Question

A study of chemical kinetics of the reaction \[\ce{A + B-> Products}\], gave the following data at 25°C:

Experiment	[A]	[B]	`bb((d["Products"])/(dt))`
1	1.0	0.15	4.20 × 10−6
2	2.0	0.15	8.40 × 10−6
3	1.0	0.20	5.60 × 10−6

Find:

1. The order of reaction with respect to A.
2. The order of reaction with respect to B.
3. The rate law.

Answer 1

Given: r = `(d["Products"])/(dt)` = k [A]^x [B]^y

i. Order w.r.t. A:

Compare Exp. 2 vs 1: [A] doubles (1.0 → 2.0), [B] same, rate doubles (4.20 → 8.40)

⇒ 2 = 2x

⇒ x = 1

ii. Compare Exp. 3 vs 1: [B] changes 0.15 → 0.20 (factor `4/3`), rate changes 4.20 → 5.60 (factor `4/3`​)

⇒ `(4/3) = (4/3)^y`

⇒ y = 1

iii. Rate law:

r = k [A] [B]

Rate constant k (using Exp. 1):

k = `(4.20 xx 10^-6)/((1.0)(0.15))`

= 2.8 × 10⁻⁵ L mol⁻¹ s⁻¹.

(Check with Exps. 2 & 3: same k).