# Arrhenius equation problem - converting equations

## Main Question or Discussion Point

Hi there

I've been trying to work this out and didn't quite succeed, so I'm hoping someone might help me out a bit.

I've been using the Arrhenius equation to calculate reaction rates at 2 temperatures, so I took the integral and got k2/k1 = e^(Ea/R(1/T1 - 1/T2))
This paper I've been reading (doing similar things as I am) is however suggesting the following equation:
k2/k1 = (T2+460)/(T1+460) * 10^((-394)*H*(1/(T2+460)-1/(T1+460)))

The second equation isn't using SI units, so temperatures are in F and entalphy is in kcal.

I've been trying to convert the second equation into the first one (or vice versa) to check everything is OK and I can't get it to work. My main problem is the first part, (T2+460)/(T1+460).
My calc is a bit rusty, so I'm not sure where I'm going wrong (or if the problem is elsewhere)...

Would really appreciate some help. Thanks!

## Answers and Replies

Borek
Mentor
No idea what you have integrated.

$$k_1 = e^{\frac {E_a} {RT_1}}$$

$$k_2 = e^{\frac {E_a} {RT_2}}$$

$$\frac {k_1} {k_2} = \frac {e^{\frac {E_a} {RT_1}}} {e^{\frac {E_a} {RT_2}}}$$

Just rearrange right side.

I don't see where (T2+460)/(T1+460) could come from (that is, 460 is conversion between Fahrenheit and Rankine scale, but ratio of temperatures before exponential part doesn't make sense to me).

Or are you trying to do something completely different?

Thanks for the reply!

Well integrating (and setting T1 & T2 as borders) the equation might be complicating things a bit, but you essentially get the same thing...

Yes, the temperature ratio is what I don't understand, as I have no idea where it could've come from. All the paper says is "Transition State Theory can accurately describe the effect of temperature changes on reaction rates. The equation for the relative rate of reaction at two (Fahrenheit) temperatures T1 and T2 is ..." (and that's the equation I wrote earlier)
- which is not the transition state theory I know, but I might be wrong...

Any ideas?