NEET Chemical Kinetics — Set 10

Question 1

A zero-order reaction has an initial concentration of $ 0.15 \, \text{mol L}^{-1} $ and takes 75 s to reach half concentration. What is the rate constant?

Accepted Answer

For zero-order, $ t_{1/2} = \frac{[\text{R}]_0}{2k} $. Given: $ [\text{R}]_0 = 0.15 \, \text{mol L}^{-1} $, $ t_{1/2} = 75 \, \text{s} $. $ 75 = \frac{0.15}{2k} $, $ k = \frac{0.15}{2 \times 75} = 1.0 \times 10^{-3} \, \text{mol L}^{-1} \text{s}^{-1} $.

Question 2

A zero-order reaction takes 90 s to reduce the concentration from $ 0.15 \, \text{mol L}^{-1} $ to $ 0.06 \, \text{mol L}^{-1} $. What is the rate constant?

Accepted Answer

For zero-order, $ k = \frac{[\text{R}]_0 - [\text{R}]}{t} $. Given: $ [\text{R}]_0 = 0.15 \, \text{mol L}^{-1} $, $ [\text{R}] = 0.06 \, \text{mol L}^{-1} $, $ t = 90 \, \text{s} $. $ k = \frac{0.15 - 0.06}{90} = \frac{0.09}{90} = 1.0 \times 10^{-3} \, \text{mol L}^{-1} \text{s}^{-1} $.

Question 3

A reaction’s rate constant increases from $ 4.0 \times 10^{-4} \, \text{min}^{-1} $ at 30°C to $ 1.2 \times 10^{-3} \, \text{min}^{-1} $ at 40°C. What is the activation energy ($ R = 8.314 \, \text{J mol}^{-1} \text{K}^{-1} $)?

Accepted Answer

$ T_1 = 303 \, \text{K} $, $ T_2 = 313 \, \text{K} $. $ \log \frac{1.2 \times 10^{-3}}{4.0 \times 10^{-4}} = \frac{E_a}{2.303 \times 8.314} \left( \frac{10}{303 \times 313} \right) $. $ \log 3 = 0.477 $, $ E_a = \frac{0.477 \times 19.147 \times 94839}{10} \approx 86,600 \, \text{J mol}^{-1} \approx 86.6 \, \text{kJ mol}^{-1} $.

NEET Chemistry: Chemical Kinetics — Practice Set 10

Q1. A zero-order reaction has an initial concentration of \( 0.15 \, \text{mol L}^{-1} \) and takes 75 s to reach half concentration. What is the rate constant?

Q2. A zero-order reaction takes 90 s to reduce the concentration from \( 0.15 \, \text{mol L}^{-1} \) to \( 0.06 \, \text{mol L}^{-1} \). What is the rate constant?

Q3. A reaction’s rate constant increases from \( 4.0 \times 10^{-4} \, \text{min}^{-1} \) at 30°C to \( 1.2 \times 10^{-3} \, \text{min}^{-1} \) at 40°C. What is the activation energy (\( R = 8.314 \, \text{J mol}^{-1} \text{K}^{-1} \))?

Q4. A first-order reaction has a rate constant of \( 0.0346 \, \text{min}^{-1} \). What is the half-life?

Q5. A reaction’s rate increases by 3.24 times when the temperature rises from 310 K to 320 K. What is the activation energy (\( R = 8.314 \, \text{J mol}^{-1} \text{K}^{-1} \))?

Q6. The molecularity of the elementary step \( \text{O}_3 \to \text{O}_2 + \text{O} \) is:

Q7. A reaction’s rate doubles when the temperature increases from 25°C to 35°C. What is the activation energy (\( R = 8.314 \, \text{J mol}^{-1} \text{K}^{-1} \))?

Q8. For the reaction \( \text{A} + 2\text{B} \to 3\text{C} \), the rate of disappearance of B is \( 0.06 \, \text{mol L}^{-1} \text{s}^{-1} \). What is the rate of formation of C?

Q9. A reaction’s rate increases by 4 times when the temperature rises from 320 K to 340 K. What is the activation energy (\( R = 8.314 \, \text{J mol}^{-1} \text{K}^{-1} \))?

Q10. A zero-order reaction has a rate constant of \( 8.0 \times 10^{-4} \, \text{mol L}^{-1} \text{s}^{-1} \). How long will it take for the concentration to decrease from \( 0.16 \, \text{mol L}^{-1} \) to \( 0.04 \, \text{mol L}^{-1} \)?