Step 1: Understanding the Concept:
The Nernst equation is a fundamental relationship in electrochemistry that relates the reduction potential of an electrochemical cell to the standard electrode potential, temperature, and the concentrations (activities) of the chemical species involved.
It allows us to predict the voltage of a cell under non-standard conditions.
Step 2: Key Formula or Approach:
The Nernst Equation is given by:
\[ E_{cell} = E^\circ_{cell} - \frac{2.303 RT}{nF} \log_{10} Q \]
Where:
\( E^\circ_{cell} \) = Standard cell potential.
\( Q \) = Reaction Quotient = \( \frac{[\text{Products}]}{[\text{Reactants}]} \).
\( n \) = Moles of electrons transferred.
\( F \) = Faraday's constant.
Step 3: Detailed Explanation:
Let's analyze the mathematical structure of the equation:
1. The expression for \( E_{cell} \) is a subtraction: \( E_{cell} = E^\circ_{cell} - (\text{constant} \times \log_{10} Q) \).
2. Effect of Concentration: If we increase the concentration of the product ions or decrease the concentration of the reactant ions, the value of the reaction quotient \( Q \) increases.
3. Logarithmic Scaling: Since \( Q \) is in the numerator of the log term, as \( Q \) increases, the value of \( \log_{10} Q \) also increases.
4. Resulting Cell Potential: Because this increasing logarithmic term is being subtracted from the standard potential, the resulting \( E_{cell} \) value will decrease.
5. Chemical Logic: This aligns with Le Chatelier's Principle. A higher concentration of products "opposes" the forward reaction that generates electrical current, thereby reducing the voltage. Conversely, high reactant concentrations "drive" the reaction and increase the voltage.
Step 4: Final Answer:
The relationship is logarithmic and inverse: as \( Q \) increases, \( E_{cell} \) decreases.
This is correctly stated in option (A).