The emf of cell $$\mathrm{Tl}\left|\underset{(0.001 \mathrm{M})}{\mathrm{Tl}^{+}}\right| \underset{(0.01 \mathrm{M})}{\mathrm{Cu}^{2+}} \mid \mathrm{Cu}$$ is $0.83 \mathrm{~V}$ at $298 \mathrm{~K}$. It could be increased by :

<p>To determine how the emf of the cell, $$\mathrm{Tl}\left|\underset{(0.001 \mathrm{M})}{\mathrm{Tl}^{+}}\right| \underset{(0.01 \mathrm{M})}{\mathrm{Cu}^{2+}} \mid \mathrm{Cu}$$, can be increased, we can use the Nernst equation. The Nernst equation for this electrochemical cell is given by:</p> <p>$$ E_{\text{cell}} = E_{\text{cell}}^\circ - \frac{0.0591}{n} \log \left( \frac{[\mathrm{Tl}^{+}]}{[\mathrm{Cu}^{2+}]} \right) $$</p> <p>where:</p> <ul> <li>$E_{\text{cell}}$ is the emf of the cell.</li> <li>$E_{\text{cell}}^\circ$ is the standard emf of the cell.</li> <li>$n$ is the number of moles of electrons transferred in the cell reaction; here, $n = 2$.</li> <li>$[\mathrm{Tl}^{+}]$ is the concentration of thallium ions.</li> <li>$[\mathrm{Cu}^{2+}]$ is the concentration of copper ions.</li> </ul> <p>Given that the emf of the cell can be expressed in terms of the concentration of the ions involved, we can see that increasing the concentration of $[\mathrm{Cu}^{2+}]$ or decreasing the concentration of $[\mathrm{Tl}^{+}]$ will affect the logarithmic term in the Nernst equation:</p> <p>$$ E_{\text{cell}} = E_{\text{cell}}^\circ - \frac{0.0591}{2} \log \left( \frac{0.001}{0.01} \right) $$</p> <p>To increase the emf ($E_{\text{cell}}$) of the cell, it is beneficial to have a less negative (or more positive) correction term. This can be achieved by:</p> <ul> <li><strong>Increasing the concentration of $[\mathrm{Cu}^{2+}]$ ions:</strong> This makes the term inside the logarithm smaller (since we are dividing by a larger number), which in turn makes the logarithmic term less negative.</li> </ul> <p>Therefore, the correct answer is:</p> <p><strong>Option B: increasing concentration of $\mathrm{Cu}^{2+}$ ions</strong></p>