For the reaction, 2A(g) + B(g) → C(g), the initial rate of the reaction at different concentrations of A and B is given in the table below. Which of the following statements are correct about the given data?
| Experiment | Initial [A]/ mol L−1 | Initial [B]/ mol L−1 | Initial rate of formation of [C] /mol L−1s−1 |
| 1 | 0.30 | 0.30 | 0.096 |
| 2 | 0.60 | 0.30 | 0.384 |
| 3 | 0.30 | 0.60 | 0.192 |
(A) The order with respect to A is one.
(B) The order with respect to B is one.
(C) The overall order of the reaction is three.
(D) The molecularity of the reaction is two.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (B) and (C) only
The order of a reaction is found from experimental data, using the rate law:
\( \displaystyle \text{Rate}=k[A]^x[B]^y \)
Comparing two experiments in which only one concentration changes gives the order with respect to that reactant.
Order with respect to A (experiments 1 and 2, [B] constant):
\( \displaystyle \frac{0.384}{0.096}=(\frac{0.60}{0.30})^x \)
\( \displaystyle 4=2^x \)
\( \displaystyle x=2 \)
Order with respect to B (experiments 1 and 3, [A] constant):
\( \displaystyle \frac{0.192}{0.096}=(\frac{0.60}{0.30})^y \)
\( \displaystyle 2=2^y \)
\( \displaystyle y=1 \)
So the rate law is Rate = k[A]2[B], and the order of the reaction is 2 + 1 = 3.
(A) The order with respect to A is one. — Incorrect. Doubling [A] makes the rate four times, so the order with respect to A is two.
(B) The order with respect to B is one. — Correct. Doubling [B] doubles the rate.
(C) The overall order of the reaction is three. — Correct. The order of the reaction is x + y = 2 + 1 = 3.
(D) The molecularity of the reaction is two. — Incorrect. Molecularity is the number of species that collide in an elementary step, and it cannot be found from rate data. If this reaction took place in a single step, 2A + B would involve three molecules, so its molecularity would be three, not two.