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Question

For a chemical reaction $$A+3B\rightarrow Product$$, it was observed that the rate of reaction increases nine times when the concentration of B increased three times by keeping the concentration of A as constant. On doubling the concentration of both rate increases eight times. Differential rate equation can be given as:


A
r=k[A][B]3
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B
r=k[A][B]2
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C
r=k[A]2[B]
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D
r=k[A]2[B]13
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Solution

The correct option is B $$r=k[A][B]^2$$
According to question,

$$rate=k[A]^m[B]^n$$ ------ 1 

$$rate_1=9 rate=k[A]^m [3B]^n$$ ----------- 2

$$rate_2=8 rate=k[2A]^m [2B]^n$$ --------- 3

From 1 and 2 equation we get, $$n=2.$$

From 1 and 3 equation after substituting $$n$$ value we get, $$m=1.$$

Hence $$m=1, n=2$$.

Option B is correct.

Chemistry
NCERT
Standard XII

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