Chemical Forums
Chemistry Forums for Students => High School Chemistry Forum => Chemistry Olympiad and other competitions => Topic started by: sn1sn2e1e2 on April 19, 2014, 04:14:24 PM

:[ This question has been giving me the chills :[
Question 30 on: http://www.acs.org/content/dam/acsorg/education/students/highschool/olympiad/pastexams/2001usncoexamparti.pdf
I chose D thinking that a reversed reaction II would require least amount of heat, thus adding more heat from increasing T would significantly increase the rate of the reaction. However, ACS chooses B which I am not sure why. Any help?

Analyze the Arhenius equation.

I did; Lnk=Ea/R(1/T) +LnA. But I can't seem to find the relationship. Delta H and the Arrhenius equation are unrelated (unless you substitute the Ea with delta H)

Look at Ea of each reaction, not ΔH.

Yes we need to look at E_{A} here but I think the answer is still actually D.
What may be confusing is that if you look at the expression for k_{2}/k_{1} using the Arrhenius equation, looks like d(k_{2}/k_{1})/d(E_{A}) is positive for any temperature increase, meaning that the relative increase in rate constant, when temperature increases by a certain amount, is greater for higher E_{A}. This would suggest we want largest activation energy (> reaction 1's reverse direction).
But the wording of the question suggests that the magnitude of increase of rate (and thus of rate constant) is what they want you to identify (find the reaction with the greatest). For this, it can be shown that the nonrelative magnitude of increase in rate constant, when temperature increases by a certain amount, decreases as E_{A} increases (for all E_{A} above RT, which can be assumed AFAIK). Therefore we should go for the minimum E_{A} to give maximum magnitude of increase in rate constant with a given temperature. So the answer should indeed be D (reaction 2's reverse direction).
I suppose the questionwriter really meant to put "relative increase in rate" but since he didn't it has to be interpreted in the second way IMO.
Edit: note: the sign of d(rate)/dt will be the same as the sign of dk/dT because the concentration and partial pressure and order terms will definitely be positive, as x^y for any positive real x and any real y is always positive. Meanwhile, though not necessary for this problem, r_{2}/r_{1} = k_{2}/k_{1} (so of course d(r_{2}/r_{1})/d(E_{A}) = d(k_{2}/k_{1})/d(E_{A}) is true too, they are the same) since you assume concentration and partial pressure and order terms stay the same for a fair test.