Read the passage carefully and answer the questions.
The speed at which a chemical reaction takes place is called the rate of reaction. The rate of reaction depends on various factors like concentration of the reactants, temperature, etc. The relation between the rate of reaction and the concentration of reacting species is represented by the equation \( r = k[A]^x[B]^y \), where \( x \) and \( y \) are the order of the reaction with respect to the reactants A and B, respectively. The overall order of the reaction is \( x + y \). The rate of reaction can also be increased by the use of a catalyst which provides an alternate pathway of lower activation energy. It increases the rate of forward and backward reaction to an equal extent. It does not alter the Gibbs energy of the reaction.
The rate law of a reaction is given by \( r = k[CH_3OCH_3]^{3/2} \), If the pressure is measured in bar and time in minutes, then the unit of rate constant will be
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(bar^{-1/2}\, min^{-1}\)
The unit of a rate constant follows from the rate law. For a gaseous reaction the rate is measured as change in pressure per unit time, so here the rate has the unit bar min−1, and the concentration term is a pressure in bar.
\( \displaystyle r = k\,[\ce{CH3OCH3}]^{3/2} \)
\( \displaystyle k = \frac{r}{[\ce{CH3OCH3}]^{3/2}} \)
\( \displaystyle \text{unit of } k = \frac{\mathrm{bar\,min^{-1}}}{\mathrm{bar^{3/2}}} = \mathrm{bar^{1-3/2}\,min^{-1}} = \mathrm{bar^{-1/2}\,min^{-1}} \)
So the rate constant has the unit bar−1/2 min−1.
Shortcut: For a reaction of order n, the unit of k is (pressure)1−n time−1. With n = 3/2 the power of bar is 1 − 3/2 = −1/2.
Note 1: This question is from NCERT (2026-27). NTA sets numerical questions from NCERT too, so do not ignore NCERT while practising numericals.
NCERT (2026-27 edition):
Intext Questions – “The decomposition of dimethyl ether leads to the formation of \( \ce{CH4} \), \( \ce{H2} \) and CO and the reaction rate is given by
\( \text{Rate} = k\,[\ce{CH3OCH3}]^{3/2} \)
The rate of reaction is followed by increase in pressure in a closed vessel, so the rate can also be expressed in terms of the partial pressure of dimethyl ether, i.e.,
\( \text{Rate} = k\,(p_{\ce{CH3OCH3}})^{3/2} \)
If the pressure is measured in bar and time in minutes, then what are the units of rate and rate constants?”
Note 2: The same/similar question has been asked in different years by NTA as per the details given below:
| 2026 | 2025 | 2024 | 2023 | 2022 |
|---|---|---|---|---|
| – | 13-05 S1 | – | – | 18-08 S1 |