Chemical Kinetics Set-9

Q1. Consider the bimolecular reaction $A + B \rightarrow$ products with rate law $\text{rate}=k[A][B]$. In an experiment $[B]$ is held constant at $0.50\ \mathrm{M}$ so the reaction follows pseudo-first-order kinetics with observed rate constant $k_{\mathrm{obs}}=0.040\ \mathrm{s^{-1}}$. Determine the true rate constant $k$ and its units.

Q2. The initial rates for a reaction were measured:
Experiment 1: $[A]=0.10\ \mathrm{M},\ [B]=0.10\ \mathrm{M},\ \text{rate}=1.0\times10^{-4}\ \mathrm{M\,s^{-1}}$
Experiment 2: $[A]=0.20\ \mathrm{M},\ [B]=0.10\ \mathrm{M},\ \text{rate}=4.0\times10^{-4}\ \mathrm{M\,s^{-1}}$
Experiment 3: $[A]=0.20\ \mathrm{M},\ [B]=0.20\ \mathrm{M},\ \text{rate}=8.0\times10^{-4}\ \mathrm{M\,s^{-1}}$. Determine the empirical rate law and the numerical value of the rate constant $k$ with units.

Q3. For a reaction the rate constants are $k_1=1.0\times10^{-4}\ \mathrm{s^{-1}}$ at $T_1=300\ \mathrm{K}$ and $k_2=3.0\times10^{-4}\ \mathrm{s^{-1}}$ at $T_2=310\ \mathrm{K}$. Using the Arrhenius equation, estimate the activation energy $E_a$ in $\mathrm{kJ\,mol^{-1}}$. (Use $R=8.314\ \mathrm{J\,mol^{-1}K^{-1}}$.)

Q4. The reversible first-order reaction $A \rightleftharpoons B$ has forward rate constant $k_f=0.020\ \mathrm{s^{-1}}$. At equilibrium $[B]_{\text{eq}}/[A]_{\text{eq}}=3$. If initially $[A]_0=1.00\ \mathrm{M}$ and $[B]_0=0$, how long (in seconds) will it take for $[A](t)$ to satisfy $[A](t)-[A]_{\text{eq}}=0.10\bigl([A]_0-[A]_{\text{eq}}\bigr)$ (i.e., to be within 10% of the initial-to-equilibrium distance)?

Q5. For consecutive first-order reactions $A \xrightarrow{k_1} B \xrightarrow{k_2} C$ with $k_1=0.02\ \mathrm{s^{-1}}$ and $k_2=0.06\ \mathrm{s^{-1}}$, and initial $[A]_0=1.00\ \mathrm{M}$ ($[B]_0=[C]_0=0$), at what time $t$ (in s) does $[B]$ attain its maximum value?

Q6. For a first-order reaction with half-life $t_{1/2}=30\ \mathrm{min}$, how long will it take for $87.5\%$ of the reactant to be consumed?

Q7. Consider the bimolecular reaction $A + B \rightarrow \text{products}$ that follows the rate law $r = k[A][B]$. When $[B]$ is kept in large excess the reaction is pseudo-first-order in $A$. In two experiments with initial $[B]_0=1.0\ \mathrm{M}$ and $3.0\ \mathrm{M}$ the measured half-lives of $A$ are $100\ \mathrm{s}$ and $33.3\ \mathrm{s}$ respectively. The true rate constant $k$ (in $\mathrm{M^{-1}s^{-1}}$) is closest to:

Q8. For the reaction $2A + B \rightarrow P$ initial rate measurements show: when $[A]$ is doubled (with $[B]$ constant) the rate becomes four times; when $[B]$ is doubled (with $[A]$ constant) the rate doubles. In an experiment with $[A]=0.10\ \mathrm{M}$ and $[B]=0.20\ \mathrm{M}$ the initial rate is $2.0\times10^{-3}\ \mathrm{M\,s^{-1}}$. The rate constant $k$ (in $\mathrm{M^{-2}s^{-1}}$) and the overall order of the reaction are:

Q9. Consider consecutive first-order reactions $A \xrightarrow{k_1} B \xrightarrow{k_2} C$. Assertion (A): If $k_2 \gg k_1$ then the intermediate $B$ attains a quasi-steady (approximately constant) low concentration during much of the reaction. Reason (R): When $k_2 \gg k_1$, $B$ is consumed rapidly as it forms, so $\dfrac{d[B]}{dt}\approx 0$ and $[B]\approx\dfrac{k_1}{k_2}[A]$, which explains the quasi-steady low concentration.

Q10. According to the Arrhenius equation $k=Ae^{-E_a/RT}$, for a certain reaction the rate constant increases by a factor of $3$ when the temperature is raised from $300\ \mathrm{K}$ to $320\ \mathrm{K}$. The activation energy $E_a$ (in $\mathrm{kJ\ mol^{-1}}$) is nearest to:

Q11. A first-order decomposition of A has rate constant $k=5.0\times10^{-3}\ \mathrm{s}^{-1}$. Using $[A]=[A]_0e^{-kt}$, how long will it take for 80% of A to be consumed?

Q12. The reaction $A+B\to\text{products}$ follows the rate law $r=k[A][B]$. If $[A]_0=0.010\ \mathrm{M}$ and $[B]_0=0.50\ \mathrm{M}$ (so $[B]$ remains effectively constant) and $k=0.20\ \mathrm{M}^{-1}\mathrm{s}^{-1}$, how long will it take for $[A]$ to decrease to $10\%$ of its initial value? (Treat it as pseudo-first-order.)

Q13. A reaction obeys $r=k[A]^n$. The time required for $[A]$ to fall from $0.40\ \mathrm{M}$ to $0.20\ \mathrm{M}$ is $20\ \mathrm{s}$, while the time to fall from $0.20\ \mathrm{M}$ to $0.10\ \mathrm{M}$ is $10\ \mathrm{s}$. What is the order $n$ of the reaction?

Q14. For the bimolecular reaction $A+B\to\text{products}$ with rate law $r=k[A][B]$, initial concentrations $[A]_0=0.10\ \mathrm{M}$, $[B]_0=0.30\ \mathrm{M}$ and $k=0.05\ \mathrm{M}^{-1}\mathrm{s}^{-1}$, calculate the time required for $[A]$ to decrease to $0.05\ \mathrm{M}$. (Use the integrated form for unequal initial concentrations.)

Q15. Experimental studies show the initial rate of decomposition of A varies as $r\propto[A]^{3/2}$. Which mechanism below most plausibly explains this fractional order? (Assume steady-state for radical species; $R\cdot$ denotes a radical.)