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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 |
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Solution
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 = 4y
Therefore, y = 1
The rate law is rate = k [A][B].
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