NUST NET Medical / Biological Sciences Chemistry Reaction Kinetics — Set 3

1. Question 1

   Q1. The decomposition of N2O5 is a first-order reaction. If the rate constant is 0.0021/min, what is the half-life?

   • A) 330.04 min
   • B) 330.04 s
   • C) 165.02 min
   • D) 0.00145 min

   Answer: 330.04 min

   Explanation: For first-order reactions, half-life = ln(2)/k = 0.693/0.0021 = 330.04 min.

2. Question 2

   Q2. The rate law for the reaction A + 2B → C is rate = k[A]^2[B]. By what factor does the rate change if [A] is doubled and [B] is halved?

   • A) 2
   • B) 4
   • C) 1/2
   • D) 8

   Answer: 2

   Explanation: New rate = k(2[A])^2([B]/2) = 2k[A]^2[B], so rate doubles.

3. Question 3

   Q3. For a certain reaction, the rate constant at 300 K is 2.5 × 10^(-3) s^(-1) and at 310 K is 5.0 × 10^(-3) s^(-1). What is the activation energy?

   • A) 53.6 kJ/mol
   • B) 50.3 kJ/mol
   • C) 100 kJ/mol
   • D) 200 kJ/mol

   Answer: 53.6 kJ/mol

   Explanation: Using Arrhenius equation, Ea = RT1T2 ln(k2/k1)/(T2-T1) = 53.6 kJ/mol.

4. Question 4

   Q4. The rate of a reaction is given by rate = k[A]. If the concentration of A is doubled, the rate increases by a factor of

   • A) 2
   • B) 4
   • C) 1/2
   • D) 1

   Answer: 2

   Explanation: For first-order reactions, rate is directly proportional to [A], so doubling [A] doubles the rate.

5. Question 5

   Q5. For the reaction 2A + B → products, the rate law is rate = k[A]^2. What is the order with respect to B?

   • A) 0
   • B) 1
   • C) 2
   • D) 3

   Answer: 0

   Explanation: B is not present in the rate law, indicating zero-order dependence on B.

6. Question 6

   Q6. The half-life of a first-order reaction is 20 minutes. What is the rate constant?

   • A) 0.0347 min^(-1)
   • B) 0.693 min^(-1)
   • C) 0.0347 s^(-1)
   • D) 20 min^(-1)

   Answer: 0.0347 min^(-1)

   Explanation: For first-order reactions, k = ln(2)/t1/2 = 0.693/20 = 0.0347 min^(-1).

7. Question 7

   Q7. The rate constant for a second-order reaction is 0.05 M^(-1)s^(-1). If the initial concentration is 0.2 M, what is the half-life?

   • A) 100 s
   • B) 50 s
   • C) 200 s
   • D) 400 s

   Answer: 100 s

   Explanation: For second-order reactions, t1/2 = 1/(k[A]0) = 1/(0.05 × 0.2) = 100 s.

8. Question 8

   Q8. The activation energy for a reaction is 50 kJ/mol. If the rate constant at 300 K is 2 × 10^(-3) s^(-1), what is the rate constant at 320 K?

   • A) 8.34 × 10^(-3) s^(-1)
   • B) 4.23 × 10^(-3) s^(-1)
   • C) 1.04 × 10^(-2) s^(-1)
   • D) 6.45 × 10^(-3) s^(-1)

   Answer: 8.34 × 10^(-3) s^(-1)

   Explanation: Using Arrhenius equation, k2 = k1 exp(Ea/R(1/T1 - 1/T2)) = 8.34 × 10^(-3) s^(-1).

9. Question 9

   Q9. A reaction is 50% complete in 20 minutes. If it is first-order, how long will it take for 75% completion?

   • A) 40 min
   • B) 60 min
   • C) 30 min
   • D) 45 min

   Answer: 40 min

   Explanation: For a first-order reaction, 50% and 75% completion correspond to 1 and 2 half-lives, so 2 × 20 = 40 min.

10. Question 10

    Q10. The rate of reaction A → products is given by rate = k[A]^n. If the rate increases 9 times when [A] is tripled, what is n?

    • A) 1
    • B) 2
    • C) 3
    • D) 0

    Answer: 2

    Explanation: 9 = (3)^n, so n = 2 because 3^2 = 9.

11. Question 11

    Q11. For the reaction A → B, the rate constant is 0.01 s^(-1). If [A] = 0.1 M, what is the rate?

    • A) 0.001 M/s
    • B) 0.01 M/s
    • C) 0.1 M/s
    • D) 1 M/s

    Answer: 0.001 M/s

    Explanation: Rate = k[A] = 0.01 × 0.1 = 0.001 M/s for a first-order reaction.

12. Question 12

    Q12. The half-life of a radioactive substance is 10 years. What fraction remains after 30 years?

    • A) 1/8
    • B) 1/4
    • C) 1/2
    • D) 1/16

    Answer: 1/8

    Explanation: After 3 half-lives (30 years), (1/2)^3 = 1/8 remains.

13. Question 13

    Q13. The rate constant of a reaction is 0.05 min^(-1). What is the time required for 90% completion?

    • A) 46.04 min
    • B) 23.02 min
    • C) 92.08 min
    • D) 11.51 min

    Answer: 46.04 min

    Explanation: For a first-order reaction, t = ln([A]0/[A])/k = ln(10)/0.05 = 46.04 min.

14. Question 14

    Q14. A catalyst lowers the activation energy from 100 kJ/mol to 80 kJ/mol. By what factor does the rate constant increase at 300 K?

    • A) 2.35 × 10^3
    • B) 1.65 × 10^2
    • C) 55.46
    • D) 1.04 × 10^4

    Answer: 55.46

    Explanation: Using Arrhenius equation, k2/k1 = exp((Ea1 - Ea2)/RT) = 55.46.

15. Question 15

    Q15. For the reaction 2NO2 → 2NO + O2, the rate of disappearance of NO2 is 0.02 M/s. What is the rate of appearance of O2?

    • A) 0.01 M/s
    • B) 0.02 M/s
    • C) 0.04 M/s
    • D) 0.005 M/s

    Answer: 0.01 M/s

    Explanation: Rate of appearance of O2 = (1/2) × rate of disappearance of NO2 = 0.01 M/s.

16. Question 16

    Q16. The rate law for a reaction is rate = k[A][B]. If [A] = [B] = 0.1 M, and k = 0.05 M^(-1)s^(-1), what is the rate?

    • A) 5 × 10^(-4) M/s
    • B) 5 × 10^(-3) M/s
    • C) 5 × 10^(-2) M/s
    • D) 5 × 10^(-5) M/s

    Answer: 5 × 10^(-4) M/s

    Explanation: Rate = k[A][B] = 0.05 × 0.1 × 0.1 = 5 × 10^(-4) M/s.

17. Question 17

    Q17. For a certain reaction, the rate constant doubles when the temperature increases from 298 K to 308 K. What is the activation energy?

    • A) 52.9 kJ/mol
    • B) 50.3 kJ/mol
    • C) 53.6 kJ/mol
    • D) 51.2 kJ/mol

    Answer: 53.6 kJ/mol

    Explanation: Using Arrhenius equation, Ea = RT1T2 ln(k2/k1)/(T2-T1) = 53.6 kJ/mol.

18. Question 18

    Q18. The decomposition of H2O2 is a first-order reaction. If the rate constant is 0.05 min^(-1), what is the time required for 75% decomposition?

    • A) 27.72 min
    • B) 13.86 min
    • C) 41.58 min
    • D) 55.44 min

    Answer: 27.72 min

    Explanation: For 75% decomposition, t = ln(4)/k = ln(4)/0.05 = 27.72 min.

19. Question 19

    Q19. The rate constant for the reaction A → B is 0.02 s^(-1). If [A] = 0.2 M, what is the initial rate?

    • A) 0.004 M/s
    • B) 0.02 M/s
    • C) 0.01 M/s
    • D) 0.1 M/s

    Answer: 0.004 M/s

    Explanation: Initial rate = k[A] = 0.02 × 0.2 = 0.004 M/s for a first-order reaction.

20. Question 20

    Q20. For the reaction 2NO + O2 → 2NO2, the rate law is given by rate = k[NO]^2[O2]. What is the order of this reaction?

    • A) 1
    • B) 2
    • C) 3
    • D) 4

    Answer: 3

    Explanation: The reaction is third-order because the sum of the exponents in the rate law is 3. Option B is incorrect because it only considers the exponent of one reactant.