[sheblindedmewithscience]

Hi,

This isn't so much a homework problem, as it is getting help understanding two concepts of rate law and equilibrium formulas. From my understanding, with the exception of a scenario where all the steps of a reaction are given, including the rate-determining (slowest) step, that would determine the rate law reaction, the rate law reaction (order of each reactant and the overall reaction order) must be determined experimentally.

For an equilibrium constant, the coefficients for the overall formula for the reverse and forward reactions, can be used to put together the equilibrium constant formula for the all necessary exponents. Is the reason one can use the coefficients for exponents in an equilibrium constant equation because you are using the equilibrium overall reaction and therefore, there will be constant amount of products and reactants formed (forward rate equals the reverse rate) versus rate law equations, where you don't know where equilibrium is and you don't know which steps will be the slowest, unless given?

From what I read, the equilibrium constant can be derived from the forward and reverse rate reaction equations, since these reactions are going in the forward and reverse directions. In rate  law formulas, only the reactants are used (I assume this is due to the kinetic properties of the rate law, where only reactants are considered for how fast a reaction and we assume for rate law problems that the reaction is driven to completion??).

In summary, could someone explain why you can always use coefficients for the equilibrium constant equation versus rate law formulas, which usually have their exponents determined experimentally? Also, could some clarify why we are using just reactants for rate law equations?

[Corribus]

First thing, rate laws and equilibrium expressions relate to different things. Rate law describes how quickly a chemical process takes place and equilibrium expressions describe what the system looks like when the process is complete.

In experimental science, rates are usually measured to determine the mechanism, not the other way around. The rate law reflects the mechanism. As an example, if one substance, A, turns into another, B, the rate at which this happens will depend on whether a single A turns into B spontaneously, or whether two A's have to hit each other to form a B (or whatever). The latter requires a collision, which affects the rate, which affects the rate law. If you know the exact mechanism ahead of time, you could probably specify the rate law accordingly. But usually you don't, hence why the exponents in the rate law vary according to experiment.

Equilibrium, on the other hand, is determined by thermodynamics. The mixture composition at equilibrium does not depend on how the system gets there. The exponents in the equilibrium expression arise from the thermodynamic definition of the equilibrium constant. Keep in mind that in most solutions that are approximately ideal, the concentration is used as a surrogate for the chemical activity, which is the quantity that is most relevant for determining the equilibrium constant.