Chemical kinetics practice · Mixed difficulty

Option B (2) is correct because the rate equation is of the form $r = k[A]^n$, and solving for n using the given data yields n = 2.

Option A ($1.15 \times 10^4\, \mathrm{~s}$) is correct because it is the time calculated using the first-order kinetics equation for 90% completion of the reaction.

Option B ($6.36 \times {10^{ - 3}}\,{s^{ - 1}}$) is correct because it is calculated using the Arrhenius equation relating rate constants at different temperatures.

Option A ($\mathrm{t = 4}\mathrm{.606/k}$) is correct because it is derived from the integrated rate law for a first-order reaction when 99% of the reaction is completed.

Option B (Powdering the lumps of coal) is correct because increasing the surface area of the coal by powdering it allows for more contact with oxygen, thus increasing the reaction rate.

Option B (13020 cal/mol) is correct because it is the calculated activation energy using the Arrhenius equation and the given half-lives at different temperatures.

Option D ($4 \times 10^{-3} \mathrm{Ms}^{-1}, 2 \times 10^{-3} \mathrm{Ms}^{-1}$) is correct because the average rate of appearance of NO2 and disappearance of N2O5 are calculated based on the stoichiometry of the reaction.

The correct answer is C (6 (app.)) because the maximum concentration of zwitterion occurs at the isoelectric point, which is the average of the pKa values of the amino and carboxyl groups.

Option A ($6.978 \mathrm{~hr}$) is correct because it accurately calculates the time required for 90% decomposition of $\mathrm{NH}_4 \mathrm{NO}_3$ using first-order kinetics.

Option C (${t_{1/2}} \propto {a^0}$) is correct because for a first-order reaction, the half-life is independent of the initial concentration, meaning it's proportional to $a^0$.

Option B (If statement I and statement II are correct but statement II is not the correct explanation of statement I) is correct because both statements are true, but the existence of higher-order reactions does not explain the definition of overall order.

Option A (${ }_{13}^{27} {Al}+{ }_2^4 {He} \longrightarrow{ }_{15}^{30} {P}+{ }_0^1 {n}$) is correct because it shows the emission of a neutron (${ }_0^1 {n}$) as a product of the nuclear reaction.

Option B (6, 5) is correct because the number of alpha particles is calculated from the mass number difference, and beta particles from the atomic number difference.

Option A (1) is correct because the rate constant is consistent throughout the given time intervals, indicating a first-order reaction.

The correct answer is C (${MgF}_2$) because it is an ionic compound where both Mg and F achieve octet configuration through electron transfer, thus not an exception to the octet rule.

Option B (1.33 y M s⁻¹) is correct because the rate of appearance of Q is calculated based on the stoichiometry of the reactions and the given rate of disappearance of B.

Option A ($10^{-3}$) is correct because it is calculated using the formula for the half-life of a first-order reaction.

Option C ($\frac{{-\mathrm{k}}}{{2.303}}, \log [\mathrm{A}]_0$) is correct because it matches the slope and intercept derived from the integrated rate law for a first-order reaction when plotting $\log[A]$ vs. time.

Option C is correct because as temperature increases, the rate of reaction, the number of activated molecules, and the collision frequency all increase.

The correct answer is Rate = k[X][Y][Z] because the rate law is determined by the slow step in the mechanism, and the concentrations of reactants in the slow step are multiplied by the equilibrium constant of the rapid equilibrium.

Option A is correct because the rate of formation of $NH_3$ is related to the rate of consumption of $H_2$ by the stoichiometric coefficients in the balanced chemical equation.

Option D (Third) is correct because if the graph of $\frac{1}{{{\left[ A \right]}^2}}$ versus time yields a straight line, it indicates a third-order reaction.

Option A (1/2) is correct because the rate of reaction is proportional to the square root of the concentration of X, indicating a half-order reaction.

Option C ($1.15 \times 10^{-3}$) is correct because the rate of a first-order reaction is directly proportional to the concentration of the reactant, and the rate constant can be calculated from the half-life.

Option A is correct because the rate expression given is consistent with the rate depending only on the concentrations of A and B.

Option A ($3: 10$) is correct because it represents the ratio of the time required for 25% completion of the first reaction to the time required for 75% completion of the second reaction, calculated using the half-life relationship for first-order reactions.

Option B (2) is correct because the half-life is inversely proportional to the initial concentration raised to the power of (n-1), where n is the order of the reaction.

Option B (Rate of a reaction increases with decrease in activation energy) is correct because the Arrhenius equation shows an inverse exponential relationship between the rate constant and activation energy.

Option A (Zero) is correct because for a zero-order reaction, the half-life is directly proportional to the initial concentration of the reactant.

Option D (All of the above) is correct because the given conditions satisfy the Arrhenius equation, and the relative magnitudes of rate constants change with temperature as described.