NEET Chemical Kinetics — Set 17

Question 1

A second-order reaction has a rate constant of $ 0.04 \, \text{L mol}^{-1} \text{s}^{-1} $ and an initial concentration of $ 0.2 \, \text{mol L}^{-1} $. What is the half-life?

Accepted Answer

For second-order, $ t_{1/2} = \frac{1}{k [\text{A}]_0} $. Given: $ k = 0.04 \, \text{L mol}^{-1} \text{s}^{-1} $, $ [\text{A}]_0 = 0.2 \, \text{mol L}^{-1} $. $ t_{1/2} = \frac{1}{0.04 \times 0.2} = \frac{1}{0.008} = 125 \, \text{s} $.

Question 2

A reaction has a rate constant with units $ \text{mol}^{-1} \text{L} \text{s}^{-1} $. What is the order of the reaction?

Accepted Answer

For a reaction of order $ n $, the unit of $ k $ is $ (\text{mol L}^{-1})^{1-n} \text{s}^{-1} $. Given unit: $ \text{mol}^{-1} \text{L} \text{s}^{-1} = (\text{mol L}^{-1})^{-1} \text{s}^{-1} $. $ 1 - n = -1 $, $ n = 2 $. Thus, the order is 2.

Question 3

A second-order reaction has a rate constant of $ 0.03 \, \text{L mol}^{-1} \text{s}^{-1} $ and an initial concentration of $ 0.25 \, \text{mol L}^{-1} $. What is the half-life?

Accepted Answer

For second-order, $ t_{1/2} = \frac{1}{k [\text{A}]_0} $. Given: $ k = 0.03 \, \text{L mol}^{-1} \text{s}^{-1} $, $ [\text{A}]_0 = 0.25 \, \text{mol L}^{-1} $. $ t_{1/2} = \frac{1}{0.03 \times 0.25} = \frac{1}{0.0075} \approx 133.33 \, \text{s} $.

NEET Chemistry: Chemical Kinetics — Practice Set 17

Q1. A second-order reaction has a rate constant of \( 0.04 \, \text{L mol}^{-1} \text{s}^{-1} \) and an initial concentration of \( 0.2 \, \text{mol L}^{-1} \). What is the half-life?

Q2. A reaction has a rate constant with units \( \text{mol}^{-1} \text{L} \text{s}^{-1} \). What is the order of the reaction?

Q3. A second-order reaction has a rate constant of \( 0.03 \, \text{L mol}^{-1} \text{s}^{-1} \) and an initial concentration of \( 0.25 \, \text{mol L}^{-1} \). What is the half-life?

Q4. For a first-order reaction, how many half-lives are required for 75% completion?

Q5. A first-order reaction has a rate constant of \( 0.0173 \, \text{min}^{-1} \). What is the time for 80% completion?

Q6. A reaction’s rate increases by 3 times when the temperature rises from 290 K to 300 K. What is the activation energy (\( R = 8.314 \, \text{J mol}^{-1} \text{K}^{-1} \))?

Q7. The rate of a reaction increases by 8 times when the concentration of the reactant is doubled. What is the order of the reaction?

Q8. The rate constant of a reaction is \( 3.0 \times 10^{-2} \, \text{min}^{-1} \) at 300 K. If the activation energy is 60 kJ/mol, what is the rate constant at 310 K (\( R = 8.314 \, \text{J mol}^{-1} \text{K}^{-1} \))?

Q9. The half-life of a second-order reaction is 25 s when the initial concentration is \( 0.4 \, \text{mol L}^{-1} \). What is the rate constant?

Q10. A second-order reaction has a rate constant of \( 0.04 \, \text{L mol}^{-1} \text{s}^{-1} \). If the initial concentration is \( 0.25 \, \text{mol L}^{-1} \), what is the half-life?