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### Topic: DELTA H and RATE  (Read 4980 times)

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#### sn1sn2e1e2

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##### DELTA H and RATE
« on: April 19, 2014, 04:14:24 PM »
This question has been giving me the chills

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?

#### Rutherford

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##### Re: DELTA H and RATE
« Reply #1 on: April 21, 2014, 06:17:19 AM »
Analyze the Arhenius equation.

#### sn1sn2e1e2

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##### Re: DELTA H and RATE
« Reply #2 on: April 21, 2014, 09:24:32 PM »
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)

#### Rutherford

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##### Re: DELTA H and RATE
« Reply #3 on: April 22, 2014, 02:49:29 AM »
Look at Ea of each reaction, not ΔH.

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##### Re: DELTA H and RATE
« Reply #4 on: April 22, 2014, 10:05:23 AM »
Yes we need to look at EA here but I think the answer is still actually D.

What may be confusing is that if you look at the expression for k2/k1 using the Arrhenius equation, looks like d(k2/k1)/d(EA) 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 EA. 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 non-relative magnitude of increase in rate constant, when temperature increases by a certain amount, decreases as EA increases (for all EA above RT, which can be assumed AFAIK). Therefore we should go for the minimum EA 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 question-writer 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, r2/r1 = k2/k1 (so of course d(r2/r1)/d(EA) = d(k2/k1)/d(EA) is true too, they are the same) since you assume concentration and partial pressure and order terms stay the same for a fair test.