The initial rates of the reaction 3A + 2B + C → Products at different initial concentrations are given below:
| Initial rate (M s−1) | [A]0 (M) | [B]0 (M) | [C]0 (M) |
| 5.0 × 10−3 | 0.010 | 0.005 | 0.010 |
| 5.0 × 10−3 | 0.010 | 0.005 | 0.015 |
| 1.0 × 10−2 | 0.010 | 0.010 | 0.010 |
| 1.25 × 10−3 | 0.005 | 0.005 | 0.010 |
The orders of the reaction with respect to A, B and C are, respectively:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 2, 1, 0
The order with respect to each reactant is found from experiment, by changing one concentration while the others stay fixed:
\( \displaystyle \text{Rate}=k[\mathrm{A}]^x[\mathrm{B}]^y[\mathrm{C}]^z \)
Order in C (runs 1 and 2): [A] and [B] fixed, [C] raised from 0.010 M to 0.015 M, rate unchanged at 5.0 × 10−3 M s−1: \( \left(\frac{0.015}{0.010}\right)^z=1 \), so z = 0.
Order in B (runs 1 and 3): [A] and [C] fixed, [B] doubled from 0.005 M to 0.010 M, rate doubled from 5.0 × 10−3 to 1.0 × 10−2 M s−1: \( 2^y=2 \), so y = 1.
Order in A (runs 1 and 4): [B] and [C] fixed, [A] halved from 0.010 M to 0.005 M, rate falls from 5.0 × 10−3 to 1.25 × 10−3 M s−1, that is to 1/4: \( \left(\frac{1}{2}\right)^x=\frac{1}{4} \), so x = 2.
\( \displaystyle \text{Rate}=k[\mathrm{A}]^2[\mathrm{B}]^1[\mathrm{C}]^0 \)
The orders with respect to A, B and C are 2, 1 and 0.