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Please help me to solve this one. I'm having a bit of a hard time grasping these concepts.

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closed as off-topic by airhuff, a-cyclohexane-molecule, A.K., Jon Custer, Mithoron Oct 7 '18 at 20:31

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In the pre-equilibrium you treat the first reaction as an equilibrium to find $[\ce{A}]$ and substitute this into the second rate expression $\mathrm d[\ce{P}]/\mathrm dt=k_2[\ce{A}][\ce{B}]$. In the steady state approach you assume that the intermediate species $[\ce{A}]$ has a small rate of change thus let $\mathrm d[\ce{A}]/\mathrm dt = 0$ and find $[\ce{A}]$ this way.

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