NEET Chemical Kinetics — Set 4

Question 1

A first-order gaseous reaction has an initial pressure of 0.6 atm. After 20 s, the total pressure is 0.9 atm. What is the rate constant?

Accepted Answer

For $ \text{A} \to 2\text{B} $, $ p_t = p_i + x $, $ x = 0.9 - 0.6 = 0.3 \, \text{atm} $. $ p_A = p_i - x = 0.6 - 0.3 = 0.3 \, \text{atm} $. $ k = \frac{2.303}{20} \log \frac{0.6}{0.3} = \frac{2.303 \times 0.301}{20} \approx 0.0346 \, \text{s}^{-1} $.

Question 2

A reaction’s rate constant increases from $ 2.0 \times 10^{-4} \, \text{min}^{-1} $ at 290 K to $ 6.0 \times 10^{-4} \, \text{min}^{-1} $ at 300 K. What is the activation energy ($ R = 8.314 \, \text{J mol}^{-1} \text{K}^{-1} $)?

Accepted Answer

$ \log \frac{6.0 \times 10^{-4}}{2.0 \times 10^{-4}} = \frac{E_a}{2.303 \times 8.314} \left( \frac{10}{290 \times 300} \right) $. $ \log 3 = 0.477 $, $ E_a = \frac{0.477 \times 19.147 \times 87000}{10} \approx 79,400 \, \text{J mol}^{-1} \approx 79.4 \, \text{kJ mol}^{-1} $.

Question 3

A first-order reaction has an initial concentration of $ 0.8 \, \text{mol L}^{-1} $. After 30 minutes, the concentration reduces to $ 0.4 \, \text{mol L}^{-1} $. What is the rate constant?

Accepted Answer

For a first-order reaction, $ k = \frac{2.303}{t} \log \frac{[\text{R}]_0}{[\text{R}]} $. Given: $ t = 30 \, \text{min} $, $ [\text{R}]_0 = 0.8 \, \text{mol L}^{-1} $, $ [\text{R}] = 0.4 \, \text{mol L}^{-1} $. $ k = \frac{2.303}{30} \log \frac{0.8}{0.4} = \frac{2.303}{30} \log 2 = \frac{2.303 \times 0.301}{30} \approx 0.0231 \, \text{min}^{-1} $.

NEET Chemistry: Chemical Kinetics — Practice Set 4

Q1. A first-order gaseous reaction has an initial pressure of 0.6 atm. After 20 s, the total pressure is 0.9 atm. What is the rate constant?

Q2. A reaction’s rate constant increases from \( 2.0 \times 10^{-4} \, \text{min}^{-1} \) at 290 K to \( 6.0 \times 10^{-4} \, \text{min}^{-1} \) at 300 K. What is the activation energy (\( R = 8.314 \, \text{J mol}^{-1} \text{K}^{-1} \))?

Q3. A first-order reaction has an initial concentration of \( 0.8 \, \text{mol L}^{-1} \). After 30 minutes, the concentration reduces to \( 0.4 \, \text{mol L}^{-1} \). What is the rate constant?

Q4. A reaction has the rate law \( \text{Rate} = k[\text{A}]^2[\text{B}]^2 \). If the concentration of A is doubled and B is reduced to half, what happens to the rate?

Q5. A reaction’s rate increases by 16 times when the concentration of the reactant is increased by 4 times. What is the order of the reaction?

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

Q7. A reaction’s rate increases by 9 times when the temperature rises from 330 K to 350 K. What is the activation energy (\( R = 8.314 \, \text{J mol}^{-1} \text{K}^{-1} \))?

Q8. The molecularity of the elementary step \( \text{NO}_2 + \text{CO} \to \text{NO} + \text{CO}_2 \) is:

Q9. A first-order reaction is 40% complete in 20 minutes. What is the rate constant?

Q10. A reaction’s rate constant is \( 1.0 \times 10^{-2} \, \text{s}^{-1} \) at 27°C. If the activation energy is 50 kJ/mol, what is the rate constant at 37°C (\( R = 8.314 \, \text{J mol}^{-1} \text{K}^{-1} \))?