FSc Pre-Engineering Chemistry Reaction Kinetics — Set 3

FSc Pre-Engineering Chemistry Reaction Kinetics — Set 3

1. Question 1

   Q1. A catalyst increases the rate of reaction by

   • A) increasing the activation energy
   • B) decreasing the activation energy
   • C) changing the equilibrium constant
   • D) increasing the frequency factor

   Answer: decreasing the activation energy

   Explanation: A catalyst works by lowering the activation energy (Ea) required for the reaction, thus speeding up the reaction rate.

2. Question 2

   Q2. For a zero-order reaction, the rate of reaction is

   • A) proportional to the concentration of reactants
   • B) independent of the concentration of reactants
   • C) proportional to the square of the concentration of reactants
   • D) proportional to the square root of the concentration of reactants

   Answer: independent of the concentration of reactants

   Explanation: In a zero-order reaction, the rate = k, where k is the rate constant, indicating that the rate is independent of reactant concentration.

3. Question 3

   Q3. The half-life of a first-order reaction is 10 minutes. The time required for 75% completion is

   • A) 10 minutes
   • B) 20 minutes
   • C) 30 minutes
   • D) 40 minutes

   Answer: 20 minutes

   Explanation: For a first-order reaction, after one half-life (10 min), 50% is reacted. After another half-life (total 20 min), 75% is reacted.

4. Question 4

   Q4. The rate constant (k) for a reaction is 1.2 x 10^-3 s^-1 at 300 K. The activation energy (Ea) is 50 kJ/mol. The frequency factor (A) is

   • A) 1.15 x 10^12 s^-1
   • B) 1.15 x 10^13 s^-1
   • C) 1.15 x 10^14 s^-1
   • D) 1.15 x 10^15 s^-1

   Answer: 1.15 x 10^13 s^-1

   Explanation: Using the Arrhenius equation: k = Ae^(-Ea/RT), rearrange to find A = k / e^(-Ea/RT), and calculate A using given values.

5. Question 5

   Q5. For the reaction A -> products, the rate law is rate = k[A]². If the concentration of A is doubled, the rate

   • A) doubles
   • B) quadruples
   • C) remains same
   • D) halves

   Answer: quadruples

   Explanation: New rate = k(2[A])² = 4k[A]², which is four times the original rate, thus quadrupling.

6. Question 6

   Q6. The unit of rate constant for a first-order reaction is

   • A) s^-1
   • B) M s^-1
   • C) M^-1 s^-1
   • D) M^-2 s^-1

   Answer: s^-1

   Explanation: For a first-order reaction, the rate = k[A], so k has units of time^-1, typically s^-1.

7. Question 7

   Q7. The reaction rate increases with temperature because

   • A) the activation energy decreases
   • B) the frequency of collisions increases
   • C) the fraction of molecules having energy greater than Ea increases
   • D) the equilibrium constant increases

   Answer: the fraction of molecules having energy greater than Ea increases

   Explanation: As temperature increases, more molecules have energy greater than or equal to Ea, thus increasing the reaction rate.

8. Question 8

   Q8. The rate law for the reaction 2A + B -> products is rate = k[A][B]. The reaction is

   • A) first-order with respect to A
   • B) second-order with respect to A
   • C) first-order overall
   • D) second-order overall

   Answer: second-order overall

   Explanation: The overall order is 1 (with respect to A) + 1 (with respect to B) = 2, making the reaction second-order overall.

9. Question 9

   Q9. For a reaction with rate law rate = k[A]², if [A] is halved, the rate

   • A) becomes 1/4
   • B) becomes 1/2
   • C) remains same
   • D) doubles

   Answer: becomes 1/4

   Explanation: New rate = k(0.5[A])² = 0.25k[A]², which is 1/4 of the original rate.

10. Question 10

    Q10. The half-life of a radioactive substance is 20 years. The time required for 90% decay is

    • A) 66.4 years
    • B) 33.2 years
    • C) 60 years
    • D) 40 years

    Answer: 66.4 years

    Explanation: Using the formula for first-order reactions, t = (2.303 / k) log([A0]/[A]), and k = 0.693 / t1/2, we can find t for 90% decay.

11. Question 11

    Q11. The rate of reaction for 2NO + Cl2 -> 2NOCl is given by rate = k[NO]²[Cl2]. The order with respect to Cl2 is

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

    Answer: 1

    Explanation: The rate law indicates the reaction is first-order with respect to Cl2 since the exponent of [Cl2] is 1.

12. Question 12

    Q12. The activation energy for a reaction is zero. The rate constant

    • A) is independent of temperature
    • B) decreases with temperature
    • C) increases with temperature
    • D) is zero

    Answer: is independent of temperature

    Explanation: Using the Arrhenius equation, if Ea = 0, then k = A, which means k is independent of temperature.

13. Question 13

    Q13. For a reaction A + B -> C, the rate law is rate = k[A]. The reaction is

    • A) first-order with respect to B
    • B) zero-order with respect to B
    • C) second-order overall
    • D) first-order overall

    Answer: zero-order with respect to B

    Explanation: Since B is not present in the rate law, the reaction is zero-order with respect to B.

14. Question 14

    Q14. The rate constant for a reaction at 300 K is 1.5 x 10^-3 s^-1. At 310 K, it is 3.0 x 10^-3 s^-1. The activation energy is

    • A) 53.6 kJ/mol
    • B) 50.3 kJ/mol
    • C) 54.0 kJ/mol
    • D) 52.9 kJ/mol

    Answer: 53.6 kJ/mol

    Explanation: Using the Arrhenius equation and given rate constants at two temperatures, we can calculate Ea.

15. Question 15

    Q15. For the reaction 2A -> B, the rate law is rate = k[A]². If [A] is doubled, the rate

    • A) quadruples
    • B) doubles
    • C) remains same
    • D) halves

    Answer: quadruples

    Explanation: New rate = k(2[A])² = 4k[A]², so the rate quadruples.

16. Question 16

    Q16. The unit of the rate constant for a second-order reaction is

    • A) M^-1 s^-1
    • B) M s^-1
    • C) s^-1
    • D) M² s^-1

    Answer: M^-1 s^-1

    Explanation: For a second-order reaction, rate = k[A]², so k has units of concentration^-1 time^-1, typically M^-1 s^-1.

17. Question 17

    Q17. The rate constant of a reaction is 1.5 x 10^-4 s^-1 at 27°C. If the activation energy is 100 kJ/mol, what is the rate constant at 37°C?

    • A) 3.0 x 10^-4 s^-1
    • B) 4.5 x 10^-4 s^-1
    • C) 2.25 x 10^-4 s^-1
    • D) 1.0 x 10^-4 s^-1

    Answer: 3.0 x 10^-4 s^-1

    Explanation: Apply the Arrhenius equation: ln(k2/k1) = (Ea/R)(1/T1 - 1/T2).

18. Question 18

    Q18. For the reaction A -> products, the rate constant is 2 x 10^-3 s^-1. If the initial concentration of A is 1 M, what is the concentration after 100 s?

    • A) 0.82 M
    • B) 0.67 M
    • C) 0.5 M
    • D) 0.33 M

    Answer: 0.82 M

    Explanation: For a first-order reaction, [A] = [A0]e^(-kt) = e^(-2 x 10^-3 x 100).

19. Question 19

    Q19. For a second-order reaction, the rate constant is 0.1 M^-1s^-1. If the initial concentration is 0.2 M, what is the half-life?

    • A) 50 s
    • B) 25 s
    • C) 100 s
    • D) 200 s

    Answer: 50 s

    Explanation: For a second-order reaction, t1/2 = 1 / (k[A0]) = 1 / (0.1 x 0.2).

20. Question 20

    Q20. The rate law for the reaction A + B -> C is rate = k[A][B]. If [A] = [B] = 0.1 M, the rate is 0.01 M/s. What is the rate constant?

    • A) 1 M^-1s^-1
    • B) 0.1 M^-1s^-1
    • C) 10 M^-1s^-1
    • D) 0.01 M^-1s^-1

    Answer: 1 M^-1s^-1

    Explanation: k = rate / ([A][B]) = 0.01 / (0.1 x 0.1).