Electrochemistry Chapter-Wise Test 15

Correct answer Carries: 4.

Wrong Answer Carries: -1.

A cell has \( E^\circ_{cell} = 1.10 \, V \) and \( \Delta_r G^\circ = -424600 \, J/mol \) at 298 K. What is the number of electrons transferred? (F = 96500 C/mol)

\( \Delta_r G^\circ = -n F E^\circ_{cell} \), \( -424600 = -n \times 96500 \times 1.10 \).

\( n = \frac{424600}{96500 \times 1.10} = \frac{424600}{106150} \approx 4 \).

2
4
3
1
2

How many electrons are involved in the reduction of 1 mole of \( ClO_4^- \) to \( Cl^- \) in acidic medium?

\( ClO_4^- + 8H^+ + 8e^- \rightarrow Cl^- + 4H_2O \). 8 electrons per mole.

6
8
4
2
2

A hydrogen electrode operates at 298 K with \( P_{H_2} = 1.5 \, atm \) and \( [H^+] = 0.0001 \, M \). What is its potential? (Given: \( E^\circ_{H^+/H_2} = 0.00 \, V \))

\( E = E^\circ - \frac{0.059}{2} \log \frac{P_{H_2}}{[H^+]^2} \).

\( E = 0 - 0.0295 \log \frac{1.5}{10^{-8}} = 0 - 0.0295 \times 8.176 = -0.2412 \, V \).

0.00 V
-0.177 V
-0.118 V
-0.2412 V
4

In a fuel cell with H\(_2\) and O\(_2\), what is the cathode reaction?

Cathode: \( O_2(g) + 2H_2O(l) + 4e^- \rightarrow 4OH^-(aq) \).

\( 2H_2 + 4OH^- \rightarrow 4H_2O + 4e^- \)
\( 2H_2O \rightarrow O_2 + 4H^+ + 4e^- \)
\( H_2 + 2OH^- \rightarrow 2H_2O + 2e^- \)
\( O_2 + 2H_2O + 4e^- \rightarrow 4OH^- \)
4

The molar conductivity of RbCl at infinite dilution is 152.7 S cm\(^2\) mol\(^{-1}\). If \( \lambda^\circ_{Rb^+} = 77.8 \, S \, cm^2 \, mol^{-1} \), what is \( \lambda^\circ_{Cl^-} \)?

\( \Lambda_m^\circ = \lambda^\circ_{Rb^+} + \lambda^\circ_{Cl^-} \).

\( 152.7 = 77.8 + \lambda^\circ_{Cl^-} \), \( \lambda^\circ_{Cl^-} = 74.9 \, S \, cm^2 \, mol^{-1} \).

74.9 S cm\(^2\) mol\(^{-1}\)
152.7 S cm\(^2\) mol\(^{-1}\)
77.8 S cm\(^2\) mol\(^{-1}\)
38.9 S cm\(^2\) mol\(^{-1}\)
1

The degree of dissociation of a weak acid is 0.02, and its molar conductivity at infinite dilution is 400 S cm\(^2\) mol\(^{-1}\). What is its molar conductivity at that concentration?

\( \alpha = \frac{\Lambda_m}{\Lambda_m^\circ} \), \( 0.02 = \frac{\Lambda_m}{400} \), \( \Lambda_m = 8 \, S \, cm^2 \, mol^{-1} \).

400 S cm\(^2\) mol\(^{-1}\)
80 S cm\(^2\) mol\(^{-1}\)
20 S cm\(^2\) mol\(^{-1}\)
8 S cm\(^2\) mol\(^{-1}\)
4

A weak acid has \( \Lambda_m^\circ = 380 \, S \, cm^2 \, mol^{-1} \) and \( \Lambda_m = 19 \, S \, cm^2 \, mol^{-1} \) at 0.02 M. What is the dissociation constant \( K_a \)?

\( \alpha = \frac{\Lambda_m}{\Lambda_m^\circ} = \frac{19}{380} = 0.05 \).

\( K_a = \frac{\alpha^2 c}{1 - \alpha} = \frac{0.05^2 \times 0.02}{1 - 0.05} = \frac{0.0025 \times 0.02}{0.95} = 5.263 \times 10^{-5} \).

1.0 \times 10^{-4}
2.5 \times 10^{-3}
1.25 \times 10^{-5}
5.263 \times 10^{-5}
4

What is the emf of the cell \( Cr(s) | Cr^{3+}(0.001 \, M) || Cu^{2+}(0.01 \, M) | Cu(s) \) at 298 K? (Given: \( E^\circ_{Cr^{3+}/Cr} = -0.74 \, V \), \( E^\circ_{Cu^{2+}/Cu} = 0.34 \, V \))

\( E^\circ_{cell} = 0.34 - (-0.74) = 1.08 \, V \).

\( E_{cell} = 1.08 - \frac{0.059}{6} \log \frac{(0.001)^2}{0.01} = 1.08 - 0.01967 = 1.06033 \, V \).

1.08 V
1.10 V
1.06033 V
1.02 V
3

The standard emf of a cell is 0.96 V, and its equilibrium constant at 298 K is \( 10^{32} \). How many electrons are transferred in the cell reaction?

\( E^\circ_{cell} = \frac{0.059}{n} \log K_c \), \( 0.96 = \frac{0.059}{n} \times 32 \), \( n = \frac{1.888}{0.96} \approx 2 \).

2
3
1
4
1

The dissociation constant of acetic acid is 1.78 × 10\(^{-5}\) mol L\(^{-1}\) at 0.001 M concentration with molar conductivity 48.15 S cm\(^2\) mol\(^{-1}\). What is its \( \Lambda_m^\circ \)?

\( \alpha = \sqrt{\frac{K_a}{c}} = \sqrt{\frac{1.78 \times 10^{-5}}{0.001}} = 0.133 \).

\( \alpha = \frac{\Lambda_m}{\Lambda_m^\circ} \), \( 0.133 = \frac{48.15}{\Lambda_m^\circ} \), \( \Lambda_m^\circ = 390.5 \, S \, cm^2 \, mol^{-1} \).

48.15 S cm\(^2\) mol\(^{-1}\)
200 S cm\(^2\) mol\(^{-1}\)
300 S cm\(^2\) mol\(^{-1}\)
390.5 S cm\(^2\) mol\(^{-1}\)
4

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