Chapter 4 Chemical Kinetics

1. The rate of a chemical reaction depends on:

a) The concentration of reactants
b) The temperature
c) The presence of catalysts
d) All of the above

Answer: d) All of the above
Explanation: The rate of a chemical reaction depends on the concentration of reactants, the temperature, and the presence of catalysts, as all these factors can influence the rate.

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2. For a reaction $A \to B$ , the rate of reaction doubles when the concentration of A is doubled. What is the order of the reaction?

a) 0
b) 1
c) 2
d) 3

Answer: b) 1
Explanation: If the rate of the reaction doubles when the concentration of A is doubled, the order of the reaction is 1. This follows the rate law $\text{rate} = k[A]^1$ .

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3. The rate constant for a zero-order reaction has units of:

a) $\text{mol} \, \text{L}^{-1} \, \text{s}^{-1}$
b) $\text{L} \, \text{mol}^{-1} \, \text{s}^{-1}$
c) $\text{s}^{-1}$
d) $\text{mol} \, \text{L}^{-1} \, \text{s}^{-1}$

Answer: c) $\text{s}^{-1}$
Explanation: For a zero-order reaction, the rate law is $\text{rate} = k$ , where the rate constant $k$ has units of $\text{s}^{-1}$ .

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4. The rate of a first-order reaction is:

a) Directly proportional to the square of the concentration of reactant
b) Inversely proportional to the concentration of reactant
c) Directly proportional to the concentration of reactant
d) Independent of the concentration of reactant

Answer: c) Directly proportional to the concentration of reactant
Explanation: For a first-order reaction, the rate is directly proportional to the concentration of the reactant, i.e., $\text{rate} = k[A]$ .

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5. For a reaction A → B, the rate law is $\text{rate} = k[A]^2$ . What is the unit of rate constant (k)?

a) $\text{mol} \, \text{L}^{-1} \, \text{s}^{-1}$
b) $\text{L} \, \text{mol}^{-1} \, \text{s}^{-1}$
c) $\text{mol} \, \text{L}^{-2} \, \text{s}^{-1}$
d) $\text{mol} \, \text{L}^{-2} \, \text{s}^{-2}$

Answer: b) $\text{L} \, \text{mol}^{-1} \, \text{s}^{-1}$
Explanation: For a second-order reaction, the rate law is $\text{rate} = k[A]^2$ , so the units of rate constant $k$ are $\text{L} \, \text{mol}^{-1} \, \text{s}^{-1}$ .

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6. Which of the following statements is true for the activation energy of a reaction?

a) It increases the rate of reaction
b) It is independent of temperature
c) It is the energy barrier for a reaction to occur
d) It decreases with an increase in temperature

Answer: c) It is the energy barrier for a reaction to occur
Explanation: Activation energy is the minimum energy that the reacting molecules must have for a reaction to occur. It acts as an energy barrier.

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7. The half-life of a first-order reaction is independent of the concentration of the reactant. What is the expression for the half-life (t₁/₂)?

a) $t_{1/2} = \frac{0.693}{k}$
b) $t_{1/2} = \frac{1}{k[A]_0}$
c) $t_{1/2} = \frac{1}{k}$
d) $t_{1/2} = \frac{2.303}{k[A]_0}$

Answer: a) $t_{1/2} = \frac{0.693}{k}$
Explanation: For a first-order reaction, the half-life is constant and is given by $t_{1/2} = \frac{0.693}{k}$ , where $k$ is the rate constant.

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8. The rate of reaction increases with an increase in temperature because:

a) The number of collisions increases
b) The average kinetic energy of molecules increases
c) Both a and b
d) The activation energy decreases

Answer: c) Both a and b
Explanation: An increase in temperature results in an increase in the number of collisions and the average kinetic energy of molecules, both of which increase the rate of reaction.

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9. Which of the following is the rate law expression for a reaction: $2A + B \to C$ ?

a) $\text{rate} = k[A]^2[B]$
b) $\text{rate} = k[A][B]^2$
c) $\text{rate} = k[A]^3[B]^2$
d) $\text{rate} = k[A]^2[B]^3$

Answer: a) $\text{rate} = k[A]^2[B]$
Explanation: The rate law depends on the stoichiometry of the reaction, which in this case is $2A + B \to C$ , so the rate law is $\text{rate} = k[A]^2[B]$ .

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10. Which of the following statements is true for the Arrhenius equation?

a) The rate constant is inversely proportional to the activation energy
b) The rate constant increases with an increase in temperature
c) The rate constant decreases with a decrease in temperature
d) Both b and c

Answer: d) Both b and c
Explanation: According to the Arrhenius equation, $k = Ae^{-E_a/RT}$ , where $E_a$ is the activation energy. The rate constant increases with an increase in temperature and decreases with a decrease in temperature.

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11. The rate of a reaction increases when the concentration of reactants is increased in:

a) Zero-order reactions
b) First-order reactions
c) Second-order reactions
d) None of the above

Answer: c) Second-order reactions
Explanation: In second-order reactions, the rate depends on the square of the concentration of reactants, so increasing the concentration increases the rate significantly.

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12. The rate constant of a reaction is affected by:

a) Temperature
b) Concentration of reactants
c) Pressure of the system
d) All of the above

Answer: a) Temperature
Explanation: The rate constant is primarily affected by temperature. It changes with temperature, following the Arrhenius equation. The concentration and pressure of reactants do not directly affect the rate constant.

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13. The method of initial rates can be used to determine:

a) The activation energy of a reaction
b) The concentration of reactants at equilibrium
c) The rate law for a reaction
d) The half-life of a reaction

Answer: c) The rate law for a reaction
Explanation: The method of initial rates involves measuring the initial rate of the reaction at various concentrations of reactants to determine the rate law.

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14. For a second-order reaction, the integrated rate law is:

a) $\ln [A] = -kt + \ln [A_0]$
b) $\frac{1}{[A]} = kt + \frac{1}{[A_0]}$
c) $[A] = [A_0] e^{-kt}$
d) $\text{rate} = k[A]^2$

Answer: b) $\frac{1}{[A]} = kt + \frac{1}{[A_0]}$
Explanation: The integrated rate law for a second-order reaction is $\frac{1}{[A]} = kt + \frac{1}{[A_0]}$ , where $[A_0]$ is the initial concentration and $[A]$ is the concentration at time $t$ .

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15. The reaction $2A \to B$ is second-order with respect to A. If the concentration of A is halved, the rate of the reaction will:

a) Be halved
b) Remain the same
c) Quadruple
d) Increase by a factor of 4

Answer: a) Be halved
Explanation: For a second-order reaction, the rate is proportional to the square of the concentration of A. Halving the concentration of A will reduce the rate by a factor of 4.

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16. What is the unit of the rate constant for a first-order reaction?

a) $\text{mol} \, \text{L}^{-1} \, \text{s}^{-1}$
b) $\text{s}^{-1}$
c) $\text{mol} \, \text{L}^{-2} \, \text{s}^{-1}$
d) $\text{L} \, \text{mol}^{-1} \, \text{s}^{-1}$

Answer: b) $\text{s}^{-1}$
Explanation: For a first-order reaction, the rate law is $\text{rate} = k[A]$ , and the unit of the rate constant is $\text{s}^{-1}$ .

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17. Which of the following is a unit of rate for a second-order reaction?

a) $\text{mol} \, \text{L}^{-1} \, \text{s}^{-1}$
b) $\text{mol} \, \text{L}^{-2} \, \text{s}^{-1}$
c) $\text{mol} \, \text{L}^{-1}$
d) $\text{s}^{-1}$

Answer: b) $\text{mol} \, \text{L}^{-2} \, \text{s}^{-1}$
Explanation: For a second-order reaction, the rate law is $\text{rate} = k[A]^2$ , so the units of rate are $\text{mol} \, \text{L}^{-2} \, \text{s}^{-1}$ .

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18. In a reaction A → B, if the rate constant is 0.005 L/mol/s and the initial concentration of A is 0.1 mol/L, what is the rate of the reaction for a second-order reaction?

a) 0.005 mol/L/s
b) 0.05 mol/L/s
c) 0.0005 mol/L/s
d) 0.5 mol/L/s

Answer: a) 0.005 mol/L/s
Explanation: For a second-order reaction, the rate is $\text{rate} = k[A]^2$ . Substituting the given values:

$$\text{rate} = 0.005 \times (0.1)^2 = 0.005 \times 0.01 = 0.00005 \, \text{mol/L/s}$$

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19. The rate constant for a reaction is determined by:

a) Temperature
b) Concentration
c) Both a and b
d) None of the above

Answer: a) Temperature
Explanation: The rate constant is primarily affected by temperature, and it follows the Arrhenius equation.

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20. The half-life for a first-order reaction is:

a) Independent of the initial concentration
b) Directly proportional to the initial concentration
c) Inversely proportional to the initial concentration
d) Inversely proportional to the square of the initial concentration

Answer: a) Independent of the initial concentration
Explanation: The half-life for a first-order reaction is independent of the initial concentration and is constant for all concentrations.

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21. In a reaction, the rate law is $\text{rate} = k[A]^2[B]^3$ What is the overall order of the reaction?

a) 2
b) 5
c) 6
d) 3

Answer: b) 5
Explanation: The overall order of the reaction is the sum of the exponents in the rate law, i.e., $2 + 3 = 5$

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22. For a zero-order reaction, the rate constant has units of:

a) $\text{mol/L/s}$
b) $\text{mol/L} \cdot \text{s}$
c) $\text{mol/L}^2 \cdot \text{s}$
d) $\text{s}^{-1}$

Answer: a) $\text{mol/L/s}$
Explanation: For a zero-order reaction, the rate law is $\text{rate} = k$ , and the units of the rate constant are $\text{mol/L/s}$ .

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23. Which of the following correctly represents the integrated rate equation for a first-order reaction?

a) $\ln[A] = -kt + \ln[A_0]$
b) $\ln[A] = kt + \ln[A_0]$
c) $\frac{1}{[A]} = kt + \frac{1}{[A_0]}$
d) $[A] = [A_0]e^{-kt}$

Answer: a) $\ln[A] = -kt + \ln[A_0]$
Explanation: The integrated rate law for a first-order reaction is $\ln[A] = -kt + \ln[A_0]$ , where $[A_0]$ is the initial concentration and $[A]$ is the concentration at time $t$ .

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24. The rate of a chemical reaction is affected by the:

a) Temperature
b) Concentration of reactants
c) Physical state of the reactants
d) All of the above

Answer: d) All of the above
Explanation: All these factors—temperature, concentration of reactants, and the physical state of the reactants—affect the rate of a chemical reaction.

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25. Which of the following is true for a reaction that follows first-order kinetics?

a) The rate is proportional to the square of the concentration of reactants.
b) The concentration of the reactant decreases exponentially with time.
c) The concentration of the reactant decreases linearly with time.
d) The rate of the reaction is constant throughout the reaction.

Answer: b) The concentration of the reactant decreases exponentially with time.
Explanation: For a first-order reaction, the concentration of the reactant decreases exponentially with time.

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26. The rate constant for a second-order reaction has units of:

a) $\text{mol/L} \cdot \text{s}$
b) $\text{mol/L}^2 \cdot \text{s}$
c) $\text{s}^{-1}$
d) $\text{mol/L} \cdot \text{s}^{-1}$

Answer: b) $\text{mol/L}^2 \cdot \text{s}$
Explanation: For a second-order reaction, the rate law is $\text{rate} = k[A]^2$ , and the units of the rate constant are $\text{mol/L}^2 \cdot \text{s}$ .

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27. Which of the following factors does not affect the rate of a reaction?

a) Catalyst
b) Temperature
c) Volume of the reaction vessel
d) Concentration of reactants

Answer: c) Volume of the reaction vessel
Explanation: The volume of the reaction vessel does not directly affect the rate of a reaction. The rate is influenced by concentration, temperature, and catalysts.

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28. Which one of the following is the correct unit of the rate constant for a first-order reaction?

a) $\text{mol/L/s}$
b) $\text{s}^{-1}$
c) $\text{mol/L} \cdot \text{s}$
d) $\text{mol/L}^2 \cdot \text{s}$

Answer: b) $\text{s}^{-1}$
Explanation: For a first-order reaction, the rate law is $\text{rate} = k[A]$ , and the unit of the rate constant is $\text{s}^{-1}$ .

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29. In a reaction, if the concentration of reactant is halved and the rate of reaction decreases by a factor of 4, the order of the reaction is:

a) Zero
b) First
c) Second
d) Third

Answer: c) Second
Explanation: If the rate decreases by a factor of 4 when the concentration is halved, the reaction is second-order, as rate is proportional to the square of the concentration.

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30. The rate of a reaction is independent of the concentration of reactants in:

a) First-order reaction
b) Zero-order reaction
c) Second-order reaction
d) All of the above

Answer: b) Zero-order reaction
Explanation: In a zero-order reaction, the rate is independent of the concentration of reactants, i.e., $\text{rate} = k$ .

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31. What is the effect of a catalyst on the activation energy of a reaction?

a) It increases the activation energy
b) It decreases the activation energy
c) It has no effect on activation energy
d) It causes a reverse reaction

Answer: b) It decreases the activation energy
Explanation: A catalyst lowers the activation energy, making it easier for the reaction to occur.

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32. The integrated rate equation for a zero-order reaction is:

a) $[A] = [A_0]e^{-kt}$
b) $[A] = [A_0] - kt$
c) $\ln[A] = \ln[A_0] - kt$
d) $\frac{1}{[A]} = kt + \frac{1}{[A_0]}$

Answer: b) $[A] = [A_0] - kt$
Explanation: For a zero-order reaction, the integrated rate law is $[A] = [A_0] - kt$ , where $k$ is the rate constant.

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33. In which type of reaction is the rate constant not affected by the concentration of reactants?

a) Zero-order reaction
b) First-order reaction
c) Second-order reaction
d) All of the above

Answer: a) Zero-order reaction
Explanation: In zero-order reactions, the rate is independent of the concentration of reactants.

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34. For a reaction $A \to B$ , the rate constant is $2.3 \times 10^{-5} \, \text{L/mol/s}$ . If the concentration of A is 0.1 mol/L, what is the rate of the reaction?

a) $2.3 \times 10^{-6} \, \text{mol/L/s}$
b) $2.3 \times 10^{-5} \, \text{mol/L/s}$
c) $2.3 \times 10^{-4} \, \text{mol/L/s}$
d) $2.3 \times 10^{-3} \, \text{mol/L/s}$

Answer: b) $2.3 \times 10^{-5} \, \text{mol/L/s}$
Explanation: For a zero-order reaction, the rate is $\text{rate} = k[A]$ . Substituting the values:

$$\text{rate} = (2.3 \times 10^{-5}) \times (0.1) = 2.3 \times 10^{-6} \, \text{mol/L/s}$$

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35. The rate of a reaction is given by $\text{rate} = k[A]^n$ . If $n = 1$ , what is the half-life of the reaction?

a) $t_{1/2} = \frac{0.693}{k}$
b) $t_{1/2} = \frac{1}{k}$
c) $t_{1/2} = k$
d) $t_{1/2} = \frac{1}{0.693k}$

Answer: a) $t_{1/2} = \frac{0.693}{k}$
Explanation: For a first-order reaction, the half-life is given by $t_{1/2} = \frac{0.693}{k}$ .

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36. For a reaction $A \to B$ , the rate law is $\text{rate} = k[A]^2$ . The units of the rate constant $k$ are:

a) $\text{mol/L} \cdot \text{s}$ >
b) $\text{mol/L}^2 \cdot \text{s}^{-1}$
c) $\text{s}^{-1}$
d) $\text{mol/L/s}$

Answer: b) $\text{mol/L}^2 \cdot \text{s}^{-1}$
Explanation: For a second-order reaction, the rate constant has units of $\text{mol/L}^2 \cdot \text{s}^{-1}$ .