Chemical Kinetics Set-2

Q1. A first-order decomposition has rate constant $k=3.0\times10^{-3}\ \mathrm{s^{-1}}$. What fraction of the original substance remains after $5.0\ \mathrm{min}$? (Use $[A]=[A]_0e^{-kt}$.)

Q2. The reaction $A+B\rightarrow P$ follows $r=k[A][B]$. In an experiment $[B]$ is kept in large excess at $0.20\ \mathrm{M}$ giving an observed pseudo-first-order rate constant $k' = 6.0\times10^{-4}\ \mathrm{s^{-1}}$. If $[A]_0=0.100\ \mathrm{M}$, how long (in minutes) will $[A]$ take to decrease to $0.025\ \mathrm{M}$? (Use $[A]=[A]_0e^{-k't}$.)

Q3. For the mechanism
$NO_2 + CO \xrightleftharpoons[k_{-1}]{k_1} NO_2CO\ (\text{fast equilibrium})$ \
$NO_2CO \xrightarrow{k_2} NO + CO_2\ (\text{slow})$,
with $k_1=1.0\times10^6\ \mathrm{M^{-1}s^{-1}}$, $k_{-1}=2.0\times10^4\ \mathrm{s^{-1}}$, $k_2=5.0\times10^2\ \mathrm{s^{-1}}$, and initial $[NO_2]=1.0\times10^{-3}\ \mathrm{M}$, $[CO]=2.0\times10^{-3}\ \mathrm{M}$, calculate the initial rate of product formation (use pre-equilibrium approximation).

Q4. For the bimolecular reaction $A+B\rightarrow$ products with rate $r=k[A][B]$, initial $[A]_0=0.012\ \mathrm{M}$ and $[B]_0=0.048\ \mathrm{M}$. If $k=50\ \mathrm{M^{-1}s^{-1}}$, how long does it take for $[A]$ to fall to $0.003\ \mathrm{M}$? (Use the integrated relation for unequal initial concentrations with $\Delta=[B]_0-[A]_0$:

)

Q5. Assertion (A): For a second-order reaction with rate law $r=k[A]^2$, the half-life is $t_{1/2}=\dfrac{1}{k[A]_0}$ (i.e., $t_{1/2}\propto 1/[A]_0$).
Reason (R): The units of the rate constant $k$ for a second-order reaction are $\mathrm{M^{-1}s^{-1}}$.

Q6. A reaction follows first-order kinetics with half-life $t_{1/2}=30\ \text{min}$. If the initial concentration is $[A]_0=0.80\ \mathrm{M}$, what is the concentration $[A]$ after $90\ \text{min}$? (Use $t_{1/2}=\ln2/k$ and $[A]=[A]_0e^{-kt}$.)