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

The correct option is A 7/2The 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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