An experimental drug, D, is known to decompose in the blood stream. Tripling the concentration of the drug increases the decomposition rate by a factor of nine. Write the rate law for decomposition of D.

R=k[D]^2

Explanation:

Given that it is a decomposition reaction;

D--->product

Hence;

The rate law is;

R= k[D]^x (1)

When we triple the concentration of D we have;

[D]' = [3D]^x

Therefore;

R'= 3R

R'= k[D]'(2)

Hence dividing (1) by (2);

R/R' = k[D]^x/k[D]'

R/9R = k[D]^x/k[3D]^x

1/9 = 1/3^x (take inverse of both sides)

9 = 3^x

3^2 = 3^x

x= 2

Hence the rate law;

R=k[D]^2