TBR: "Directly Proportional" Clarificiation

[justadream]

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TBR GC Book II page 231 #15



TBR provides this equation for reaction rate:

ln(k) = -Ea / (RT) + ln(A)



TBR says that –Ea / (RT) is “directly proportional to ln(k)



There must be some math trick with logs I am not seeing. How are they directly proportional when there is the “ln(A)” on the right side?



BTW: it is derived from k = Ae^(-Ea / RT)



To me it looks like



X = Y + Z

Here, you can’t say X and Y are “directly proportional”

 

[t5Nitro]

They are when Z is constant. Holding terms constant seems to happen a lot in MCAT practice. When you look at a complex equation, look to see what happens when you change each variable, one at a time. That's probably the best approach for working with MCAT equations. Likewise, X and Z are directly proportional in the same sense.