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The pre-equilibirum approach uses a psuedo-equilibrium situation where one of the steps of the reaction is said to be at equilibrium and set equal to K, the equilibirum constant. This equation involving K is then manipulated and subsituted into the other reaction rate equation, so that the the reaction rate equation of the steps ends up looking like the observed reaction rate. It is a lot simpler method than the steady-state approach, which involves calculus.
The pre-equilibrium approach starts with has a fast elementary step followed by a slow elementary step. With the pre-equilibrium approach, we can't have intermediates between the fast and slow in the rate law. This approach also doesn't factor in account the reverse reaction that is occurring in the fast reaction, therefore, we want to substitute a term in for the intermediate step to have an overall rate law that is based on the slow step and does not include in intermediates.
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