Electrochemistry · JEE Advanced previous year questions

In an electrochemical cell, dichromate ions in aqueous acidic medium are reduced to $\mathrm{C}{\mathrm{r}}^{3+}$. The current (in amperes) that flows through the cell for 48.25 minutes to produce 1 mole of $\mathrm{C}{\mathrm{r}}^{3+}$ is ____. $\text{Use:}$ 1 Faraday = $96500\mathrm{C}\mathrm{mo}{\mathrm{l}}^{-1}$

An electrochemical cell is fueled by the combustion of butane at $1\text{ bar}$ and $298\text{ K}$. Its cell potential is $\frac{\mathbf{X}}{F}\times 10^3\text{ volts}$, where $F$ is the Faraday constant. The value of $\mathbf{X}$ is _________. $\text{Use:}$ Standard Gibbs energies of formation at $298\text{ K}$ are: ${\Delta }_f{G}_{{\mathrm{CO}}_2}^{\circ }=-394{\text{ kJ mol}}^{-1}$; ${\Delta }_f{G}_{\text{water}}^{\circ }=-237{\text{ kJ mol}}^{-1}$; ${\Delta }_f{G}_{\text{butane}}^{\circ }=-18{\text{ kJ mol}}^{-1}$

1. A.P-4, Q-3, R-2, S-5
2. B.P-2, Q-4, R-3, S-1
3. C.P-3, Q-4, R-2, S-5
4. D.P-4, Q-3, R-2, S-1

An aqueous solution of hydrazine (${\mathrm{N}}_2{\mathrm{H}}_4$) is electrochemically oxidized by ${\mathrm{O}}_2$, thereby releasing chemical energy in the form of electrical energy. One of the products generated from the electrochemical reaction is ${\mathrm{N}}_2(\mathrm{g})$. Choose the correct statement(s) about the above process

1. A.$\mathrm{O}{\mathrm{H}}^{-}$ ions react with ${\mathrm{N}}_2{\mathrm{H}}_4$ at the anode to form ${\mathrm{N}}_2(\mathrm{g})$ and water, releasing 4 electrons to the anode.
2. B.At the cathode, ${\mathrm{N}}_2{\mathrm{H}}_4$ breaks to ${\mathrm{N}}_2(\mathrm{g})$ and nascent hydrogen released at the electrode reacts with oxygen to form water.
3. C.At the cathode, molecular oxygen gets converted to $\mathrm{O}{\mathrm{H}}^{-}$.
4. D.Oxides of nitrogen are major by-products of the electrochemical process.

Plotting $1/{\Lambda }_{\mathrm{m}}$ against $c{\Lambda }_{\mathrm{m}}$ for aqueous solutions of a monobasic weak acid ($\mathrm{HX}$) resulted in a straight line with y-axis intercept of P and slope of S. The ratio P/S is $[{\Lambda }_{\mathrm{m}}=\text{molar conductivity}$ ${\Lambda }_{\mathrm{m}}^{\circ }=\text{limiting molar conductivity}$ $c=\text{molar concentration}$ $K_{\mathrm{a}}=\text{dissociation constant of HX}]$

1. A.$K_{\mathrm{a}}{\Lambda }_{\mathrm{m}}^{\circ }$
2. B.$K_{\mathrm{a}}{\Lambda }_{\mathrm{m}}^{\circ }/2$
3. C.$2K_{\mathrm{a}}{\Lambda }_{\mathrm{m}}^{\circ }$
4. D.$1/(K_{\mathrm{a}}{\Lambda }_{\mathrm{m}}^{\circ })$

1. A.$\mathbf{P}$ is a primary alcohol with four carbons.
2. B.$\mathbf{Q}$ undergoes Kolbe's electrolysis to give an eight-carbon product.
3. C.$\mathbf{R}$ has six carbons and it undergoes Cannizzaro reaction.
4. D.$\mathbf{S}$ is a primary amine with six carbons.