Question

Don't understand how I would find the rate law for this?
Step1: Z2→Z+Z (slow)
Step2: X2Y2+Z→X2Y2Z (fast)
Step3: X2Y2+Z→X2Y2Z (fast)

Answer 1

It's supposed to be rate law= \[k[Z _{2}]\] But I don't understand how the elimination gets us to that point.

Answer 2

The rate is determined by the slowest step in the reaction mechanism. The first step is the slowest, so your rate depends only on the reactant in that step - in this case Z2.

Think of an assembly line with three workers. The first worker (the breaker) takes Z2 and breaks it into Z+Z, but it's hard to do and takes him an hour each time. After he's done, the first Z is passed to a second guy (the combiner), who combines it with X2Y2. Then, the second Z is passed to a third guy, who combines it with X2Y2. But in both cases, the combining with X2Y2 is pretty easy and only takes these guys a minute to do.

The combiners can do 60 combinations in the time it takes the breaker to break 1. But if they don't have the materials to do their job, they can't do it, even if they can do it very fast. They can only do their job once they get the materials from the breaker, so the rate of production of the finally product (X2Y2Z) depends on the speed of the slowest step - the breaking of Z2.