Question

If the rate of reaction increases 27 times , when temperature is increased by 30K, then temperature coefficient of the reaction is

Answer 1

Temperature coefficient of the reaction is given by :
Temperature coefficient(n) =
Rate constant at Temperature (T+10) K
Rate constant at Temperature T K
........... eq 1

similarly we can write:
n=
Rate constant at Temperature (T+20) K
Rate constant at Temperature (T+ 10 )K
........... eq 2

n =
Rate constant at Temperature (T+30) K
Rate constant at Temperature (T+20) K
........... eq 3

Multiplying eq1 , eq2 and eq3, we get :

n3 =
Rate constant at Temperature (T+30) K
Rate constant at Temperature T K

Since it is given that rate of the reaction becomes 27 times at temperature T+30 K Thus we have,


Rate constant at Temperature (T+30) K
Rate constant at Temperature T K
= 27

and hence ​n3 = 27
thus n = 3

Thus temperature coefficient of reaction is 3.