# Arrhenius Equation

Submitted by vainash on Tue, 04/26/2011 - 22:26

When a reaction is run at 292 Celcius, data shows that k=18.35 s-1 and Ea= 58.23 kJ/mol. At what temperature would the reaction have to be run in order for k to be 1325 s-1?

The answer is 589.7 C according to the key.  I have plugged in the numbers into the equations at least 20 times and I can not figure out how to get to this number. I keep getting -1.65 Celcius. Thank you for any help.

Did you remember to convert from Celsius to Kelvin?

Hello, yes I converted to Kelvin. I have tried every conversion possible and can not seem to get the correct answer.

Use Arrhenius' equation and solve for  ln A
ln k = -Ea /R T + ln A

ln (18.35) = -58.23E3 J/ (565 x 8.314 J/mol K) + ln A

ln A = 2.91 + 12.4 = +15.3

Now plug in the second set of data and solve for T.
ln (1325) = -58.23E3 J / (T x 8.314 J/mol K)  +  15.3
7.19   -  15.3 =  -7001 / T
T = - 7001 / -8.11 =871 K = 589 C

I was using the formula:

ln k2/k1 = Ea/R(1/T1-1/T2)