Rate laws - 2 | Chemical Kinetics: Rate Laws

Rate = k [NO]^α [Cl₂]^β

Let’s determine α:

[NO]_exp2 = 0.5 x [NO]_exp1
[Cl₂]_exp2 = [Cl₂]_exp1
rate_exp2 = 0.25 x rate_exp1

rate_exp2 = 0.25 x rate_exp1
⇒ k [NO]_exp2^α [Cl₂]_exp2^β = 0.25 k [NO]_exp1^α [Cl₂]_exp1^β
⇒ k 0.5^α x [NO]_exp1 ^α [Cl₂]_exp1^β = 0.25 k [NO]_exp1^α [Cl₂]_exp1^β
⇒ 0.5^α = 0.25
⇒ α = 2

Let’s determine β:

[NO]_exp3 = [NO]_exp2
[Cl₂]_exp3 = 4 [Cl₂]_exp2
rate_exp3 = 4 x rate_exp2

rate_exp3 = 4 x rate_exp2
⇒ k [NO]_exp3^α [Cl₂]_exp3^β = 4 k [NO]_exp2^α [Cl₂]_exp2^β
⇒ k [NO]_exp2 ^α 4 ^β [Cl₂]_exp2^β = 4 k [NO]_exp2^α [Cl₂]_exp2^β
⇒ 4 ^β = 4
⇒ β = 1

Rate = k [NO]² [Cl₂]

Rate_exp1 = k [NO]_exp1² [Cl₂]_exp1

k = $\frac{{\mathrm{Rate}}_{\exp 1}}{{{\left[\mathrm{NO}\right]}_{\exp 1}}^2 {[\mathrm{Cl}}_{}}$₂]exp1 = $\frac{0.020}{0.{030}^2 \times 0.010}$ = 2.2 x 10³ M^-2.s^-1