NEET Chemical Kinetics — Set 9

Question 1

A first-order reaction has an initial concentration of $ 1.0 \, \text{mol L}^{-1} $. After 40 minutes, the concentration reduces to $ 0.25 \, \text{mol L}^{-1} $. What is the rate constant?

Accepted Answer

For first-order, $ k = \frac{2.303}{t} \log \frac{[\text{R}]_0}{[\text{R}]} $. Given: $ [\text{R}]_0 = 1.0 \, \text{mol L}^{-1} $, $ [\text{R}] = 0.25 \, \text{mol L}^{-1} $, $ t = 40 \, \text{min} $. $ k = \frac{2.303}{40} \log \frac{1.0}{0.25} = \frac{2.303 \times 0.602}{40} \approx 0.0346 \, \text{min}^{-1} $.

Question 2

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 $ 0.18 \, \text{mol L}^{-1} $, how long will it take for 50% decomposition?

Accepted Answer

For zero-order, $ t_{1/2} = \frac{[\text{R}]_0}{2k} $. Given: $ [\text{R}]_0 = 0.18 \, \text{mol L}^{-1} $, $ k = 3.0 \times 10^{-3} \, \text{mol L}^{-1} \text{s}^{-1} $. $ t_{1/2} = \frac{0.18}{2 \times 3.0 \times 10^{-3}} = \frac{0.18}{6.0 \times 10^{-3}} = 30 \, \text{s} $.

Question 3

A zero-order reaction reduces the concentration from $ 0.1 \, \text{mol L}^{-1} $ to $ 0.04 \, \text{mol L}^{-1} $ in 60 s. What is the rate constant?

Accepted Answer

For zero-order, $ k = \frac{[\text{R}]_0 - [\text{R}]}{t} $. Given: $ [\text{R}]_0 = 0.1 \, \text{mol L}^{-1} $, $ [\text{R}] = 0.04 \, \text{mol L}^{-1} $, $ t = 60 \, \text{s} $. $ k = \frac{0.1 - 0.04}{60} = \frac{0.06}{60} = 1.0 \times 10^{-3} \, \text{mol L}^{-1} \text{s}^{-1} $.

NEET Chemistry: Chemical Kinetics — Practice Set 9

Q1. A first-order reaction has an initial concentration of \( 1.0 \, \text{mol L}^{-1} \). After 40 minutes, the concentration reduces to \( 0.25 \, \text{mol L}^{-1} \). What is the rate constant?

Q2. 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 \( 0.18 \, \text{mol L}^{-1} \), how long will it take for 50% decomposition?

Q3. A zero-order reaction reduces the concentration from \( 0.1 \, \text{mol L}^{-1} \) to \( 0.04 \, \text{mol L}^{-1} \) in 60 s. What is the rate constant?

Q4. A reaction has the rate law \( \text{Rate} = k[\text{A}]^{2.5} \). What is the overall order?

Q5. A reaction’s rate increases 8 times when the temperature rises from 300 K to 330 K. What is the approximate activation energy (\( R = 8.314 \, \text{J mol}^{-1} \text{K}^{-1} \))?

Q6. A zero-order reaction has a rate constant of \( 1.0 \times 10^{-3} \, \text{mol L}^{-1} \text{min}^{-1} \). How long will it take for 80% of a \( 0.2 \, \text{mol L}^{-1} \) reactant to decompose?

Q7. A first-order reaction has a rate constant of \( 0.01155 \, \text{min}^{-1} \). What is the half-life?

Q8. A reaction’s rate constant is \( 2.5 \times 10^{-3} \, \text{s}^{-1} \) at 25°C and \( 7.5 \times 10^{-3} \, \text{s}^{-1} \) at 35°C. What is the activation energy (\( R = 8.314 \, \text{J mol}^{-1} \text{K}^{-1} \))?

Q9. For the reaction \( 2\text{A} + \text{B} \to 3\text{C} \), the rate of disappearance of B is \( 0.01 \, \text{mol L}^{-1} \text{s}^{-1} \). What is the rate of formation of C?

Q10. A reaction’s rate increases by 1.414 times when the concentration of the reactant is doubled. What is the order of the reaction?