numericals related to rate of reaction and activation energy


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Dhruv
When we solve numericals in chemistry, pay attention to the information given to us and the equation which we want to use to solve this question.
They are asking us to calculate activation energy .
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This can be written as
log k = -Ea/RT (2.303) + log A
Now compare it with given equation in the question. You can immediately recognize the log A value and you can compare -Ea/RT (2.303) with other factor in the given question.
However if T was given to us we could use
-Ea/RT (2.303)  = -1.0*10^4/T  ---(1)
convert half life in seconds (SI Unit) and get k in sec^-1
But T is not given here
So now what to do??
If we know k (rate constant) we can calculate T and then we can calculate Ea by using equation 1 
Order of the reaction and half life is given to us.
so we can use half life equation  to get k
t_1/2  = 0.693 / k
Then get T (in kelvin ) using equation given in the question and then use equation one to get Ea

Answer will be in J/mol which you can convert in KJ /mol
Now you can solve it.Please solve it and submit answer here.