## rate constant k

Arrhenius Equation: $\ln k = - \frac{E_{a}}{RT} + \ln A$

Abigail Urbina 1K
Posts: 102
Joined: Thu Jul 27, 2017 3:01 am

### rate constant k

We know that the equilibrium constant K (capital K) is equal to k/k'. However is rate constant k (lowercase k) equal to k'/k? I was looking in the solution manual for question 15.61, and I wasn't entirely sure where ln(k'/k) came from or how exactly you get to that step. Can someone please clarify this question? And perhaps could someone explain how they derived the equation they got in the solutions manual?

Brigitte Phung 1F
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Joined: Thu Jul 27, 2017 3:00 am
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### Re: rate constant k

For 15.61, the ln(k'/k) simply comes from the equation, ln(k'/k) = Ea/R * (1/T1 - 1/T2). This equation is no longer on Lavelle's online equations sheet, however it was on one of his older equation sheets!
Here is the derivation:
lnk = -Ea/R (1/T1) + lnA
lnk' = -Ea/R (1/T2) + lnA
lnk' - lnk = [-Ea/R (1/T2) + lnA] - [ -Ea/R (1/T1) + lnA]
lnk' - lnk = -Ea/R (1/T2) + lnA + Ea/R (1/T1) - lnA
ln(k'/k) = -Ea/R (1/T2 - 1/T1) or Ea/R (1/T1 - 1/T2) (The negative sign in front of Ea/R determines which T is subtracted from which)

Hope this helps!