Question

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

[A](M)	Initial rate (M/s)
0.15	0.024
0.30	0.191
0.60	1.525

Estimate the value of the rate constant, k.

Answer 1

Rate law

Rate = K[A]^x

0.024   = K(0.15)^x -------->1

0.191   = K(0.30)^x ---------> 2

1.525    = K(0.60)^x ---------->3

equation 1 divide by equation 2

0.024/0.191 = K(0.15)^x/K(0.3)^x

0.125              = (0.15/0.3)^x

(0.5)^3           = (0.5)^x

x   = 3

Rate law

Rate = K[A]^3

0.024   = K(0.15)^x -------->1

0.024 = K(0.15)^3

K    = 0.024/(0.15)^3   = 7.11 M^-2 s^-1 >>>answer

The rate constant = 7.11 M^-2 s^-1 >>>answer

Answer 2

Reactions within the table are 2nd order reactions, giving us the equation of:

 rate = k[A]² 

I will be using experiment 1

Given:

rate = 0.024

k = ?

[A] = 0.15

Therefore, 0.024 = k[0.15]²

                k = 1.06 M^-1s^-1