Chemical Kinetics Set-7

Q1. A reaction follows first-order kinetics with rate constant $k=1.2\times10^{-3}\ \mathrm{s^{-1}}$. How long will it take for the concentration to fall to $10\%$ of its initial value? Use $[A]_t=[A]_0e^{-kt}$.

Q2. The bimolecular reaction $A+B\rightarrow\text{products}$ follows the rate law $r=k[A][B]$ with $k=0.10\ \mathrm{M^{-1}s^{-1}}$. If $[A]_0=0.020\ \mathrm{M}$ and $[B]_0=0.20\ \mathrm{M}$ (B in large excess), estimate the time required for $[A]$ to fall to $25\%$ of its initial value using the pseudo-first-order approximation $k'=k[B]_0$.

Q3. Initial rate data for a reaction are: Exp.1: $[A]=0.10\ \mathrm{M},\ [B]=0.10\ \mathrm{M},\ \text{rate}=2.0\times10^{-4}\ \mathrm{M\,s^{-1}}$; Exp.2: $[A]=0.20\ \mathrm{M},\ [B]=0.10\ \mathrm{M},\ \text{rate}=8.0\times10^{-4}\ \mathrm{M\,s^{-1}}$; Exp.3: $[A]=0.10\ \mathrm{M},\ [B]=0.20\ \mathrm{M},\ \text{rate}=4.0\times10^{-4}\ \mathrm{M\,s^{-1}}$. Deduce the rate law and calculate the initial rate when $[A]=0.050\ \mathrm{M}$ and $[B]=0.20\ \mathrm{M}$.

Q4. For the consecutive first-order reactions $A\xrightarrow{k_1}B\xrightarrow{k_2}C$ with $k_1=0.05\ \mathrm{s^{-1}}$ and $k_2=0.20\ \mathrm{s^{-1}}$, at what time $t$ will the concentration of intermediate $B$ be maximum? (Hint: $t_{\max}=\dfrac{1}{k_2-k_1}\ln\!\dfrac{k_2}{k_1}$.)

Q5. The reaction $A+B\rightarrow\text{products}$ (1:1 stoichiometry) has $k=1.0\ \mathrm{M^{-1}s^{-1}}$. If $[A]_0=0.050\ \mathrm{M}$ and $[B]_0=0.150\ \mathrm{M}$, calculate the time required for $[A]$ to decrease to $0.020\ \mathrm{M}$ using the integrated rate expression for unequal initial concentrations:

Q6. A first-order decomposition $\mathrm{A} \rightarrow \mathrm{B}$ has rate constant $k = 0.346\ \mathrm{min^{-1}}$. If $[A]_0 = 0.80\ \mathrm{M}$, what is $[A]$ after $2\ \mathrm{min}$? (Use $[A]=[A]_0 e^{-kt}$.)

Q7. For the reaction $2\mathrm{A}+\mathrm{B}\rightarrow\text{products}$ the observed rate law is $r = k[\mathrm{A}]^2[\mathrm{B}]$. In one experiment $[\mathrm{A}]_0=0.10\ \mathrm{M}$, $[\mathrm{B}]_0=0.20\ \mathrm{M}$ and the initial rate is $4.0\times10^{-5}\ \mathrm{M\,s^{-1}}$. If in a second experiment $[\mathrm{A}]_0$ is doubled to $0.20\ \mathrm{M}$ while $[\mathrm{B}]_0$ is halved to $0.10\ \mathrm{M}$, the initial rate in the second experiment will be:

Q8. A reaction follows second-order kinetics $r = k[\mathrm{A}]^2$ with $k = 0.8\ \mathrm{L\,mol^{-1}s^{-1}}$. If $[\mathrm{A}]_0 = 0.50\ \mathrm{M}$, after what time $t$ will $[\mathrm{A}]$ fall to $0.10\ \mathrm{M}$? (Use integrated form $\dfrac{1}{[\mathrm{A}]} = kt + \dfrac{1}{[\mathrm{A}]_0}$.)

Q9. Assertion (A): For the reversible reaction $\mathrm{A} \rightleftharpoons \mathrm{B}$ at equilibrium the ratio of forward and reverse rate constants equals the equilibrium constant, $K_{eq}=\dfrac{k_{\mathrm{f}}}{k_{\mathrm{r}}}$.
Reason (R): The activation energies for the forward and reverse reactions need not be equal; their difference equals the reaction enthalpy $\Delta H^\circ$.

Q10. Consider the unimolecular decomposition of $\mathrm{A}$ via the Lindemann mechanism with a bath gas $\mathrm{M}$:

Using steady-state approximation the observed rate is $r=\dfrac{k_1k_2[\mathrm{A}][\mathrm{M}]}{k_{-1}[\mathrm{M}]+k_2}$. Which statement correctly describes the dependence of the observed rate on $[\mathrm{M}]$ as $[\mathrm{M}]$ increases?

Q11. For a first-order reaction the concentration decays as $[A]_t=[A]_0e^{-kt}$. If $[A]_0=0.100\ \mathrm{M}$ and $[A]_{40\ \mathrm{min}}=0.025\ \mathrm{M}$, the half-life $t_{1/2}$ is:

Q12. Initial rate data for a reaction are: Exp‑1: $[A]=0.10\ \mathrm{M},\ [B]=0.10\ \mathrm{M},\ r_1=2.0\times10^{-3}\ \mathrm{M\,s^{-1}}$; Exp‑2: $[A]=0.20\ \mathrm{M},\ [B]=0.10\ \mathrm{M},\ r_2=8.0\times10^{-3}\ \mathrm{M\,s^{-1}}$; Exp‑3: $[A]=0.10\ \mathrm{M},\ [B]=0.20\ \mathrm{M},\ r_3=4.0\times10^{-3}\ \mathrm{M\,s^{-1}}$. Using $r=k[A]^m[B]^n$, the rate when $[A]=0.15\ \mathrm{M}$ and $[B]=0.05\ \mathrm{M}$ is:

Q13. A reaction $2A\rightarrow$ products follows second order kinetics $r=k[A]^2$. If $[A]_0=0.100\ \mathrm{M}$ and $[A]=0.050\ \mathrm{M}$ at $t=50\ \mathrm{s}$, how long (from $t=0$) will it take to reach $[A]=0.025\ \mathrm{M}$? ($1/[A]_t-1/[A]_0=kt$)

Q14. For consecutive first‑order steps $A\xrightarrow{k_1}B\xrightarrow{k_2}C$ with $k_1=0.020\ \mathrm{s^{-1}}$ and $k_2=0.100\ \mathrm{s^{-1}}$, at what time $t$ (in s) does $[B](t)$ reach its maximum? (For $k_1\neq k_2$, $t_{\max}=\dfrac{1}{k_2-k_1}\ln\!\dfrac{k_2}{k_1}$.)

Q15. A reaction can proceed via two parallel elementary pathways with Arrhenius parameters: Path‑1: $A_1=1.0\times10^{12}\ \mathrm{s^{-1}},\ E_{a1}=40.0\ \mathrm{kJ\,mol^{-1}}$; Path‑2: $A_2=1.0\times10^{16}\ \mathrm{s^{-1}},\ E_{a2}=80.0\ \mathrm{kJ\,mol^{-1}}$. Using $k=Ae^{-E_a/RT}$ and $R=8.314\ \mathrm{J\,mol^{-1}K^{-1}}$, which statement is correct about the dominant pathway?