Editing Rate-determining step (section)

===First step rate-determining===
In fact, however, the observed reaction rate is [[order of reaction|second-order]] in {{NOx|x=2}} and zero-order in CO,<ref>Whitten K. W., Galley K. D., Davis R. E. ''General Chemistry'' (4th edition, Saunders 1992), p. 638–639.</ref> with rate equation ''r'' = ''k''[{{NOx|x=2}}]<sup>2</sup>. This suggests that the rate is determined by a step in which two {{NOx|x=2}} molecules react, with the CO molecule entering at another, faster, step. A possible mechanism in two elementary steps that explains the rate equation is:
# {{NOx|x=2}} + {{NOx|x=2}} → NO + {{NOx|x=3}} ''(slow step, rate-determining)''
# {{NOx|x=3}} + CO → {{NOx|x=2}} + {{CO2}} ''(fast step)''
In this mechanism the [[reactive intermediate]] species {{NOx|x=3}} is formed in the first step with rate ''r''<sub>1</sub> and reacts with CO in the second step with rate ''r''<sub>2</sub>. However, {{NOx|x=3}} can also react with NO if the first step occurs in the ''reverse direction'' (NO + {{NOx|x=3}} → 2 {{NOx|x=2}}) with rate ''r''<sub>−1</sub>, where the minus sign indicates the rate of a reverse reaction.

The concentration of a reactive intermediate such as [{{NOx|x=3}}] remains low and almost constant. It may therefore be estimated by the [[steady state (chemistry)|steady-state]] approximation, which specifies that the rate at which it is formed equals the (total) rate at which it is consumed. In this example {{NOx|x=3}} is formed in one step and reacts in two, so that
: <math chem>\frac{d\ce{[NO3]}}{dt} = r_1 - r_2 - r_{-1} \approx 0.</math>

The statement that the first step is the slow step actually means that the first step ''in the reverse direction'' is slower than the second step in the forward direction, so that almost all {{NOx|x=3}} is consumed by reaction with CO and not with NO. That is, ''r''<sub>−1</sub> ≪ ''r''<sub>2</sub>, so that ''r''<sub>1</sub> − ''r''<sub>2</sub> ≈ 0. But the overall rate of reaction is the rate of formation of final product (here {{CO2}}), so that ''r'' = ''r''<sub>2</sub> ≈ ''r''<sub>1</sub>. That is, the overall rate is determined by the rate of the first step, and (almost) all molecules that react at the first step continue to the fast second step.