Question

The activation energy for the decomposition of HI is 183 kJ/mol. At 573 K, the rate constant was measured to be 2.91 x 10^{-6} M/s. At what temperature in Kelvin does the reaction have a rate constant of 0.0760 M/s

Answer 1

`T_2=453.05K`

Step-by-step explanation:

Hello,

In this case, the temperature-variable Arrhenius equation is written as:

`(k(T_2))/(k(T_1))=exp((Ea)/(R)((1)/(T_2)-(1)/(T_1) ))`

Now, for us to solve for the temperature by which the reaction rate constant is 0.0760M/s we proceed as shown below:

`ln((k(T_2))/(k(T_1)))=(Ea)/(R)((1)/(T_2)-(1)/(T_1) )\\ln((0.0760M/s)/(0.00000291M/s) )=(183000J/mol)/(8.314J/(mol*K)) *((1)/(T_2) -(1)/(573K) )\\(1)/(T_2) -(1)/(573K) =(10.17)/(22011.06K^(-1)) \\\\(1)/(T_2)=4.62x10^(-4)K^(-1)+(1)/(573K)\\\\(1)/(T_2)=2.21x10^(-3)K^(-1)\\\\T_2=453.05K`

Regards.