Rate Laws & Chemical Kinetics practice questions

Question 1

A student analyzes experimental kinetic data for the gas-phase reaction reactant decomposition reaction and determines that the rate law is $\text{rate} = k[\text{NO}_2]^2$. If concentration is expressed in $\text{M}$ and the reaction rate is expressed in $\text{M}\cdot\text{s}^{-1}$, which of the following represents the correct units for the rate constant, $k$?

Accepted Answer

$\text{M}^{-1}\cdot\text{s}^{-1}$

Answer

$\text{M}\cdot\text{s}^{-1}$

Answer

$\text{s}^{-1}$

Answer

$\text{M}^{-2}\cdot\text{s}^{-1}$

Question 2

A student injects a sample of colorless $\text{N}_2\text{O}_4\text{(g)}$ into an evacuated, sealed rigid container at a constant temperature. Over time, brown $\text{NO}_2\text{(g)}$ forms according to the reaction $\text{N}_2\text{O}_4\text{(g)} \rightleftharpoons 2\text{NO}_2\text{(g)}$. After several minutes, the intensity of the brown color inside the container remains constant. Which of the following best describes the state of the system after the brown color stops changing, and provides the correct justification?

Accepted Answer

The system has reached dynamic equilibrium because the rate of the forward reaction equals the rate of the reverse reaction.

Answer

The reaction has stopped because all of the $\text{N}_2\text{O}_4\text{(g)}$ has been converted into $\text{NO}_2\text{(g)}$.

Answer

The system has reached dynamic equilibrium because the concentration of $\text{N}_2\text{O}_4\text{(g)}$ is equal to the concentration of $\text{NO}_2\text{(g)}$.

Answer

The reaction has stopped because the rates of both the forward and reverse reactions have decreased to zero.

Question 3

Nitric oxide gas reacts with ozone gas in the atmosphere in an elementary reaction step represented below.

$\text{NO(g)} + \text{O}_3\text{(g)} \rightarrow \text{NO}_2\text{(g)} + \text{O}_2\text{(g)}$

Which of the following correctly identifies the molecularity and the rate law for this elementary step?

Accepted Answer

Bimolecular, with a rate law of $\text{Rate} = k[\text{NO}][\text{O}_3]$

Answer

Unimolecular, with a rate law of $\text{Rate} = k[\text{NO}]$

Answer

Bimolecular, with a rate law of $\text{Rate} = k[\text{NO}_2][\text{O}_2]$

Answer

Termolecular, with a rate law of $\text{Rate} = k[\text{NO}][\text{O}_3][\text{NO}_2]$

Question 4

A student monitors the decomposition of hydrogen peroxide according to the equation $2\text{H}_2\text{O}_2(aq) \rightarrow 2\text{H}_2\text{O}(l) + \text{O}_2(g)$. The concentration of $\text{H}_2\text{O}_2(aq)$ measured at various times during the reaction is recorded in the table below.

| Time (s) | $[\text{H}_2\text{O}_2]$ (M) |
|---|---|
| 0.0 | 1.00 |
| 10.0 | 0.80 |
| 50.0 | 0.20 |
| 60.0 | 0.10 |

Based on the data in the table, what is the average rate of disappearance of $\text{H}_2\text{O}_2(aq)$ between $t = 10.0\text{ s}$ and $t = 50.0\text{ s}$?

Accepted Answer

$0.015\text{ M}\cdot\text{s}^{-1}$

Answer

$0.0033\text{ M}\cdot\text{s}^{-1}$

Answer

$0.0050\text{ M}\cdot\text{s}^{-1}$

Answer

$0.020\text{ M}\cdot\text{s}^{-1}$

Question 5

A student investigates the thermal decomposition of nitryl chloride, $\text{NO}_2\text{Cl(g)}$. The first step of the proposed reaction mechanism is a unimolecular elementary step:

$\text{NO}_2\text{Cl(g)} \rightarrow \text{NO}_2\text{(g)} + \text{Cl(g)}$

Which of the following is the correct rate law expression for this elementary step?

Accepted Answer

$\text{Rate} = k [\text{NO}_2\text{Cl}]$

Answer

$\text{Rate} = k [\text{NO}_2\text{Cl}]^2$

Answer

$\text{Rate} = k [\text{NO}_2][\text{Cl}]$

Answer

$\text{Rate} = k \dfrac{[\text{NO}_2][\text{Cl}]}{[\text{NO}_2\text{Cl}]}$

Question 6

A hospital uses the radioactive isotope $^{18}\text{F}$ as a medical imaging tracer. The isotope undergoes first-order decay with a rate constant of $6.30 \times 10^{-3}\ \text{min}^{-1}$.

What is the half-life of $^{18}\text{F}$?

Accepted Answer

$110\ \text{min}$

Answer

$9.09 \times 10^{-3}\ \text{min}$

Answer

$159\ \text{min}$

Answer

$1100\ \text{min}$

Question 7

A student investigates the gas-phase decomposition of dinitrogen pentoxide at a constant temperature in a rigid container, as represented by the balanced equation below:

$2\text{N}_2\text{O}_5\text{(g)} \rightarrow 4\text{NO}_2\text{(g)} + \text{O}_2\text{(g)}$

At a particular instant during the reaction, the student measures the rate of concentration change for each species. Which of the following correctly ranks the absolute rates of concentration change, $\left|\dfrac{\Delta[\text{X}]}{\Delta t}\right|$, for the three gases at this instant, from greatest to least?

Accepted Answer

$\left|\dfrac{\Delta[\text{NO}_2]}{\Delta t}\right| > \left|\dfrac{\Delta[\text{N}_2\text{O}_5]}{\Delta t}\right| > \left|\dfrac{\Delta[\text{O}_2]}{\Delta t}\right|$

Answer

$\left|\dfrac{\Delta[\text{O}_2]}{\Delta t}\right| > \left|\dfrac{\Delta[\text{N}_2\text{O}_5]}{\Delta t}\right| > \left|\dfrac{\Delta[\text{NO}_2]}{\Delta t}\right|$

Answer

$\left|\dfrac{\Delta[\text{NO}_2]}{\Delta t}\right| > \left|\dfrac{\Delta[\text{O}_2]}{\Delta t}\right| > \left|\dfrac{\Delta[\text{N}_2\text{O}_5]}{\Delta t}\right|$

Answer

$\left|\dfrac{\Delta[\text{N}_2\text{O}_5]}{\Delta t}\right| > \left|\dfrac{\Delta[\text{NO}_2]}{\Delta t}\right| > \left|\dfrac{\Delta[\text{O}_2]}{\Delta t}\right|$

Question 8

A student investigates the thermal decomposition of gas-phase nitrogen dioxide according to the reaction $\text{2 NO}_2\text{(g)} \rightarrow \text{2 NO(g)} + \text{O}_2\text{(g)}$. The student measures the concentration of $\text{NO}_2\text{(g)}$ as a function of time at a constant temperature and constructs three integrated rate law plots, as shown below. Which of the following best identifies the order of the reaction with respect to $\text{NO}_2$ and provides the correct justification?

Accepted Answer

Second order, because the plot of $1/[\text{NO}_2]$ versus time is linear.

Answer

First order, because the plot of $\ln[\text{NO}_2]$ versus time is linear.

Answer

Zero order, because the plot of $[\text{NO}_2]$ versus time shows a continuous decrease in concentration.

Answer

First order, because the plot of $1/[\text{NO}_2]$ versus time has a positive slope.

Question 9

A student proposes the following two-step mechanism for the reaction $\text{NO}_2\text{(g)} + \text{CO(g)} \rightarrow \text{NO(g)} + \text{CO}_2\text{(g)}$:

Step 1: $\text{NO}_2\text{(g)} + \text{NO}_2\text{(g)} \rightarrow \text{NO}_3\text{(g)} + \text{NO(g)}$ (slow)
Step 2: $\text{NO}_3\text{(g)} + \text{CO(g)} \rightarrow \text{NO}_2\text{(g)} + \text{CO}_2\text{(g)}$ (fast)

Which of the following rate laws is consistent with the proposed mechanism, and why?

Accepted Answer

$\text{Rate} = k [\text{NO}_2]^2$, because Step 1 is the slow rate-determining step and its rate depends on the bimolecular collision of two $\text{NO}_2$ reactant molecules.

Answer

$\text{Rate} = k [\text{NO}_2][\text{CO}]$, because the reaction orders in the rate law must match the stoichiometric coefficients of the reactants in the overall balanced equation.

Answer

$\text{Rate} = k [\text{NO}_2][\text{CO}]$, because $\text{CO}$ is a reactant in Step 2, which rapidly converts the intermediate $\text{NO}_3$ into products.

Answer

$\text{Rate} = k [\text{NO}_2]^2$, because $\text{NO}_2$ acts as a catalyst that is consumed in Step 1 and regenerated in Step 2.

Question 10

A student investigates the kinetics of the reaction between solid calcium carbonate and hydrochloric acid, represented by the balanced equation below:

$$\text{CaCO}_3\text{(s)} + 2\text{HCl(aq)} \rightarrow \text{CaCl}_2\text{(aq)} + \text{H}_2\text{O(l)} + \text{CO}_2\text{(g)}$$

In Trial 1, the student adds a single $2.0 \text{ g}$ chip of $\text{CaCO}_3\text{(s)}$ to $50.0 \text{ mL}$ of $1.0 \text{ M HCl(aq)}$ at $25^\circ\text{C}$ and measures the initial rate of $\text{CO}_2\text{(g)}$ production. In Trial 2, the student repeats the experiment using $2.0 \text{ g}$ of finely powdered $\text{CaCO}_3\text{(s)}$ with $50.0 \text{ mL}$ of $1.0 \text{ M HCl(aq)}$ at $25^\circ\text{C}$. Which of the following best predicts and explains the effect of using powdered $\text{CaCO}_3\text{(s)}$ on the initial reaction rate?

Accepted Answer

The initial rate increases because crushing the solid exposes a greater surface area, increasing the frequency of collisions per unit time between $\text{H}^+\text{(aq)}$ ions and $\text{CaCO}_3\text{(s)}$.

Answer

The initial rate increases because crushing the solid increases the average kinetic energy of the $\text{CaCO}_3\text{(s)}$ particles, increasing the fraction of collisions with energy equal to or greater than $E_a$.

Answer

The initial rate remains unchanged because the mass of $\text{CaCO}_3\text{(s)}$, temperature, and initial concentration of $\text{HCl(aq)}$ are identical in both trials.

Answer

The initial rate decreases because smaller particles have less mass per particle, which reduces the force of collision upon impact with $\text{H}^+\text{(aq)}$ ions.

Question 11

A student investigates the kinetics of the gas-phase reaction $2\text{ NO}_2(g) \rightarrow 2\text{ NO}(g) + \text{O}_2(g)$ at a constant temperature. Based on experimental data, the reaction is determined to be second order with respect to $\text{NO}_2(g)$. The student collects the data shown in the table below.

| Trial | Initial $[\text{NO}_2]$ (M) | Initial Rate of Consumption of $\text{NO}_2$ (M/s) |
|---|---|---|
| 1 | 0.20 | $1.2 \times 10^{-3}$ |
| 2 | 0.40 | ? |

Which of the following best predicts the initial rate of consumption of $\text{NO}_2(g)$ in Trial 2 and provides the correct justification?

Accepted Answer

The initial rate will be $4.8 \times 10^{-3}\text{ M/s}$ because doubling the concentration of a second-order reactant increases the reaction rate by a factor of $2^2$.

Answer

The initial rate will be $4.8 \times 10^{-3}\text{ M/s}$ because two moles of $\text{NO}_2(g)$ react for every one mole of $\text{O}_2(g)$ produced.

Answer

The initial rate will be $2.4 \times 10^{-3}\text{ M/s}$ because the rate of a reaction is directly proportional to the reactant concentration.

Answer

The initial rate will be $2.4 \times 10^{-3}\text{ M/s}$ because the stoichiometric coefficient of $\text{NO}_2(g)$ in the balanced chemical equation is 2.

Question 12

A student studies the decomposition of hydrogen peroxide in an antimicrobial rinse at constant temperature. Under the experimental conditions, the reaction follows first-order kinetics.

$2\text{H}_2\text{O}_2\text{(aq)} \rightarrow 2\text{H}_2\text{O(l)} + \text{O}_2\text{(g)}$

| Time (min) | $[\text{H}_2\text{O}_2]$ (M) |
|------------|----------------------------------|
| 0.0        | $0.800$                        |
| 14.0       | $0.400$                        |

What is the concentration of $\text{H}_2\text{O}_2\text{(aq)}$ after $42.0\text{ min}$?

Accepted Answer

$0.100\text{ M}$

Answer

$0.0500\text{ M}$

Answer

$0.200\text{ M}$

Answer

$0.400\text{ M}$

Question 13

A student investigates the elementary gas-phase reaction between carbon monoxide and nitrogen dioxide, represented by the equation below.

$\text{CO(g)} + \text{NO}_2\text{(g)} \rightarrow \text{CO}_2\text{(g)} + \text{NO(g)}$

The reaction occurs via a single bimolecular collision in which a carbon-oxygen bond is formed and a nitrogen-oxygen bond is broken. Which of the following particulate representations best shows a collision orientation that can lead to the formation of products?

Accepted Answer

Diagram C

Answer

Diagram A

Answer

Diagram B

Answer

Diagram D

Question 14

A student investigates the kinetics of the gas-phase reaction represented by the equation 2 $\text{NO(g)}$ + $\text{Cl}_2\text{(g)}$ $\rightarrow$ 2 $\text{NOCl(g)}$. The initial-rate data collected from three experimental trials at 298 K are shown in the table below.

| Trial | Initial $[\text{NO}]$ (M) | Initial $[\text{Cl}_2]$ (M) | Initial rate of formation of $\text{NOCl}$ (M/s) |
|---|---|---|---|
| 1 | 0.10 | 0.10 | $1.2 \times 10^{-3}$ |
| 2 | 0.20 | 0.10 | $4.8 \times 10^{-3}$ |
| 3 | 0.10 | 0.30 | $3.6 \times 10^{-3}$ |

Based on these data, what is the value and units of the specific rate constant, $k$, for the reaction?

Accepted Answer

$1.2 \text{ M}^{-2}\text{s}^{-1}$

Answer

$1.2 \text{ M}^{-1}\text{s}^{-1}$

Answer

$12 \text{ M}^{-2}\text{s}^{-1}$

Answer

$12 \text{ M}^{-1}\text{s}^{-1}$

Question 15

A student investigates the rate at which dissolved ozone, $\text{O}_3\text{(aq)}$, oxidizes a hypothetical dissolved contaminant, $\text{P(aq)}$. The student obtains the following initial-rate data at constant temperature.

| Trial | $[\text{P}]$ (M) | $[\text{O}_3]$ (M) | Initial rate (M/s) |
|-------|---------------------|-------------------------|--------------------|
| 1     | 0.010               | 0.060                   | $6.0 \times 10^{-5}$ |
| 2     | 0.030               | 0.020                   | $1.8 \times 10^{-4}$ |
| 3     | 0.030               | 0.060                   | $5.4 \times 10^{-4}$ |

Which of the following rate laws is consistent with the data?

Accepted Answer

$\text{rate}=k[\text{P}]^2[\text{O}_3]$

Answer

$\text{rate}=k[\text{P}][\text{O}_3]$

Answer

$\text{rate}=k[\text{P}][\text{O}_3]^2$

Answer

$\text{rate}=k[\text{P}]^2[\text{O}_3]^2$

Question 16

A student tests a powdered substance, $\text{Z}$, that increases the rate at which residual hydrogen peroxide decomposes in treated water.

$$
2\text{H}_2\text{O}_2\text{(aq)} \rightarrow 2\text{H}_2\text{O(l)}+\text{O}_2\text{(g)}
$$

The student wants to determine whether $\text{Z}$ acts as a catalyst rather than as a reactant that is consumed. Which additional experimental result would provide the strongest evidence that $\text{Z}$ is a catalyst?

Accepted Answer

After each trial, $\text{Z}$ is recovered with the same mass and composition within experimental uncertainty and produces the same rate enhancement when reused with fresh $\text{H}_2\text{O}_2\text{(aq)}$.

Answer

When the initial mass of $\text{Z}$ is doubled at constant temperature and hydrogen peroxide concentration, the initial rate doubles and the same volume of $\text{O}_2\text{(g)}$ is eventually collected.

Answer

An Arrhenius plot gives a smaller apparent activation energy when $\text{Z}$ is present, and the measured rate constant is greater at every temperature tested.

Answer

For equal initial amounts of $\text{H}_2\text{O}_2\text{(aq)}$, the total amount of $\text{O}_2\text{(g)}$ collected is the same with or without $\text{Z}$, although the trial containing $\text{Z}$ finishes sooner.

Question 17

A student studies an aqueous reaction that degrades a food dye. The student performs the reaction at both $295\text{ K}$ and $315\text{ K}$, using the same initial reactant concentrations and no catalyst. The molecular kinetic-energy distributions are represented in the graph, where $E_a$ is the activation energy for the reaction.

Which statement best predicts and explains the effect of increasing the temperature from $295\text{ K}$ to $315\text{ K}$ on the initial reaction rate?

Accepted Answer

The initial rate increases because a larger fraction of collisions at $315\text{ K}$ have enough energy to overcome the unchanged $E_a$.

Answer

The initial rate decreases because the lower maximum of the $315\text{ K}$ distribution indicates that fewer reactant particles are moving.

Answer

The initial rate decreases because the $315\text{ K}$ distribution has fewer particles with kinetic energies below $E_a$.

Answer

The initial rate increases because heating lowers $E_a$, allowing more collisions to overcome the energy barrier.

Question 18

At a particular temperature, the reaction

$2\text{SO}_2\text{(g)}+\text{O}_2\text{(g)}\rightleftharpoons2\text{SO}_3\text{(g)}$

is at equilibrium in a sealed, rigid vessel. A small amount of solid $\text{V}_2\text{O}_5$, which acts as a catalyst and has negligible volume, is added while the temperature remains constant. Which choice correctly predicts both the forward and reverse reaction rates immediately after the catalyst is added and the partial pressure of $\text{SO}_3\text{(g)}$ after sufficient time?

Accepted Answer

Forward and reverse rates: both increase and remain equal; final $P_{\text{SO}_3}$: unchanged

Answer

Forward and reverse rates: both decrease and remain equal; final $P_{\text{SO}_3}$: increases

Answer

Forward and reverse rates: both decrease and remain equal; final $P_{\text{SO}_3}$: unchanged

Answer

Forward and reverse rates: both increase and remain equal; final $P_{\text{SO}_3}$: increases

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