# Help Determining the Activation Energy

#### aquabug918

This question comes from a study guide and I can't get it. Any help would be greatly appreciated.

A number of experiments were performed to determine the effect of the temperature on the rate constant, k, for the reaction X + Y --> Z which had been determined to be first order in X. The data are shown below

Temperature °C.......k (the rate constant)
0 ........................ 0.010
25....................... 0.084
40....................... 0.129
60....................... 0.176

From this data, determine the value of the activation energy for the reaction.

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#### gravenewworld

what do the k (s-1) mean? It is not too clear to me

can you write out the rate law for the reaction?
how can you use the arrhenius equation here?

#### aquabug918

I fixed the format a little, sorry about that. This was the exact question given. The answer given is 30.3 Joules. I have tried everything and can't get an answer close to it. I know that we are supposed to use Arrenhuis's equation and something about a slope of a graph. I just can't put everything together.

#### gravenewworld

Ahh much better now. The Arrhenius eq. which you probably have seen before is

k=Ae^-(Ea/RT).

What happens when you take the natural log of both sides?
you get from simple algebra-

lnK=-(Ea/RT) + lnA

Doesn't this look exactly almost like y=mx+b??? (here y is the lnk, m is -Ea/R, and x is 1/T) which means this equation is a straight line.

The variables are lnk, and 1/T so if you plot lnk vs. 1/T you will get a straight line. It should be clear how to find Ea now.

MAKE SURE YOU ALWAYS ALWAYS WORK IN SI UNITS! Make sure to use kelvins,joules, etc.

#### aquabug918

Ahh, yes that's what I was missing. Thank you very much for helping me out!

"Help Determining the Activation Energy"

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