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QUESTION

# What is the rate law for the following mechanism in terms of the overall rate constant k? Step 1: A + B leftrightarrow C (fast) Step 2:  B + C -&gt; D (slow)

The is "rate" = k["A"]["B"]^2.

The reaction is

"A + B"color(white)(l) ⇌ "C" (fast) "B + C" color(white)(l)stackrelcolor(blue)(k_2color(white)(m))(→) "D" (slow)

The rate of the reaction is governed by the slow step.

This gives the rate equation

"rate" = k["B"]["C"]

The problem is that "C" isn't one of the reactants.

We must express "[C]" in terms of "[A]" and "[B]".

We can do that because the first step is an equilibrium.

K = "[C]"/"[A][B]"

∴ ["C"] = K["A"]["B"]

Substituting into the original rate expression, we get

"rate" = k_2["B"] × K["A"]["B"] = kK["A"]["B"]^2

Let k = k_2K, and the rate law becomes

"rate" = k["A]["B"]^2