Question

For the reaction A + B-> C, the rate constant at 315 ^oC is 5.0 x 10^-3 and the rate constant at 652^o C is 1.2 x 10^-1.

a) What is the activation energy in kJ/mol?

b) What is the rate constant at 100^o C

Please show work.

Answer 1

a)
Given:
T1 = 315 oC
=(315+273)K
= 588 K
T2 = 652 oC
=(652+273)K
= 925 K
K1 = 5*10^-3
K2 = 0.12

use:
ln(K2/K1) = (Ea/R)*(1/T1 - 1/T2)
ln(0.12/5*10^-3) = ( Ea/8.314)*(1/588.0 - 1/925.0)
3.1781 = (Ea/8.314)*(6.196*10^-4)
Ea = 42644 J/mol
Ea = 42.6 KJ/mol
Answer: 42.6 KJ/mol

b)
Given:
T1 = 315 oC
=(315+273)K
= 588 K
T2 = 100 oC
=(100+273)K
= 373 K
K1 = 5*10^-3
Ea = 42.644 KJ/mol
= 42644 J/mol

use:
ln(K2/K1) = (Ea/R)*(1/T1 - 1/T2)
ln(K2/5*10^-3) = (42644.0/8.314)*(1/588.0 - 1/373.0)
ln(K2/5*10^-3) = 5129*(-9.803*10^-4)
K2 = 3.276*10^-5
Answer: 3.3*10^-5