Question

The emf of cell Tl$\vert^{Tl^+}_{_{(0.001M)}}\vert^{Cu^{2+}}_{_{(0.01M)}}$Cu is 0.83 V at 298 K. It could be increased by:

• A. increasing concentration of Tl$^+$ ions
• B. increasing concentration of both Tl$^+$ and Cu$^{2+}$ ions
• C. decreasing concentration of both Tl$^+$ and Cu$^{2+}$ ions
• D. increasing concentration of Cu$^{2+}$ ions

Answer 1

The Correct Option is D

The given problem involves a galvanic cell with a specified cell notation: Tl$\vert^{Tl^+}_{_{(0.001M)}}\vert^{Cu^{2+}}_{_{(0.01M)}}$Cu. We are tasked with determining how the emf (electromotive force) of this cell could be increased. The correct answer is increasing the concentration of Cu$^{2+}$ ions.

Let's analyze why this choice is correct using the Nernst Equation, which describes how the emf of a cell changes with concentration. The general form of the Nernst Equation for a cell reaction is:

\(E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{RT}{nF} \ln Q\)

Where:

• \(E_{\text{cell}}\) = emf of the cell
• \(E^\circ_{\text{cell}}\) = standard emf of the cell
• \(R\) = universal gas constant (8.314 J/mol K)
• \(T\) = temperature in Kelvin (298 K in this case)
• \(n\) = number of moles of electrons exchanged
• \(F\) = Faraday's constant (96485 C/mol)
• \(Q\) = reaction quotient

For the cell reaction: 
\(\text{Tl}^+ + \text{Cu} \rightarrow \text{Tl} + \text{Cu}^{2+}\)

The reaction quotient \(Q\) can be expressed as:

\(Q = \frac{[\text{Tl}^+]}{[\text{Cu}^{2+}]}\)

To increase the emf of the cell (\(E_{\text{cell}}\)), we need to reduce the value of \(Q\). This can be done by increasing the concentration of the denominator (Cu$^{2+}$ ions) since \(Q\) is inversely proportional to the concentration of Cu$^{2+}$.

Now, let's rule out the other options:

• Increasing the concentration of Tl$^+$ ions: This would increase \(Q\), thereby decreasing the emf.
• Increasing concentration of both Tl$^+$ and Cu$^{2+}$ ions: The increase in Tl$^+$ would likely offset the increase in Cu$^{2+}$, not necessarily increasing the emf.
• Decreasing concentration of both Tl$^+$ and Cu$^{2+}$ ions: This would increase \(Q\) due to a reduction in the denominator, potentially decreasing the emf.

Thus, the correct choice is increasing the concentration of Cu$^{2+}$ ions to increase the cell's emf.

Answer 2

The emf of the cell is given by the Nernst equation:
\[ E = E^\circ - \frac{0.0591}{n} \log \frac{\text{[Products]}}{\text{[Reactants]}}. \]
For the cell:
\[ \text{Tl|Tl}^+ \, || \, \text{Cu}^{2+}| \text{Cu}, \]
the cell reaction is:
\[ \text{Tl} + \text{Cu}^{2+} \rightarrow \text{Tl}^+ + \text{Cu}. \]
Effect of concentration: Increasing the concentration of Cu$^{2+}$ ions (product-side reactant) decreases the denominator in the reaction quotient, shifting the reaction to the right and increasing the emf.
Increasing the concentration of Tl$^+$ ions (reactant-side product) increases the numerator in the reaction quotient, decreasing the emf.
Decreasing concentrations of both ions would reduce the driving force of the reaction, lowering the emf.
Thus, the emf can be increased by: [Increasing the concentration of Cu$^{2+}$ ions (Option 4).]