Question

Consider the following data showing the initial rate of a reaction (A→products) at several different concentrations of A.

[A](M)	Initial rate (M/s)
0.15	0.018
0.30	0.073
0.60	0.293

Estimate the value of the rate constant, k. Express your answer using two significant figures.

Answer 1

to get rate constant we need to get order of reaction
for that let us use the general rate law

Rate = K[A}^x where x is the order.

when [A] = 0.15 M and Rate = 0.018 M/s

(1)... 0.018 M/s= K[ 0.15 M ]^x

when [A] = 0.30 M and Rate = 0.073 M/s

0.073 M/s= K[ 0.30 M ]^x

(2)...0.073 M/s= K[2* 0.15 M ]^x
when [A] = 0.60 M and Rate = 0.293 M/s

0.293 M/s= K[ 0.60 M ]^x
(3)... 0.093 M/s= K[ 2* 0.15 M ]^x
On dividing (2)/(1)

we get 4 = [2]^x
so 2^2 = 2^x

x=2

if we divide (3)/(2) also we get

4 = [2]^x
x=2

Thus order of reaction = 2
********************************
rate law will become
Rate = k[A]^2

use any of the three equation to get rate constant K

0.073 M/s= K[ 0.30 M ]^2

K=0.073 M/s/[ 0.30 M ]^2 = 0..81 M^-1 s^-1
**************
hope it is helpful