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Question

What is the order of a chemical reaction $$A+2B\xrightarrow {k} C$$, if the rate of formation of $$C$$ increases by a factor of 2.82 on doubling the concentration of $$A$$ and increases by a factor of 9 on tripling the concentration of $$B$$?


A
7/2
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B
7/4
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C
5/2
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D
5/4
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Solution

The correct option is A 7/2
The rate law expression is $$R=K[A]^m[B]^n$$                    ......(1)

The rate of formation of $$C$$ increases by a factor of 2.82 on doubling the concentration of $$A$$.

The rate law expression becomes $$R'=2.82R=K2^m[A]^m[B]^n$$                      ......(2)
Divide equation (2) with equation (1)

$$\frac {2.82R} {R}= \dfrac {K2^m[A]^m[B]^n} {K[A]^m[B]^n}$$

Hence,

$$2.82=2^m$$ or $$m= \dfrac {3} {2}$$

The rate of formation of $$C$$ increases by a factor of 9 on tripling the concentration of $$B$$

The rate law expression becomes $$R"=9R=K[A]^m3^n[B]^n$$                      ......(3)

Divide equation (3) with equation (1)

$$\dfrac {9R} {R}= \dfrac {K[A]^m3^n[B]^n} {K[A]^m[B]^n}$$

Hence,
$$9=3^n$$ or $$n= 2$$

The overall order of the reaction is $$m+n=\dfrac {3} {2}+2=\dfrac {7} {2}$$

Chemistry

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