Question

During an electrochemistry lab session, a student uses the Nernst Equation to calculate the cell potential (\( E_{\text{cell}} \)) of a galvanic system at a non-standard temperature. Which parameter option accurately defines the scaling behavior of the cell potential relative to changes in the reaction quotient (\( Q \))?

• A. As the concentration of product ions increases relative to reactant ions (increasing \( Q \)), the value of \( E_{\text{cell}} \) decreases.
• B. The value of \( E_{\text{cell}} \) increases linearly with an increase in the value of \( Q \).
• C. The value of \( E_{\text{cell}} \) remains completely independent of any concentration shifts in \( Q \).
• D. An increase in \( Q \) causes an exponential jump in the net electrical voltage produced.

Hint:

To increase the cell potential of a galvanic cell:

• Keep reactant concentration high
• Keep product concentration low

This minimizes \(Q\) and increases \(E_{\text{cell}}\).

Answer 1

The Correct Option is A

Concept: The Nernst Equation relates the cell potential of an electrochemical cell to the concentrations of reactants and products. The equation is: \[ E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{2.303RT}{nF}\log Q \] where:

• \(E^\circ_{\text{cell}}\) = Standard cell potential
• \(R\) = Gas constant
• \(T\) = Temperature
• \(n\) = Number of electrons transferred
• \(F\) = Faraday constant
• \(Q\) = Reaction quotient

Step 1: Understand the role of the reaction quotient \(Q\).
The reaction quotient is given by: \[ Q = \frac{[\text{Products}]^p}{[\text{Reactants}]^r} \] Thus:

• Increase in product concentration \(\Rightarrow Q\) increases
• Increase in reactant concentration \(\Rightarrow Q\) decreases

Step 2: Analyze the effect of increasing \(Q\) on cell potential.
In the Nernst equation: \[ E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{2.303RT}{nF}\log Q \] the logarithmic term is subtracted from the standard cell potential. Therefore:

• If \(Q\) increases, then \(\log Q\) increases.
• A larger value is subtracted from \(E^\circ_{\text{cell}}\).
• Hence, \(E_{\text{cell}}\) decreases.

Thus, cell potential decreases as the concentration of products increases relative to reactants.

Step 3: Evaluate the options.

• [(A)] Correct — Increasing \(Q\) decreases the value of \(E_{\text{cell}}\).
• [(B)] Incorrect — \(E_{\text{cell}}\) does not increase linearly with \(Q\).
• [(C)] Incorrect — Cell potential depends directly on concentration changes through \(Q\).
• [(D)] Incorrect — The variation is logarithmic, not exponential.

Hence, the correct answer is: \[ \boxed{\text{(A)}} \]