Among the following, which are examples of first-order reactions?
(A) \( {}^{226}_{88}\mathrm{Ra} \rightarrow {}^{4}_{2}\mathrm{He} + {}^{222}_{86}\mathrm{Rn} \)
(B) \( \ce{2NH3} \xrightarrow[\text{Pt catalyst}]{\text{1130K}} \ce{N2(g) + 3H2(g)} \)
(C) 2N2O5 (g) → 2N2O4 (g) + O2 (g)
(D) C2H4 (g) + H2 → C2H6 (g)
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A), (C) and (D) only
In a first order reaction the rate is proportional to the first power of the concentration of one reactant, Rate = k[R]. In a zero order reaction the rate does not depend on concentration at all, Rate = k. The order is found by experiment and cannot be read from the coefficients of the balanced equation.
(A) \( {}^{226}_{88}\mathrm{Ra} \rightarrow {}^{4}_{2}\mathrm{He} + {}^{222}_{86}\mathrm{Rn} \) — Correct. Every radioactive decay is first order: the rate is proportional to the number of nuclei present, and the half-life does not depend on the amount taken.
(B) \( \ce{2NH3} \xrightarrow[\text{Pt catalyst}]{\text{1130K}} \ce{N2(g) + 3H2(g)} \) — Incorrect. On a hot platinum surface at high pressure, the metal surface is completely covered by ammonia molecules. Adding more ammonia cannot increase the rate, so the reaction is zero order: Rate = k[NH3]0 = k.
(C) 2N2O5 (g) → 2N2O4 (g) + O2 (g) — Correct. The thermal decomposition of \( \ce{N2O5} \) is first order, Rate = k[N2O5], even though the coefficient of \( \ce{N2O5} \) in the equation is 2.
(D) C2H4 (g) + H2 → C2H6 (g) — Correct. The hydrogenation of ethene is first order, Rate = k[C2H4], although two reactants appear in the equation.
NCERT (2026-27 edition):
First Order Reactions – “… Hydrogenation of ethene is an example of first order reaction.
\( \ce{C2H4(g) + H2(g) -> C2H6(g)} \qquad \text{Rate} = k\,[\ce{C2H4}] \)
All natural and artificial radioactive decay of unstable nuclei take place by first order kinetics.
\( {}^{226}_{88}\mathrm{Ra} \rightarrow {}^{4}_{2}\mathrm{He} + {}^{222}_{86}\mathrm{Rn} \qquad \text{Rate} = k\,[\mathrm{Ra}] \)
Decomposition of N2O5 and N2O are some more examples of first order reactions.”
Zero Order Reactions – “… Zero order reactions are relatively uncommon but they occur under special conditions. Some enzyme catalysed reactions and reactions which occur on metal surfaces are a few examples of zero order reactions. The decomposition of gaseous ammonia on a hot platinum surface is a zero order reaction at high pressure.”