What is the rate law for the following mechanism in terms of the overall rate constant k?

Step 1: A + B ↔ C (fast)

Step 2: B + C → D (slow)

We’re asked to determine the overall rate constant K for the given two steps mechanism.

When a **reaction mechanism **is given, the **rate law will depend on reactants and products in the slow step**.

▪Rate law only *involves the reactants*

▪ The *coefficients *of the reactants in the slow step are the *order* of the reaction with respect to that reactant

▪ Rate Law has a general form of:

$\overline{){\mathbf{Rate}}{\mathbf{}}{\mathbf{Law}}{\mathbf{=}}{\mathbf{k}}{\left[\mathbf{X}\right]}^{{\mathbf{a}}}{\left[\mathbf{Y}\right]}^{{\mathbf{b}}}}$

Where

k = rate constant

X & Y = reactants

a & b = reactant orders

▪ The equilibrium constant has a general form of:

$\overline{){{\mathbf{K}}}_{{\mathbf{r}}}{\mathbf{=}}\frac{\mathbf{p}\mathbf{r}\mathbf{o}\mathbf{d}\mathbf{u}\mathbf{c}\mathbf{t}\mathbf{s}}{\mathbf{r}\mathbf{e}\mathbf{a}\mathbf{c}\mathbf{t}\mathbf{a}\mathbf{n}\mathbf{t}\mathbf{s}}}$