# Rate laws - 1 | Chemical Kinetics: Rate Laws

Here is a reaction: NH4(aq) + NO2(aq) → N(g) + 2 H2O (l)

We measure the rate of reaction of 3 experiments with different concentration.

Determine the rate law for the reaction.

Exp1: [NH4+] = 0.010 M; [NO2-] = 0.020 M; rate = 0.020 M.s-1

Exp2: [NH4+] = 0.015 M; [NO2-] = 0.020 M; rate = 0.030 M.s-1

Exp3: [NH4+] = 0.010 M; [NO2-] = 0.010 M; rate = 0.005 M.s-1

Rate = k [NH4+]α [NO2-]β

Let’s determine α:

[NH4+]exp2 = 1.5 x [NH4+]exp1
[NO2-]exp2 = [NO2-]exp1
rateexp2 = 1.5 x rateexp1

rateexp2 = 1.5 x rateexp1
⇒ k [NH4+]exp2α [NO2-]exp2β = 1.5 k [NH4+]exp1α [NO2-]exp1β
⇒ k 1.5α x [NH4+]exp1 α [NO2-]exp1β = 1.5 k [NH4+]exp1α [NO2-]exp1β
⇒ 1.5α = 1.5
⇒ α = 1

Let’s determine β:

[NH4+]exp3 = [NH4+]exp1
[NO2-]exp3 = 0.5 [NO2-]exp1
rateexp3 = 0.25 x rateexp1

rateexp3 = 0.25 x rateexp1
⇒ k [NH4+]exp3α [NO2-]exp3β = 0.25 k [NH4+]exp1α [NO2-]exp1β
⇒ k [NH4+]exp1 α 0.5 β [NO2-]exp1β = 0.25 k [NH4+]exp1α [NO2-]exp1β
⇒ 0.5 β = 0.25
⇒ β = 2

Rate = k [NH4+] [NO2-]2