Oh okay. So in a way, each step hate its own rate. The rate law is essentially the rate for the slow step. The rate law describes the rate of the whole reaction. Since the slow step governs the rate of the whole reaction, rate of the slow step=rate law?
One more question. What about the net reaction though? What is the use of that in terms of kinetics. To me, it's use is for "substitution". Occasionally, the slow step has an intermediate in it. If that's the case, we have be replace the intermediate in terms of reactants that are in the net equation only.
You are exactly right.
As for the net reaction, say aA + bB --> cC, what you may find is, is that reactant A doesn't effect the reaction at all. Ultimately, we take advantage of the effect of each reactant and altering the concentration to determine their effect on rate. If for example, doubling reactant A concentration does nothing to the overall rate, it's zero order and is eliminated from the rate law (since anything to the power of zero is just 1). If instead doubling reactant A doubles the rate, then it's first order. If doubling quadruples, second order, and so on. We'd also do the same for reactant B, or any additional reactants to determine their effect on the rate.
This is why whenever this topic is introduced, professors stress on the fact that rate laws are determined experimentally. You cannot just look at a net reaction and say that the overall rate law for example is: rate=k[A]^a[.B]
^b, etc. BUT if you know the detailed mechanism for that reaction (which includes intermediate steps) and you know the slow step, then you can express the rate law based on the slow step. But ultimately, the mechanism comes from experimental data so at the end of the day, it's all experimentally obtained. The only exception is if they say the net reaction is elementary, meaning there's no intermediates and both reactants effect the rate. In that case, you can simply express both reactants and their coefficients in the rate law. A question would specify this if that was the case. Usually though, they would present a table and ask you to determine the rate law by looking at how different reactant concentrations effect the rate.
Just be careful though because if they asked for a
rate expression for a single step of a given reaction mechanism - this is different from the rate law and can be used to express any given step of a reaction (even the slow step) simply by: rate = k[reactant 1]^x[reactant 2]^y, etc (where k is the rate for that step in the forward direction to the next product/intermediate)
Hope this makes sense.