CHEMISTRY COMMUNITY

I've been under the assumption that k and k' are used to refer to the forward and reverse reaction rates for the reaction at a constant temperature, and that k1 and k2 are used to refer to the forward rate of the same reaction at two different temperatures, but the solutions manual for 15.61 and 15.63 use k and k' to refer to the same forward reactions at different temperatures.

My question is, are k/k' and k2/k2 notations interchangeable? ( i know they're all arbitrary variables but i don't know whether they have designated meaning or not)

Primes can sometimes become overused in scientific notations. Sometimes they are just used to distinguish two variables depending on the context.

In terms of mechanisms, k and k' will nearly always refer to a forward and reverse rate constant, respectively. Yes, k₁ and k₂ can be used to mean the forward rate constant for two different steps in a mechanism. They can also refer to the same reaction rate at two different temperatures. It all depends on context.