Electrochemistry Chapter-Wise Test 3

Correct answer Carries: 4.

Wrong Answer Carries: -1.

What is the standard Gibbs energy change for a cell with \( E^\circ_{cell} = 1.23 \, V \) and 2 electrons transferred? (F = 96500 C/mol)

\( \Delta_r G^\circ = -n F E^\circ_{cell} = -2 \times 96500 \times 1.23 = -237390 \, J/mol = -237.39 \, kJ/mol \).

-118.695 kJ/mol
-474.78 kJ/mol
-237.39 kJ/mol
-96.5 kJ/mol
3

The molar conductivity of NaCl at infinite dilution is 126.4 S cm\(^2\) mol\(^{-1}\). If \( \lambda^\circ_{Na^+} = 50.1 \, S \, cm^2 \, mol^{-1} \), what is \( \lambda^\circ_{Cl^-} \)?

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

\( 126.4 = 50.1 + \lambda^\circ_{Cl^-} \), \( \lambda^\circ_{Cl^-} = 76.3 \, S \, cm^2 \, mol^{-1} \).

76.3 S cm\(^2\) mol\(^{-1}\)
50.1 S cm\(^2\) mol\(^{-1}\)
126.4 S cm\(^2\) mol\(^{-1}\)
26.3 S cm\(^2\) mol\(^{-1}\)
1

In a dry cell, what acts as the cathode?

In a dry cell, the cathode is a graphite rod surrounded by MnO\(_2\).

Zn container
Graphite rod
NH\(_4\)Cl paste
MnO\(_2\) alone
2

In a mercury cell, if 0.68 g of Zn (atomic mass 68 g/mol) is oxidized at the anode, how many Faradays are involved?

\( Zn + 2OH^- \rightarrow ZnO + H_2O + 2e^- \). 1 mol Zn (68 g) requires 2F.

Moles = \( \frac{0.68}{68} = 0.01 \, mol \), Charge = \( 0.01 \times 2 = 0.02 \, F \).

0.01 F
0.04 F
0.02 F
0.005 F
3

The conductivity of a 0.05 M solution is 0.006 S cm\(^{-1}\). What is its molar conductivity?

\( \Lambda_m = \frac{\kappa \times 1000}{c} = \frac{0.006 \times 1000}{0.05} = 120 \, S \, cm^2 \, mol^{-1} \).

60 S cm\(^2\) mol\(^{-1}\)
240 S cm\(^2\) mol\(^{-1}\)
6 S cm\(^2\) mol\(^{-1}\)
120 S cm\(^2\) mol\(^{-1}\)
4

How many electrons are involved in the reduction of 1 mole of \( Cr_2O_7^{2-} \) to \( Cr^{3+} \) in acidic medium?

\( Cr_2O_7^{2-} + 14H^+ + 6e^- \rightarrow 2Cr^{3+} + 7H_2O \). 6 electrons per mole.

3
6
4
8
2

During electrolysis of aqueous NiSO\(_4\) with Ni electrodes, 0.59 g of Ni (atomic mass 59 g/mol) is deposited at the cathode. If the same charge oxidizes water at the anode, what volume of O\(_2\) (STP) is produced? (F = 96500 C/mol)

Cathode: \( Ni^{2+} + 2e^- \rightarrow Ni \). Moles = \( \frac{0.59}{59} = 0.01 \, mol \), Charge = \( 0.01 \times 2 \times 96500 = 1930 \, C \).

Anode: \( 2H_2O \rightarrow O_2 + 4H^+ + 4e^- \). 1 mol O\(_2\) (22.4 L) requires 4F.

Faradays = \( \frac{1930}{96500} = 0.02 \, F \), Moles O\(_2\) = \( \frac{0.02}{4} = 0.005 \, mol \), Volume = \( 0.005 \times 22.4 = 0.112 \, L \).

0.224 L
0.056 L
0.448 L
0.112 L
4

In the electrolysis of molten Al\(_2\)O\(_3\), what is the product at the anode?

Anode: \( 2O^{2-} \rightarrow O_2 + 4e^- \). Oxygen gas is produced.

Al
H\(_2\)
O\(_2\)
Al\(_2\)O\(_3\)
3

The limiting molar conductivity of MgSO\(_4\) is 266 S cm\(^2\) mol\(^{-1}\). If \( \lambda^\circ_{Mg^{2+}} = 106 \, S \, cm^2 \, mol^{-1} \), what is \( \lambda^\circ_{SO_4^{2-}} \)?

\( \Lambda_m^\circ = \lambda^\circ_{Mg^{2+}} + \lambda^\circ_{SO_4^{2-}} \).

\( 266 = 106 + \lambda^\circ_{SO_4^{2-}} \), \( \lambda^\circ_{SO_4^{2-}} = 160 \, S \, cm^2 \, mol^{-1} \).

106 S cm\(^2\) mol\(^{-1}\)
266 S cm\(^2\) mol\(^{-1}\)
160 S cm\(^2\) mol\(^{-1}\)
53 S cm\(^2\) mol\(^{-1}\)
3

A weak electrolyte has \( \Lambda_m^\circ = 400 \, S \, cm^2 \, mol^{-1} \) and \( \Lambda_m = 40 \, S \, cm^2 \, mol^{-1} \) at 0.1 M. What is the dissociation constant \( K_a \)?

\( \alpha = \frac{\Lambda_m}{\Lambda_m^\circ} = \frac{40}{400} = 0.1 \).

\( K_a = \frac{\alpha^2 c}{1 - \alpha} = \frac{0.1^2 \times 0.1}{1 - 0.1} = \frac{0.01 \times 0.1}{0.9} = 1.111 \times 10^{-3} \).

1.0 \times 10^{-2}
2.5 \times 10^{-4}
5.0 \times 10^{-3}
1.111 \times 10^{-3}
4

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