Chemical Kinetics Set-1

Q1. A substance X decomposes via first-order kinetics with rate constant $k = 1.5\times10^{-3}\ \mathrm{s^{-1}}$. What percentage of X remains after $1.0\ \mathrm{h}$ ($3600\ \mathrm{s}$)?

Q2. For the reaction $2A + B \rightarrow$ products the initial rate data are: Experiment 1: $[A]=0.10\ \mathrm{M}$, $[B]=0.10\ \mathrm{M}$, rate $=2.0\times10^{-3}\ \mathrm{M\,s^{-1}}$; Experiment 2: $[A]=0.20\ \mathrm{M}$, $[B]=0.10\ \mathrm{M}$, rate $=8.0\times10^{-3}\ \mathrm{M\,s^{-1}}$; Experiment 3: $[A]=0.10\ \mathrm{M}$, $[B]=0.20\ \mathrm{M}$, rate $=4.0\times10^{-3}\ \mathrm{M\,s^{-1}}$. Determine the rate law and the value of the rate constant $k$ (with units).

Q3. Using the Arrhenius equation $k = A e^{-E_a/(RT)}$, the rate constants for a reaction are measured as $k_1=2.0\times10^{-4}\ \mathrm{s^{-1}}$ at $T_1=300\ \mathrm{K}$ and $k_2=6.0\times10^{-4}\ \mathrm{s^{-1}}$ at $T_2=320\ \mathrm{K}$. Estimate the activation energy $E_a$ in $\mathrm{kJ\,mol^{-1}}$ (use $R=8.314\ \mathrm{J\,mol^{-1}K^{-1}}$).

Q4. For consecutive first-order reactions $A\overset{k_1}{\rightarrow}B\overset{k_2}{\rightarrow}C$ with $[A]_0=1.00\ \mathrm{M}$ and $[B]_0=0$, the time at which $[B]$ is maximum is given by

Calculate $t_{\max}$ (in s) for $k_1=0.10\ \mathrm{s^{-1}}$ and $k_2=0.02\ \mathrm{s^{-1}}$.

Q5. Consider the reversible first-order reaction $A\overset{k_1}{\rightleftharpoons}\overset{k_{-1}}{ }B$ with $k_1=0.50\ \mathrm{s^{-1}}$, $k_{-1}=0.30\ \mathrm{s^{-1}}$, and initial concentrations $[A]_0=1.00\ \mathrm{M}$, $[B]_0=0$. Using the integrated solution

calculate the time $t$ (in s) when $[A](t)=0.600\ \mathrm{M}$.

Q6. A first-order reaction A → products has its concentration fall to $60\%$ of the initial value in $10\ \mathrm{s}$. Using the integrated rate law $[A]=[A]_0e^{-kt}$, how long will it take for $[A]$ to fall to $10\%$ of $[A]_0$?

Q7. The rate constant $k$ for a reaction doubles when the temperature is raised from $298\ \mathrm{K}$ to $308\ \mathrm{K}$. Using the Arrhenius equation $k=Ae^{-E_a/(RT)}$ and $R=8.314\ \mathrm{J\,mol^{-1}K^{-1}}$, the activation energy $E_a$ is approximately:

Q8. For the reaction $2A+B\rightarrow$ products the initial rate data are:
Experiment 1: $[A]=0.10\ \mathrm{M},\ [B]=0.10\ \mathrm{M},\ \text{rate}=2.00\times10^{-5}\ \mathrm{M\,s^{-1}}$
Experiment 2: $[A]=0.20\ \mathrm{M},\ [B]=0.10\ \mathrm{M},\ \text{rate}=8.00\times10^{-5}\ \mathrm{M\,s^{-1}}$
Experiment 3: $[A]=0.10\ \mathrm{M},\ [B]=0.20\ \mathrm{M},\ \text{rate}=4.00\times10^{-5}\ \mathrm{M\,s^{-1}}$
From these data determine the numerical value and units of the rate constant $k$ in $rate=k[A]^x[B]^y$.

Q9. For the bimolecular reaction $A+B\rightarrow$ products with rate law $rate=k[A][B]$, the rate constant is $k=0.50\ \mathrm{M^{-1}s^{-1}}$. If initially $[A]_0=0.050\ \mathrm{M}$ and $[B]_0=0.150\ \mathrm{M}$, how long will it take for $[A]$ to decrease to $0.010\ \mathrm{M}$? (Use the integrated form for $1:1$ stoichiometry.)

Q10. Consider the catalytic mechanism:

Given $K=1.0\times10^4\ \mathrm{M^{-1}}$, $k_2=10\ \mathrm{s^{-1}}$ and $[X]_0=1.0\times10^{-4}\ \mathrm{M}$, the initial rate is $v_0=\dfrac{k_2K[X]_0[A]}{1+K[A]}$. Calculate $v_0$ and the apparent order with respect to $[A]$ for (i) $[A]=1.0\times10^{-6}\ \mathrm{M}$ and (ii) $[A]=1.0\times10^{-2}\ \mathrm{M}$.