Q: A reaction mechanism for the decomposition of hydrogen peroxide is proposed as follows: Step 1 (slow): $$\mathrm{H_2O_2} \rightarrow \mathrm{H_2O} + \mathrm{O}$$ Step 2 (fast): $$\mathrm{O} + \mathrm{H_2O_2} \rightarrow \mathrm{H_2O} + \mathrm{O_2$}$$ What is the expected rate law for this reaction?

$$\text{rate} = k[\mathrm{H_2O_2}]$$

Question 1

A reaction mechanism for the decomposition of hydrogen peroxide is proposed as follows:

Step 1 (slow): $$\mathrm{H_2O_2} \rightarrow \mathrm{H_2O} + \mathrm{O}$$

Step 2 (fast): $$\mathrm{O} + \mathrm{H_2O_2} \rightarrow \mathrm{H_2O} + \mathrm{O_2$}$$

What is the expected rate law for this reaction?

Accepted Answer

$$	ext{rate} = k[\mathrm{H_2O_2}]$$

Question 2

Which of the following statements about the activation energy ($$E_a) $$and the rate constant ($$k) is $$correct according to the Arrhenius equation?

Accepted Answer

A higher $$E_a$$ leads to a lower $$k at a $$given temperature.

Question 3

For the reaction $$2\mathrm{NO}_2 ightarrow 2\mathrm{NO} + \mathrm{O}_2$$, the rate law is found to be $$	ext{rate} = k[\mathrm{NO}_2]^2. $$What is the order of the reaction with respect to $$\mathrm{NO}_2$$ and the overall order?

Accepted Answer

Second order with respect to $$\mathrm{NO}_2$$; second order overall.

Question 4

A student is given the following data for a reaction:

$$\begin{align*}
	ext{[A]} & 	ext{(mol/L)} & 	ext{Initial Rate (mol/L·s)} \
0.10 & 0.020 \
0.20 & 0.080 \
\end{align*}$$

What is the order of the reaction with respect to A?

Accepted Answer

Second order

Question 5

Which of the following best describes the transition state in a chemical reaction?

Accepted Answer

It is the highest energy point along the reaction pathway, where bonds are partially broken and formed.

Question 6

The decomposition of a certain compound follows first-order kinetics. If the half-life of the reaction is 10 minutes, what fraction of the compound remains after 30 minutes?

Accepted Answer

$$\dfrac{1}{8}$$

Question 7

For the reaction $$\mathrm{A} + \mathrm{B} \rightleftharpoons \mathrm{C}$$, the equilibrium constant $$K is$$ $$10^5 at $$room temperature. Which statement is true?

Accepted Answer

At equilibrium, the concentration of C is much greater than that of A and B.

Question 8

A reaction has $$\Delta G^\circ = +10 kJ/$$mol at 298 K. What can you conclude about the equilibrium constant $$K$$ for this reaction?

Accepted Answer

$$K \u003c 1$$, so reactants are favored at equilibrium.

Question 9

Given the reaction $$\mathrm{N_2O_4} \rightleftharpoons 2\mathrm{NO_2$}$$, the equilibrium constant $$K is 0.15 at a $$certain temperature. If $$[\mathrm{N_2O_4}] = 0.50 M $$and $$[\mathrm{NO_2$}] = 0.10 M$$, what is the value of the reaction quotient $$Q$$ and in which direction will the reaction proceed to reach equilibrium?

Accepted Answer

$$Q = \dfrac{[\mathrm{NO_2$}]^2}{[\mathrm{N_2O_4}]} = \dfrac{(0.10)^2$}{0.50} = 0.02$$; the reaction will proceed forward.

Question 10

Which of the following best explains why a catalyst increases the rate of a chemical reaction?

Accepted Answer

It provides an alternative pathway with a lower activation energy ($$E_a).$$

Question 11

A reaction has the following rate law: $$	ext{rate} = k[\mathrm{A}][\mathrm{B}]^2. If $$the concentration of A is doubled and the concentration of B is tripled, by what factor does the rate increase?

Accepted Answer

The rate increases by a factor of 18.

Question 12

Which of the following is true about a system at equilibrium?

Accepted Answer

The rates of the forward and reverse reactions are equal.

Question 13

The Arrhenius equation is $$k = Ae$$^{-E_a/(RT)}$$. If the activation energy E_a$ is 50 kJ/mol, A = 1.0$$ 	imes $$10^{13}$$ \ \mathrm{s}^{-1}$$, R = 8.314$$ \ \mathrm{J/(mol\cdot K)}$$, and T = 298$ K, what is the value of k$? (Use E_a$ in J/mol.)

Accepted Answer

$$k \approx 1.9 	imes 10^4$ \ \mathrm{s}^{-1}$$

Question 14

A reaction is found to be zero order in reactant A. Which of the following statements is true?

Accepted Answer

The rate of the reaction does not depend on the concentration of A.

Question 15

For the reaction $$\mathrm{CO} + \mathrm{Cl_2$} ightarrow \mathrm{$$COCl_2$$}$$, the following data are collected:

$$\begin{align*}
[\mathrm{CO}] & [\mathrm{Cl_2$}] & 	ext{Initial Rate} \
0.10 & 0.10 & 0.014 \
0.20 & 0.10 & 0.028 \
0.10 & 0.20 & 0.014 \
\end{align*}$$

What is the rate law for this reaction?

Accepted Answer

$$	ext{rate} = k[\mathrm{CO}]$$

Question 16

A reaction mixture initially contains 1.0 M A and 0 M B. After reaching equilibrium, the concentration of A is 0.4 M. If the reaction is $$2\mathrm{A} \rightleftharpoons \mathrm{B}$$, what is the equilibrium constant $$K$$?

Accepted Answer

$$K = \dfrac{[\mathrm{B}]}{[\mathrm{A}]^2} = \dfrac{0.3}{(0.4)^2$} = 1.88$$

Question 17

Which of the following best describes the effect of increasing temperature on a reaction at equilibrium?

Accepted Answer

It increases the rate constants for both the forward and reverse reactions.

Question 18

A reaction has a rate law $$	ext{rate} = k[\mathrm{A}]^2[\mathrm{B}]. If $$the initial rate is $$0.10$$ mol/L·s when $$[\mathrm{A}] = 0.50 M $$and $$[\mathrm{B}] = 0.20 M$$, what is the value of $$k$$?

Accepted Answer

$$k = \dfrac{0.10}{(0.50)^2$ 	imes 0.20} = 2.0 L$^2$$mol$$^{-2}s$^{-1}$$

Question 19

Which of the following statements about the relationship between $$\Delta G^\circ$$ and $$K is $$correct?

Accepted Answer

$$\Delta G^\circ = -RT \ln K$$

Study Notes: Chemical Kinetics and Chemical Equilibrium

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