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Question
In a reaction between A and B, the initial rate of reaction (r0) was measured for different initial concentrations of A and B as given below:
| A/mol L−1 | 0.20 | 0.20 | 0.40 |
| B/mol L−1 | 0.30 | 0.10 | 0.05 |
| r0/mol L−1 s−1 | 5.07 × 10−5 | 5.07 × 10−5 | 1.43 × 10−4 |
What is the order of the reaction with respect to A and B?
Solution
`"dx"/"dt"` = k[A]x [B]y
5.07 × 10−5 = k(0.2)x (0.3)y ...(i)
5.07 × 10−5 = k(0.2)x (0.10)y ...(ii)
Dividing (i) by (ii), we get
1 = 3y ⇒ 30
3y ⇒ y = 0
5.07 × 10−5 = k(0.2)x (0.1)0 ...(iii)
1.43 × 10−4 = k(0.4)x (0.05)0 ...(iv)
Dividing (iv) by (iii), we get 2.8 = 2x
log 2.8 = x log 2
or x = `log2.8/log2.0`
= `0.4472/0.3010`
= 1.48
≈ 1.5
The order of reaction is 1.5 with respect to 'A' and zero with respect to 'B'.
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