why is 1/t used as initial rate in some experiment? and in varying temp, why is 1/t used as rate constant?

Question

im confused why is 1/t or 1/time is used as initial rate in the determining the rate law...
and in another experiment, 1/t was used as a measure of rate constant k...

Answer 1

First order rate constants have the dimension of (1/t). With some reactions, the early part of a higher order reaction curve closely approximates the descent of a first order curve, so the initial rate of the first-order reaction can be used.