NEET Chemical Kinetics — Set 16

Question 1

A first-order reaction is 30% complete in 15 minutes. What is the rate constant?

Accepted Answer

For first-order, $ k = \frac{2.303}{t} \log \frac{[\text{R}]_0}{[\text{R}]} $. 30% complete means 70% remains, $ \frac{[\text{R}]}{[\text{R}]_0} = 0.7 $, $ \frac{[\text{R}]_0}{[\text{R}]} = \frac{1}{0.7} \approx 1.429 $. $ k = \frac{2.303}{15} \log 1.429 = \frac{2.303 \times 0.155}{15} \approx 0.0238 \, \text{min}^{-1} $.

Question 2

A second-order reaction has a rate constant of $ 0.06 \, \text{L mol}^{-1} \text{min}^{-1} $ and an initial concentration of $ 0.3 \, \text{mol L}^{-1} $. What is the time for 66.67% completion?

Accepted Answer

For second-order, $ \frac{1}{[\text{A}]} - \frac{1}{[\text{A}]_0} = kt $. 66.67% completion means $ [\text{A}] = \frac{1}{3} \times 0.3 = 0.1 \, \text{mol L}^{-1} $. $ \frac{1}{0.1} - \frac{1}{0.3} = 0.06 \times t $, $ 10 - 3.33 = 0.06 t $, $ t = \frac{6.67}{0.06} \approx 111.17 \, \text{min} $.

Question 3

A reaction has the rate law $ \text{Rate} = k[\text{A}]^{1/2}[\text{B}] $. If the concentration of A is quadrupled and B is halved, what happens to the rate?

Accepted Answer

Initial rate = $ k [\text{A}]^{1/2} [\text{B}] $. New rate = $ k (4[\text{A}])^{1/2} \left( \frac{[\text{B}]}{2} \right) = k \times 2 [\text{A}]^{1/2} \times \frac{[\text{B}]}{2} = k [\text{A}]^{1/2} [\text{B}] $. Rate remains the same.

NEET Chemistry: Chemical Kinetics — Practice Set 16

Q1. A first-order reaction is 30% complete in 15 minutes. What is the rate constant?

Q2. A second-order reaction has a rate constant of \( 0.06 \, \text{L mol}^{-1} \text{min}^{-1} \) and an initial concentration of \( 0.3 \, \text{mol L}^{-1} \). What is the time for 66.67% completion?

Q3. A reaction has the rate law \( \text{Rate} = k[\text{A}]^{1/2}[\text{B}] \). If the concentration of A is quadrupled and B is halved, what happens to the rate?

Q4. A reaction’s rate increases by 2.83 times when the temperature rises from 300 K to 310 K. What is the activation energy (\( R = 8.314 \, \text{J mol}^{-1} \text{K}^{-1} \))?

Q5. A first-order reaction has a half-life of 20 minutes. What fraction of the reactant remains after 60 minutes?

Q6. A reaction has the rate law \( \text{Rate} = k[\text{A}][\text{B}]^{1/2} \). What is the unit of the rate constant?

Q7. A first-order reaction has a rate constant of \( 0.0462 \, \text{min}^{-1} \). What percentage of the reactant remains after 15 minutes?

Q8. A reaction has the rate law \( \text{Rate} = k[\text{A}]^{1/2}[\text{B}]^{3/2} \). What is the overall order?

Q9. A second-order reaction has a rate constant of \( 0.1 \, \text{L mol}^{-1} \text{min}^{-1} \). If the initial concentration is \( 0.2 \, \text{mol L}^{-1} \), what is the time for 50% completion?

Q10. A zero-order reaction has a rate constant of \( 3.0 \times 10^{-3} \, \text{mol L}^{-1} \text{s}^{-1} \). If the initial concentration is \( 0.09 \, \text{mol L}^{-1} \), how long will it take for 66.67% decomposition?