Question

Consider the following data for the reaction:

\[\ce{A + B -> Product}\]

Experiment Number	[A] mol L−1	[B] mol L−1	Rate mol sec−1
1.	0.10 M	1.0	2.1 × 10−3
2.	0.20 M	2.0	8.4 × 10−3
3.	0.30 M	3.0	8.4 × 10−3

Determine the order of reaction with respect to A and with respect to B and the overall order of a reaction.

Answer 1

The rate law may be expressed as

Rate = k[A]^p [B]^q

Comparing experiments 2 and 3

(Rate)₂ = k[0.2]^p [1.0]^q = 8.4 × 10⁻³ ...........(i)

(Rate)₃ = k[0.2]^p [2.0]^q = 8.4 × 10⁻³ ...........(ii)

Dividing eqⁿ. by (ii) by (i),

`(("Rate")_3)/(("Rate")_2) = ("k"[0.2]^"p" [2.0]^"q")/("k"[0.2]^"p" [1.0]^"q") = (8.4 xx 10^-3)/(8.4 xx 10^-3)`

[2]^q = [2]⁰ or q = 0

Comparing experiments (i) and (ii)

(Rate)₂ = k[0.20]^p [1.0]^q = 8.4 × 10⁻³ ...........(iii)

(Rate)₁ = k[0.10]^p [1.0]^q = 2.1 × 10⁻³ ...........(iv)

Dividing eqⁿ. (iii) by (iv),

`(("Rate")_2)/(("rate")_1) = ("k"[0.20]^"p" [1.0]^"q")/("k"[0.10]^"p" [1.0]^"q") = (8.4 xx 10^-3)/(2.7 xx 10^-3) = 4`

[2]^q = [2]² or q = 2

order with respect to A = 2

order with respect to B = 0

overall order of reaction = 2