Practice Questions

Examine the following rate constant value and identify the overall order of the reaction: $k = 3.5 \times 10^{-4} \text{ mol}^{-1} \text{ L s}^{-1}$.

Define the instantaneous rate of a chemical reaction.

Propose a justification for why elementary reactions with a molecularity greater than three are exceedingly rare.

Compare how the half-life ($t_{1/2}$) of a reaction depends on the initial concentration of the reactant, $[R]_0$, for a zero-order reaction versus a first-order reaction.

A first-order reaction has a rate constant of $1.15 \times 10^{-3} \text{ s}^{-1}$. Calculate the half-life ($t_{1/2}$) of this reaction.

Justify why the molecularity of a chemical reaction cannot be zero, a fraction, or a negative number.

Identify the key difference between an elementary reaction and a complex reaction.

Name two factors that influence the rate of a chemical reaction.

Recall the integrated rate equation for a first-order reaction.

List the units of the rate constant (k) for zero-order, first-order, and second-order reactions, assuming concentration is in $\text{mol L}^{-1}$ and time is in seconds.

Define activation energy ($E_a$) and explain its role in a chemical reaction.

Summarize the main points of the collision theory of chemical reactions.

Explain the difference between the molecularity and the order of a reaction.

The hydrolysis of ethyl acetate ($CH_3COOC_2H_5$) in an aqueous solution is a second-order reaction, but it behaves as a pseudo-first-order reaction. Calculate the value of the pseudo-first-order rate constant if the true second-order rate constant is $2.0 \times 10^{-3} \text{ L mol}^{-1} \text{s}^{-1}$ and the concentration of water is taken as a constant $55.5 \text{ mol L}^{-1}$.

Critique the Arrhenius equation, $k = A e^{-E_a/RT}$. While it effectively models the temperature dependence of the rate constant, what crucial physical aspect of a chemical reaction is represented implicitly by the pre-exponential factor, A, which is later made explicit by collision theory?

For the reaction $2N_2O_5(g) \rightarrow 4NO_2(g) + O_2(g)$, the concentration of $N_2O_5$ decreases from $1.20 \times 10^{-2} \text{ mol L}^{-1}$ to $0.80 \times 10^{-2} \text{ mol L}^{-1}$ in 10 minutes. Calculate the average rate of this reaction and the average rate of formation of $NO_2$ during this interval.

Analyze the following experimental data for the reaction $A + 2B \rightarrow C$ and determine the rate law and the overall order of the reaction.

Compare and contrast the molecularity and the order of a reaction by providing two distinct points of difference.

Examine the role of a catalyst in a chemical reaction by explaining its effect on the activation energy and the overall Gibbs free energy change ($\Delta G$) of the reaction.

A reaction has the rate law: Rate $= k[X]^2[Y]$. Analyze how the rate of reaction is affected if: (a) the concentration of Y is doubled, keeping X constant. (b) the concentrations of both X and Y are doubled.

For a zero-order reaction $R \rightarrow P$, demonstrate the derivation of the integrated rate equation. Also, analyze the graphical plot of reactant concentration $[R]$ versus time $t$ and state what the slope and intercept represent.

A first-order reaction has a rate constant, $k = 5.5 \times 10^{-14} \text{ s}^{-1}$. Recall the formula and calculate the half-life of this reaction.

For the reaction $2N_2O_5(g) \rightarrow 4NO_2(g) + O_2(g)$, explain how the rate of reaction is expressed in terms of the change in concentration of each reactant and product.

Critique the statement: 'For any chemical reaction, the order of reaction is always equal to the sum of the stoichiometric coefficients of the reactants in the balanced chemical equation.' Justify your position with an example.

Recall the Arrhenius equation and name each variable in it.

Evaluate the limitations of the simple collision theory. Propose how the theory is modified to better align with experimental observations for reactions involving complex molecules.

A student proposes that the rate of decomposition of hydrogen peroxide, $2H_2O_2(aq) \rightarrow 2H_2O(l) + O_2(g)$, is second order with respect to $H_2O_2$ because its stoichiometric coefficient is 2. Critique this reasoning and justify the correct approach to determine the order of this reaction.

Formulate the integrated rate law for a zero-order reaction $R \rightarrow P$ and justify why its half-life depends on the initial concentration of the reactant, in contrast to a first-order reaction.

The hydrolysis of an ester like ethyl acetate in an acidic medium is technically a second-order reaction. Formulate the specific experimental conditions under which this reaction can be treated as a pseudo-first-order reaction and justify your reasoning.

For a first-order reaction, formulate a mathematical proof to show that the time required for $99.9\%$ completion is approximately 10 times the half-life ($t_{1/2}$). Evaluate the practical significance of this finding.

Propose a graphical method to distinguish between a zero-order and a first-order reaction. Describe the specific plots you would create from concentration versus time data and explain how the slope and intercept of each plot would confirm the reaction order.

Define the order of a reaction and identify the overall order for a reaction with the rate law: Rate $= k[A]^{3/2}[B]^{-1}$.

Design a plausible two-step reaction mechanism for the overall reaction $2A + B \rightarrow C + D$, given that the experimentally determined rate law is Rate $= k[A][B]$. Justify that your proposed mechanism is consistent with both the overall stoichiometry and the observed rate law.

A chemical process has an activation energy $E_a = 80 \text{ kJ mol}^{-1}$. Evaluate whether it is more effective to increase its rate by increasing the temperature from $300 \text{ K}$ to $310 \text{ K}$ or by using a catalyst that lowers the activation energy by $20 \text{ kJ mol}^{-1}$ at $300 \text{ K}$. Justify your conclusion quantitatively. (Use $R = 8.314 \text{ J K}^{-1} \text{mol}^{-1}$)

Explain how a catalyst increases the rate of a reaction, using a potential energy diagram as a reference.

Describe what is meant by a 'pseudo first-order reaction' and name an example.

Analyze the following two-step mechanism for the decomposition of ozone: Step 1: $O_3(g) \rightleftharpoons O_2(g) + O(g)$ (fast, equilibrium) Step 2: $O(g) + O_3(g) \rightarrow 2O_2(g)$ (slow) From this mechanism, derive the rate law for the overall reaction $2O_3(g) \rightarrow 3O_2(g)$.

The thermal decomposition of sulfuryl chloride ($SO_2Cl_2$) is a first-order gas-phase reaction: $SO_2Cl_2(g) \rightarrow SO_2(g) + Cl_2(g)$. At 600 K, the initial pressure of $SO_2Cl_2$ in a closed container is $0.50$ atm. After 100 seconds, the total pressure of the system is $0.60$ atm. Calculate the rate constant ($k$) for this reaction.

A first-order reaction is $40\%$ complete in 50 minutes. Calculate the time it will take for the reaction to be $80\%$ complete.

For a first-order reaction, the rate constant is $k = 4.606 \times 10^{-3} \text{ s}^{-1}$. If the initial concentration of the reactant is $1.0 \text{ mol L}^{-1}$, calculate: (a) The concentration of the reactant remaining after 100 s. (b) The time required for $75\%$ of the reaction to be completed.

Propose a two-step mechanism for the reaction $2NO_2(g) + F_2(g) \rightarrow 2NO_2F(g)$, for which the experimentally determined rate law is Rate $= k[NO_2][F_2]$. Justify which step in your proposed mechanism is the rate-determining step.

Design a series of experiments using the initial rates method to determine the rate law for the reaction: $A + 2B \rightarrow C$. Describe the data you would collect and formulate the process for analyzing this data to find the order with respect to A, the order with respect to B, and the overall rate constant $k$.

The decomposition of ammonia on a hot platinum surface, $2NH_3(g) \xrightarrow{Pt} N_2(g) + 3H_2(g)$, is observed to be a zero-order reaction at high pressures. Create a conceptual model to justify this observation.

The rate constant of a reaction is $1.5 \times 10^{-4} \text{ s}^{-1}$ at $27^\circ\text{C}$ and $3.0 \times 10^{-4} \text{ s}^{-1}$ at $37^\circ\text{C}$. Calculate the activation energy ($E_a$) for this reaction. (Given: $R = 8.314 \text{ J K}^{-1} \text{mol}^{-1}$)