Chemical Kinetics Chapter-Wise Test 13

Correct answer Carries: 4.

Wrong Answer Carries: -1.

For the reaction \( \text{A} + 2\text{B} \to 3\text{C} \), the rate of formation of C is \( 0.15 \, \text{mol L}^{-1} \text{s}^{-1} \). What is the rate of disappearance of B?

Rate = \( -\frac{1}{2} \frac{\Delta[\text{B}]}{\Delta t} = \frac{1}{3} \frac{\Delta[\text{C}]}{\Delta t} \).

Given: \( \frac{\Delta[\text{C}]}{\Delta t} = 0.15 \, \text{mol L}^{-1} \text{s}^{-1} \).

Rate = \( \frac{0.15}{3} = 0.05 \), \( -\frac{\Delta[\text{B}]}{\Delta t} = 2 \times 0.05 = 0.1 \, \text{mol L}^{-1} \text{s}^{-1} \).

0.1 mol L\(^{-1}\) s\(^{-1}\)
0.05 mol L\(^{-1}\) s\(^{-1}\)
0.15 mol L\(^{-1}\) s\(^{-1}\)
0.2 mol L\(^{-1}\) s\(^{-1}\)
1

A first-order gaseous reaction has an initial pressure of 2.4 atm. After 40 s, the total pressure is 3.0 atm. What is the rate constant?

For \( \text{A} \to \text{B} + \text{C} \), \( p_t = p_i + x \), \( x = 3.0 - 2.4 = 0.6 \, \text{atm} \).

\( p_A = p_i - x = 2.4 - 0.6 = 1.8 \, \text{atm} \).

\( k = \frac{2.303}{40} \log \frac{2.4}{1.8} = \frac{2.303 \times 0.125}{40} \approx 0.0072 \, \text{s}^{-1} \).

0.0058 s\(^{-1}\)
0.0096 s\(^{-1}\)
0.0072 s\(^{-1}\)
0.0115 s\(^{-1}\)
3

A first-order reaction has a rate constant of \( 0.0346 \, \text{min}^{-1} \). What is the half-life?

For first-order, \( t_{1/2} = \frac{0.693}{k} \).

Given: \( k = 0.0346 \, \text{min}^{-1} \).

\( t_{1/2} = \frac{0.693}{0.0346} \approx 20 \, \text{min} \).

15 min
20 min
25 min
30 min
2

A first-order reaction has an initial concentration of \( 0.5 \, \text{mol L}^{-1} \) and a rate constant of \( 0.0693 \, \text{min}^{-1} \). What is the concentration after 20 minutes?

For first-order, \( \log \frac{[\text{R}]_0}{[\text{R}]} = \frac{k t}{2.303} \).

\( \log \frac{0.5}{[\text{R}]} = \frac{0.0693 \times 20}{2.303} \approx 0.602 \), \( \frac{0.5}{[\text{R}]} = 10^{0.602} \approx 4 \).

\( [\text{R}] = \frac{0.5}{4} = 0.125 \, \text{mol L}^{-1} \).

0.25 mol L\(^{-1}\)
0.1 mol L\(^{-1}\)
0.125 mol L\(^{-1}\)
0.05 mol L\(^{-1}\)
3

The rate constant of a reaction increases from \( 2.0 \times 10^{-3} \, \text{s}^{-1} \) at 320 K to \( 8.0 \times 10^{-3} \, \text{s}^{-1} \) at 340 K. What is the activation energy (\( R = 8.314 \, \text{J mol}^{-1} \text{K}^{-1} \))?

\( \log \frac{k_2}{k_1} = \frac{E_a}{2.303 R} \left( \frac{T_2 - T_1}{T_1 T_2} \right) \).

\( \log \frac{8.0 \times 10^{-3}}{2.0 \times 10^{-3}} = \frac{E_a}{2.303 \times 8.314} \left( \frac{340 - 320}{320 \times 340} \right) \).

\( \log 4 = 0.602 \), \( E_a = \frac{0.602 \times 19.147 \times 108800}{20} \approx 62,700 \, \text{J mol}^{-1} \approx 62.7 \, \text{kJ mol}^{-1} \).

31.4 kJ mol\(^{-1}\)
47.1 kJ mol\(^{-1}\)
62.7 kJ mol\(^{-1}\)
78.4 kJ mol\(^{-1}\)
2

A reaction has the rate law \( \text{Rate} = k[\text{A}]^{1/3}[\text{B}]^{2/3} \). What is the overall order?

Overall order = \( \frac{1}{3} + \frac{2}{3} = \frac{3}{3} = 1 \).

1.5
2
0.5
1
4

The rate of a reaction is \( \text{Rate} = k[\text{A}]^{0.5}[\text{B}]^{0.5} \). What is the overall order?

Overall order = \( 0.5 + 0.5 = 1 \).

0.5
1.5
2
1
4

A second-order reaction has a rate constant of \( 0.03 \, \text{L mol}^{-1} \text{min}^{-1} \) and an initial concentration of \( 0.15 \, \text{mol L}^{-1} \). What is the half-life?

For second-order, \( t_{1/2} = \frac{1}{k [\text{A}]_0} \).

Given: \( k = 0.03 \, \text{L mol}^{-1} \text{min}^{-1} \), \( [\text{A}]_0 = 0.15 \, \text{mol L}^{-1} \).

\( t_{1/2} = \frac{1}{0.03 \times 0.15} = \frac{1}{0.0045} \approx 222.22 \, \text{min} \).

200 min
250 min
222.22 min
150 min
3

A second-order reaction has a rate constant of \( 0.06 \, \text{L mol}^{-1} \text{s}^{-1} \). If the initial concentration is \( 0.2 \, \text{mol L}^{-1} \), what is the time for 60% completion?

For second-order, \( \frac{1}{[\text{A}]} - \frac{1}{[\text{A}]_0} = kt \).

60% completion means \( [\text{A}] = 0.4 \times 0.2 = 0.08 \, \text{mol L}^{-1} \).

\( \frac{1}{0.08} - \frac{1}{0.2} = 0.06 \times t \), \( 12.5 - 5 = 0.06 t \), \( t = \frac{7.5}{0.06} = 125 \, \text{s} \).

100 s
150 s
83.3 s
125 s
4

A zero-order reaction has an initial concentration of \( 0.24 \, \text{mol L}^{-1} \) and a rate constant of \( 3.0 \times 10^{-3} \, \text{mol L}^{-1} \text{s}^{-1} \). What is the half-life?

For zero-order, \( t_{1/2} = \frac{[\text{R}]_0}{2k} \).

Given: \( [\text{R}]_0 = 0.24 \, \text{mol L}^{-1} \), \( k = 3.0 \times 10^{-3} \, \text{mol L}^{-1} \text{s}^{-1} \).

\( t_{1/2} = \frac{0.24}{2 \times 3.0 \times 10^{-3}} = \frac{0.24}{6.0 \times 10^{-3}} = 40 \, \text{s} \).

20 s
30 s
40 s
50 s
2

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