4.11   The following results have been obtained during the kinetic studies of the reaction:
             2A + B \rightarrow C + D

          

           Determine the rate law and the rate constant for the reaction.

Answers (1)
M manish

Let assume the rate of reaction wrt A is x and wrt B is y . So, the rate of reaction is expressed as-
Rate = k[A]^{x}[B]^{y}

According to given data,
\\6\times 10^{-3}=k[0.1]^{x}[0.1]^{y}\\ 7.2\times 10^{-2}=k[0.3]^{x}[0.2]^{y}\\ 2.88\times 10^{-2} =k[0.3]^{x}[0.4]^{y}\\ 2.4\times 10^{-2} =k[0.4]^{x}[0.1]^{y} these are the equation 1, 2, 3 and 4 respectively

Now,  divide the equation(iv) by (i) we get,
4 = (0.4/0.1)^{x}
from here we calculate that x =1

Again, divide equation (iii) by (ii)
4 =(0.4/0.2)^{y}
from here we can calculate the value of y is 2

Thus, the rate law is now,  Rate = k[A][B]^{2}
So, k = rate/[A][B]^{2}
          \\= 6\times 10^{-3}/(0.1)\times (0.1)^{2}\\ =6\ L^{2}\ mol^{-2}\ min^{-1}
 

Hence the rate constant of the reaction is =6\ L^{2}\ mol^{-2}\ min^{-1}

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