the activation energy for the decomposition of HI(g) to H2(g) and I2(g) is 186kj/mol. the rate constant at 555k is 3.42 x 10^-7 L/mol*s. What is the rate constant at 645K?

Question

Please show all steps USING THE ARRHENIUS EQUATION.

Here is my work so far:

K = A e^(-Ea/RT)

3.52 x 10^-7 = A e^(-186000 J/mol / 8.314 J/mol*K x 555k)

A = 1.13 x 10^11

1.13 x 10^11 e^(-186000 J/mol /8.314 J/mol*K x 645) = 9.76 x 10^-5

However, according to the book, the answer should be 9.5 x 10^-5

Answer 1

Here is how I do it.
ln(k2/k1) = (Ea/RT)(1/T1- 1/T2)
k2 = ?? @ 645 K
k1 = 3.42 x 10^-7 @ 555K

ln(??/3.42 x 10^-7) = (186,000/8.314)*(1/555 - 1/645)
solve for ??. I get 9.47 x 10^-5 with a few quick steps on the calculator. You should do the work more precisely than I but this shows you how to do it.

Answer 2

My answer is K2 = 9.479 x 10 ^-5