Question

Answer the following in brief.

For the reaction 2A + B → products, find the rate law from the following data.

[A]/M	[B]/M	rate/M s-1
0.3	0.05	0.15
0.6	0.05	0.30
0.6	0.2	1.20

Answer 1

From above observations (i) and (ii)

0.15 = (0.3)^x (0.05)^y  ......(i)

0.30 = (0.6)^x (0.05)^y  .......(ii)

Dividing (2) by (1)

`0.30/0.15 = 2 = ((0.6)^x (0.05)^y)/((0.3)^x (0.05)^y) = ((0.6)/(0.3))^x = 2^x`

Hence, x = 1

From observation (i) and (iii) separately in the rate law gives

0.15 = (0.3)^x (0.05)^y   ....(iii)

1.20 = (0.6)^x (0.2)^y  .......(iv)

Dividing (4) by (3)

`1.20/0.15 = 0.6/0.3 (0.2/0.05)^y`   (∵ x = 1)

∴ `8 = 2(0.2/0.05)^y = 2 xx 4^"y"`

∴ 4 = 4^y

Therefore, y = 1

The rate law is rate = k [A][B].