Question

How do I calculate the rate law constant and find the overall rate law?

Answer 1

Answer – When we need to calculate the rate constant we need to know the rate law of the reaction. For the rate law we need to know the order with respect to each reactant in the reaction. If in the problem, we already given the rate law like for the reaction A + B ----> C is Rate = k [A][B] then from that we can directly calculate the rate constant. But when we are not given, then from the given data like concentration of each reactant and rate we can calculate the order of each reactant.

We will see one solved problem here for the idea how calculate the order of each reactant –

A + B -----> C . Calculate the rate constant and rate law for this reaction from the following data-

[A]	[B]	Rate
1.5	1.5	3.20*10-1
1.5	2.50	3.20*10-1
3.00	1.50	6.40*10-1

In this one there are given concentrations of both reactant and rate of formation

First we need to calculate the order of reaction

Rate = k [A]^m [B]ⁿ

We assume m and n order with respect to A and B,

so rate law is as follow -

Rate1 = k [A]₁^m [B]₁ⁿ

Rate2 = k [A]₂^m [B]₂ⁿ

Rate 3 = k [A]₃^m [B]₃ⁿ

Now first we need to calculate order of A -

Rate3/ Rate1 = k [A]₃^m [B]₃ⁿ / k [A]₁^m [B]₁ⁿ

6.40*10^-1 / 3.2*10^-1 = (3.0^m /(1.50)^m * (1.50)ⁿ / (1.50)ⁿ

2 = (2)^m

So, m = 1

Order with respect to A is first order

Now order of B

Rate2/Rate1 = k [A]₂^m [B]₂ⁿ / k [A]₁^m [B]₁ⁿ

3.2*10^-1 / 3.20*10^-1 = (1.50)^m /(1.50)^m *(2.50)ⁿ /(1.50)ⁿ

1 = (1.666)ⁿ

So, n = 0 ,Order with respect B is zero

Overall order = 1 + 0 = 1

So rate law, rate = k [A]

So overall order is first order and rate of react is depend on only A and not on the B

Now we need to calculate the rate constant

We know rate law

Rate = k [A]

0.320 M/s = k *(1.50 M)

k = 0.320 M.s^-1/ 1.50 M

= 0.213 s^-1