Chemical Kinetics Set-1

Q1. For the first-order reaction $A \xrightarrow{k} \text{products}$ with $k = 2.0\times10^{-3}\ \text{s}^{-1}$, the time required for $90\%$ of $A$ to be consumed is approximately

Q2. For the bimolecular reaction $A + B \rightarrow$ products with rate law $r = k[A][B]$ and $k = 0.10\ \text{M}^{-1}\text{s}^{-1}$, if $[B]_0 = 1.00\ \text{M}$ (large excess) and $[A]_0 = 0.050\ \text{M}$, treating $[B]$ as constant, the time required for $[A]$ to decrease to $0.025\ \text{M}$ is

Q3. Initial rate measurements for the reaction $2A + B \rightarrow$ products give:
Experiment 1: $[A]_0=0.10\ \text{M},\ [B]_0=0.10\ \text{M},\ \text{rate}=2.0\times10^{-4}\ \text{M s}^{-1}$;
Experiment 2: $[A]_0=0.20\ \text{M},\ [B]_0=0.10\ \text{M},\ \text{rate}=8.0\times10^{-4}\ \text{M s}^{-1}$;
Experiment 3: $[A]_0=0.10\ \text{M},\ [B]_0=0.20\ \text{M},\ \text{rate}=4.0\times10^{-4}\ \text{M s}^{-1}$.
The rate law and value of the rate constant $k$ (with appropriate units) are:

Q4. For the consecutive first-order reactions $A \xrightarrow{k_1} B \xrightarrow{k_2} C$ with $k_1 = 0.10\ \text{s}^{-1}$ and $k_2 = 0.40\ \text{s}^{-1}$, and initial concentrations $[A]_0=1.0\ \text{M},\ [B]_0=[C]_0=0$, the time at which $[B]$ reaches its maximum is approximately

Q5. Consider the mechanism for the overall reaction $A + 2B \rightarrow P$:
(1) $A + B \xrightleftharpoons[k_{-1}]{k_1} I$
(2) $I + B \xrightarrow{k_2} P$
Given $k_1 = 1.0\times10^{6}\ \text{M}^{-1}\text{s}^{-1}$, $k_{-1}=1.0\times10^{3}\ \text{s}^{-1}$, $k_2 = 1.0\times10^{4}\ \text{M}^{-1}\text{s}^{-1}$, use the steady-state approximation for intermediate $I$. Which statement is correct?

Q6. A first‑order reaction has a half‑life $t_{1/2}=2.00\times10^{3}\ \text{s}$. How long is required for $90\%$ of the reactant to be consumed?

Q7. For the reaction $A + 2B \rightarrow$ products the initial rate data are:
Experiment 1: $[A]_0=0.10\ \text{M},\ [B]_0=0.10\ \text{M},\ r_1=2.0\times10^{-4}\ \text{M s}^{-1}$;
Experiment 2: $[A]_0=0.20\ \text{M},\ [B]_0=0.10\ \text{M},\ r_2=4.0\times10^{-4}\ \text{M s}^{-1}$;
Experiment 3: $[A]_0=0.10\ \text{M},\ [B]_0=0.20\ \text{M},\ r_3=8.0\times10^{-4}\ \text{M s}^{-1}$.
Which rate law fits the data and what is the value of $k$ (with units)?

Q8. For consecutive first‑order reactions $A \xrightarrow{k_1} B \xrightarrow{k_2} C$ with $k_1=1.0\times10^{-3}\ \text{s}^{-1}$ and $k_2=3.0\times10^{-3}\ \text{s}^{-1}$, at what time $t$ is the concentration of intermediate $B$ maximum?

Q9. Consider the bimolecular reaction $A + B \rightarrow$ products with rate law $r=k[A][B]$ where $k=0.02\ \text{M}^{-1}\text{s}^{-1}$. If $[A]_0=0.100\ \text{M}$ and $[B]_0=0.300\ \text{M}$, how long will it take for $[A]$ to decrease to $0.010\ \text{M}$? (Use the integrated expression for unequal initial concentrations.)

Q10. The rate constants for a certain reaction are $k_1=1.5\times10^{-3}\ \text{s}^{-1}$ at $T_1=300\ \text{K}$ and $k_2=6.0\times10^{-3}\ \text{s}^{-1}$ at $T_2=320\ \text{K}$. Using the Arrhenius relation $k=Ae^{-E_a/RT}$, the activation energy $E_a$ (in kJ mol$^{-1}$) is closest to:

Q11. For the reaction $A + B \rightarrow$ products, experiments show that when $[A]$ is doubled (with $[B]$ constant) the initial rate increases fourfold, and when $[B]$ is doubled (with $[A]$ constant) the initial rate doubles. Which rate law and overall order is consistent with these observations?

Q12. The bimolecular reaction with rate law $r = k[A][B]$ is studied under pseudo-first-order conditions by keeping $[B]$ constant at $0.10\ \mathrm{M}$. Initially $[A]_0 = 0.100\ \mathrm{M}$ and after $100\ \mathrm{s}$ $[A]$ falls to $0.025\ \mathrm{M}$. Using the pseudo-first-order approximation, how long (in seconds) will it take for $[A]$ to decrease from $0.100\ \mathrm{M}$ to $0.005\ \mathrm{M}$?

Q13. Consider the mechanism: (1) $A + B \rightleftharpoons P$ (fast equilibrium; $k_1 = 2.0\ \mathrm{L\,mol^{-1}s^{-1}}$, $k_{-1} = 10.0\ \mathrm{s^{-1}}$), (2) $P \xrightarrow{k_2}$ products (slow; $k_2 = 1.0\ \mathrm{s^{-1}}$). If $[A]_0 = [B]_0 = 1.00\ \mathrm{M}$, what is the initial rate $r_0$ (in $\mathrm{M\,s^{-1}}$)?

Q14. For the mechanism $A \xrightarrow{k_1} I$, $I + B \xrightarrow{k_2} P$, $I \xrightarrow{k_3} R$, applying the steady-state approximation for intermediate $I$ yields the rate law $r = \dfrac{k_1 k_2 [A][B]}{k_3 + k_2 [B]}$. Which statement correctly describes the order of reaction with respect to $B$ in the indicated limits?

Q15. A first-order reaction has half-life $t_{1/2} = 120\ \mathrm{s}$ at $T_1 = 300\ \mathrm{K}$. The activation energy is $E_a = 50.0\ \mathrm{kJ\,mol^{-1}}$. Assuming Arrhenius behaviour $k = A e^{-E_a/RT}$ with temperature-independent $A$, estimate the half-life at $T_2 = 320\ \mathrm{K}$ (to three significant figures).