Read the passage carefully and answer the Questions.
The decomposition of \( N_2O_5 (g) \) is given as
\( N_2O_5 (g) → 2NO_2(g) +\frac{1}{2}O_2(g) \)
The above reaction is found to be of first order.
What is the unit of rate constant for the reaction given in the passage
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(s^{-1}\)
The unit of a rate constant follows from the rate law. For a reaction of order n, rate \( = k[\mathrm{A}]^{n} \), so
\( \displaystyle k = \frac{\text{rate}}{[\mathrm{A}]^{n}} = \frac{\mathrm{mol\,L^{-1}\,s^{-1}}}{(\mathrm{mol\,L^{-1}})^{n}} = (\mathrm{mol\,L^{-1}})^{1-n}\,\mathrm{s^{-1}} \)
The passage states that the decomposition of \( \ce{N2O5} \) is of first order, rate \( = k[\ce{N2O5}] \), so n = 1:
\( \displaystyle k = \frac{\mathrm{mol\,L^{-1}\,s^{-1}}}{\mathrm{mol\,L^{-1}}} = \mathrm{s^{-1}} \)
The concentration units cancel, so a first order rate constant has the unit of reciprocal time, s−1.
NCERT (2026-27 edition):
Order of a Reaction – …
