NEET Chemical Kinetics — Set 11

Question 1

A first-order reaction has a half-life of 20 minutes. How long will it take for 87.5% of the reactant to decompose?

Accepted Answer

87.5% decomposition means 12.5% remains, $ \frac{[\text{R}]}{[\text{R}]_0} = 0.125 = \left( \frac{1}{2} \right)^3 $. Number of half-lives = 3, $ t = 3 \times t_{1/2} = 3 \times 20 = 60 \, \text{min} $.

Question 2

A reaction follows second-order kinetics with a rate constant of $ 0.02 \, \text{L mol}^{-1} \text{s}^{-1} $. If the initial concentration is $ 0.5 \, \text{mol L}^{-1} $, what is the half-life?

Accepted Answer

For a second-order reaction, $ t_{1/2} = \frac{1}{k [\text{A}]_0} $. Given: $ k = 0.02 \, \text{L mol}^{-1} \text{s}^{-1} $, $ [\text{A}]_0 = 0.5 \, \text{mol L}^{-1} $. $ t_{1/2} = \frac{1}{0.02 \times 0.5} = \frac{1}{0.01} = 100 \, \text{s} $.

Question 3

For a reaction, the initial rate doubles when the concentration of the reactant is quadrupled. What is the order of the reaction?

Accepted Answer

Rate = $ k [\text{A}]^n $. Initial rate: $ r_1 = k [\text{A}]^n $. New rate: $ r_2 = k (4[\text{A}])^n = 2 r_1 $, so $ 4^n = 2 $. $ n \log 4 = \log 2 $, $ n \times 0.602 = 0.301 $, $ n = 0.5 $.

NEET Chemistry: Chemical Kinetics — Practice Set 11

Q1. A first-order reaction has a half-life of 20 minutes. How long will it take for 87.5% of the reactant to decompose?

Q2. A reaction follows second-order kinetics with a rate constant of \( 0.02 \, \text{L mol}^{-1} \text{s}^{-1} \). If the initial concentration is \( 0.5 \, \text{mol L}^{-1} \), what is the half-life?

Q3. For a reaction, the initial rate doubles when the concentration of the reactant is quadrupled. What is the order of the reaction?

Q4. A reaction has the rate law \( \text{Rate} = k[\text{A}][\text{B}] \). If the concentration of A is tripled and B is halved, what happens to the rate?

Q5. A first-order reaction has a half-life of 15 minutes. What percentage of the reactant decomposes in 45 minutes?

Q6. A reaction has a rate constant of \( 1.5 \times 10^{-2} \, \text{s}^{-1} \). What is its order if the unit of the rate constant is \( \text{s}^{-1} \)?

Q7. A second-order reaction has a rate constant of \( 0.02 \, \text{L mol}^{-1} \text{s}^{-1} \) and an initial concentration of \( 0.25 \, \text{mol L}^{-1} \). What is the time for 80% completion?

Q8. A second-order reaction has a rate constant of \( 0.02 \, \text{L mol}^{-1} \text{min}^{-1} \) and an initial concentration of \( 0.5 \, \text{mol L}^{-1} \). What is the half-life?

Q9. The rate law of a reaction is \( \text{Rate} = k[\text{A}]^{3/2} \). What is the overall order?

Q10. A first-order reaction has a rate constant of \( 0.0289 \, \text{min}^{-1} \). What percentage of the reactant decomposes in 48 minutes?