Read the passage carefully and answer the Questions.
The concentration dependence of the rate of a reaction is called the differential rate equation. It is not always convenient to determine the instantaneous rate, as it is measured by calculating the slope of the tangent at point 't' in the concentration vs time plot. This makes it difficult to determine the rate and hence the order of the reaction. This difficulty is overcome by integrating the differential rate equation. This integrated rate equation gives a direct relation between concentrations at different times and the rate constant. The integrated rate equations are different for the reactions having different reaction orders.
Choose the correct statement regarding kinetics of a chemical reaction.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → For complex reactions, order is given by the slowest step and the molecularity of the slowest step is the same as the order of the overall reaction.
A complex reaction takes place through a sequence of elementary steps. The whole reaction cannot go faster than its slowest step, so this step, the rate-determining step, fixes the rate law and hence the order. For such reactions the molecularity of the slowest step is the same as the order of the reaction as a whole.
The decomposition of hydrogen peroxide catalysed by iodide ions shows this. It occurs in two steps, and the first one is slow:
\( \displaystyle \ce{H2O2 + I^- -> H2O + IO^-} \quad (\text{slow}) \)
\( \displaystyle \ce{H2O2 + IO^- -> H2O + I^- + O2} \quad (\text{fast}) \)
\( \displaystyle \text{Rate} = k[\ce{H2O2}][\ce{I^-}] \)
The slow step is bimolecular, and the reaction is of second order.
Why the other options are incorrect
Option (1) The unit of rate constant for a second order reaction is \(L\, mol^{-1}\, s^{-2}\). — Incorrect. From rate \( = k[\mathrm{A}]^2 \), \( k = \frac{\mathrm{mol\,L^{-1}\,s^{-1}}}{(\mathrm{mol\,L^{-1}})^2} = \mathrm{L\,mol^{-1}\,s^{-1}} \). Time always appears as s−1, whatever the order, because the rate is a change per second.
Option (3) For zero order reaction, \(t_{1/2}\) is independent of the initial concentration of the reactant. — Incorrect. For a zero order reaction \( t_{1/2} = \frac{[\mathrm{R}]_0}{2k} \), so the half-life is directly proportional to the initial concentration. It is the half-life of a first order reaction, \( 0.693/k \), that does not depend on it.
Option (4) Decomposition of \(N_2O_5\) is an example of pseudo first order reaction. — Incorrect. The decomposition \( \ce{2N2O5 -> 4NO2 + O2} \) has rate \( = k[\ce{N2O5}] \): it is a true first order reaction with a single reactant. A pseudo first order reaction has two reactants, one in large excess, as in the acid hydrolysis of ethyl acetate in excess water.
NCERT (2026-27 edition):
Molecularity of a Reaction – “… (i) Order of a reaction is an experimental quantity. It can be zero and even a fraction but molecularity cannot be zero or a non integer.
(ii) Order is applicable to elementary as well as complex reactions whereas molecularity is applicable only for elementary reactions. For complex reaction molecularity has no meaning.
(iii) For complex reaction, order is given by the slowest step and molecularity of the slowest step is same as the order of the overall reaction.”