1. Reaction Mechanisms and Equilibrium
The rates of the forward and reverse reactions are the same when a system is at equilibrium.
At equilibrium: rateforward = ratereverse
Example: ClNO2(g) + NO(g) ⇄ NO2(g) ClNO(g)
At equilibrium: kf[ClNO2][NO] = kr[NO2][ClNO]
Kf = [NO2][ClNO] = kc (the equilibrium constant)
Kr [ClNO2][NO]

2. Solving a rate law involving equilibrium
Find the slowest step (the rate-determining step)
Write a temporary rate law using the slowest step.
Write the equilibium expression for the fast-forward reversible elementary step. (the one at equilibrium with the double arrow)
Substitute the equation from step 3 into the temporary rate law from step 2 so that only reactant are present (no intermediates or products!) and solve.

3. Example: Given the following mechanism, determine the rate law:
Step 1: NO + Br2 ⇄ NOBr Fast-Equilibrium
Step 2: NOBr2 + NO ⇄ 2NOBr Slow
Notice: Step 1 includes the forward and reverse reaction!
Temporary Rate law: Rate = k[NOBr2]1[NO]1
Since Rate of forward = Rate of reverse
kfor[NO][Br2] = krev[NOBr2]
keq= [NOBr2]
[NO][Br2]

4. NOBr2 is an intermediate, solve for it [NOBr2] = k[NO][Br2]
Use the equilibrium expression to solve for the product on the equilibrium step:
keq = [NOBr2]
[NO][Br2]
NOBr2 is an intermediate, solve for it
[NOBr2] = k[NO][Br2]
Substitute into temporary law:
Rate = k[NOBr2]1[NO]1
Rate = k[NO]1[Br2]1[NO]1
Rate = k[Br2]1[NO]2
Is this a valid mechanism?
Yes

5. Example: Given the following mechanism, determine the rate law:
Step 1: NO + H2 ⇄ N + H2 O Fast-Equilibrium
Step 2: N + NO  N2O Slow
Step 2: N2O + H2 N2 + H2 O Fast
Notice: Step 1 includes the forward and reverse reaction!
Temporary Rate law: Rate = k[N]1[NO]1
Since Rate of forward = Rate of reverse
kfor[NO][H2] = krev[H2O][N]
keq= [H2O][N]
[NO][H2]

6. Substitute into temporary law: Rate = k[N]1[NO]1
Use the equilibrium expression to solve for the product on the equilibrium step:
keq = [H2O][N]
[NO][H2]
N is an intermediate , solve for it & substitute
[N] = k[NO][H2]
[H2O]
Substitute into temporary law:
Rate = k[N]1[NO]1
Rate = k[NO]1[H2]1[NO]1
Rate = k[H2]1[NO]2 [H2O]-1
Is this a valid mechanism? No

7. The end.