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Chemical Kinetics

Question
CBSEENCH12006305

The rate law for the gas phase reaction of chlorform with chlorine.
CHCl3(g) + Cl2(g) → CCl 4(g) + HCl(g)
is given by rate = k[CHCl3] [Cl2]1/2. How would the rate of reaction vary when (a) the concentration of CHCl3 is doubled (b) the concentration of Cl2 is doubled. What is the effect of each of these two changes on the rate constant.


Solution
The rate law for the gas phase reaction of chlorform with chlorine.
CHCl3(g) + Cl2(g) → CCl 4(g) + HCl(g)
 the rate is given by 

 rate1 =k[CHCl3] [Cl2]1/2 .....1

if the concentration of CHCl3 is doubled
then 

rate2 =k[CHCl3]2 [Cl2]1/2 .....2
divide 1by 2 we get

rate1 =k[CHCl3] [Cl2]1/2 .rate2 =k[CHCl3]2 [Cl2]1/2  rate become doublerate1rate2= 122rate1= rate2thus rate 1 become double

if the concentration of Cl2  is doubled
then .
rate3 =k[CHCl3] [Cl2]2/2........3

divide 1 by 3 
we get 

rate1 =k[CHCl3] [Cl2]1/2 .rate3 =k[CHCl3] [Cl2] rate become doublerate1rate3= 122rate1= rate2thus rate 1 become double

thus the rate reaction is double in both case.