I Hate Exponentials

I've never been good at maths but this takes the cake,

so,

k= exp(-dG/RT)

R=8.314 (the universal gas constant in case anyone's wondering)
T=298
k=0.007

All I want to do is find out what value they have used for dG, I even know that it should be between 20 and 33 but all I get are syntax errors on my calculator when I try to do this (I got this kinetic equation from a web site) I'm also wanting to see what the effect of lowering T is, down to a min of 273 but if I can't get the bloody thing to work as it is written out then I have no chance.

If I understand Le Chateliers Principle correctly then k should get smaller as I reduce T for this experiment, does this fit with the kinetic equation above??

It's easy to solve.

k=exp(-dG/RT)
gives
ln(k)=-dG/RT
gives
-ln(k)*RT=dG

Easy. With you values, though, dG=12293.3, so check that your k is right.

To get the variation:
Let's call -dG/RT=f(T)
We then have
deltak/deltaT=(deltaf(T)/deltaT)*exp(f(T))
deltak/deltaT=(dG*R/((RT)^2))*exp(f(T))

Since dG, R, f(T) > 0, deltak/deltaT > 0
T and k vary in the same direction (reducing T reduces k) if dG is positive.

Thanks man, I completely forgot I had posted this thread, I made the silly mistake of mixing up kilojoules with joules so when I said deltaG should be between 20 and 33, I should have said 20,000 an 33,000 as R is given in joules per kelvin per mole.

I eventually got to the same answer for dG as you did which I find interesting but enough chemistry talk, thanks man!