is given as: $$\frac{2.303 RT}{F} \approx 0.0591\text{ V}$$ Thus, the practical formula at $25^\circ\text{C}$ is: $$E^\circ_{\text{cell}} = \frac{0.0591\text{ V}}{n} \log_{10} K_c$$ Step 2 - Identify Given Parameters and Rearrange the Formula We are given the following values: * Number of electrons transferred ($n$) = $2$ * Standard electromotive force ($E^\circ_{\text{cell}}$) = $0.295\text{ V}$ * Temperature ($T$) = $25^\circ\text{C}$ To find the equilibrium constant ($K_c$), we first rearrange the formula to isolate $\log_{10} K_c$: $$\log_{10} K_c = \frac{n \times E^\circ_{\text{cell}}}{0.0591\text{ V}}$$ Step 3 - Substitute Values and Calculate $\log_{10} K_c$ Now, substitute the given values with units into our rearranged formula: $$\log_{10} K_c = \frac{2 \times 0.295\text{ V}}{0.0591\text{ V}}$$ $$\log_{10} K_c = \frac{0.590\text{ V}}{0.0591\text{ V}}$$ $$\log_{10} K_c \approx 9.983 \approx 10$$ Step 4 - Calculate the Equilibrium Constant ($K_c$) To determine $K_c$, we take the base-10 antilogarithm of both sides of the equation: $$K_c = 10^{10} = \boxed{1 \times 10^{10}}$$ Step 5 - Evaluate and Explain the Options * **Option (A) is correct:** As shown by the calculation, $K_c = 1 \times 10^{10}$. * **Option (B) is incorrect:** This value ($1 \times 10^{-10}$) represents a highly non-spontaneous cell reaction, which would correspond to a negative standard potential of $-0.295\text{ V}$. * **Option (C) is incorrect:** This value ($29.5 \times 10^{-2} = 0.295$) is a mathematical error where the numerical value of the standard EMF ($E^\circ_{\text{cell}}$) is mistakenly written as the equilibrium constant. * **Option (D) is incorrect:** This value ($2 \times 10^{10}$) corresponds to a standard cell potential of approximately $0.304\text{ V}$, which does not match our given $0.295\text{ V}$. $$\text{Correct Option: } \boxed{\text{A}}$$