Homework problem 7D1

[sarahtang4B]

In the solutions manual it says to use a certain equation but I do not remember learning it in class and it's not on the constants and equations page. where did this equation come from?

[whitney_2C]

I noticed the same thing. The equation is another form of the Arrhenius equation where the natural log is taken and the reverse reaction is taken into account I believe.

[Ryan Danis 1J]

It comes from the Arrhenius equation in the form of ln kr + ln A - (Ea/RT).

When we are given two different temperatures, we can find the activation energy by using the Arrhenius equation for each temperature.:

At temperature T1: ln kr1 = lnA - (Ea/RT1)
At temperature T2: ln kr2 = lnA - (Ea/RT2)

Then, subtracting the first equation from the second, we get: ln kr2 - ln kr1 = -(Ea/RT2) + (Ea/RT1).

Using the natural log rule, and factoring out Ea/R, we can rearrange this equation into: ln(kr2/kr1 = (Ea/R)(1/T1-1/T2).
To answer 7D.1, solve for Ea.

This is all done on page 623 of the 7th edition if you have the 7th edition and want to see this in a clearer format. Hope this helps!

[sarahtang4B]

do we need to memorize this equation?

[Ryan Danis 1J]

Since it appeared in homework but it isn’t on the formula sheet, you probably need to memorize it if you don’t know how to derive it from the form of the Arrhenius equation given on the constants and equations sheet. (Assuming the constants and equations sheet on the class website will be the same as on the final).

[Danielle Hoekstra 1C]

I believe we have to memorize it.