Express the rate of the following reaction in terms of disappearance of the reactants and appearance of products:
2NO(g) + O₂(g) → 2NO₂(g)

Rate of reaction in terms of disappearance of the reactants and appearance of product.

2NO(g) + O₂(g) → 2NO₂(g)

$\mathrm{rate} = -\frac{\mathrm{d}\left[\mathrm{NO}\right]}{2\mathrm{dt}}=\frac{-\mathrm{d}\left[{\mathrm{O}}_2\right]}{\mathrm{dt}}=\frac{+\mathrm{d}\left[{\mathrm{NO}}_2\right]}{2\mathrm{dt}}$

The rate expression is derived by step II of the mechanism, as it is the slower one

rate = k[NOBr₂][NO] ...(i)

However, NOBr₂ is an intermediate and thus its concentration should be replaced from equation (i)
From step (i),

Equilibrium constant, ${\mathrm{K}}_{\mathrm{c}} = \frac{\left[{\mathrm{NOBr}}_2\right]}{{\left[\mathrm{NO}\right]}_2 \left[{\mathrm{Br}}_2\right]}$

$\therefore$          $\left[{\mathrm{NOBr}}_2\right] = {\mathrm{k}}_{\mathrm{c}} \left[\mathrm{NO}\right] \left[{\mathrm{Br}}_2\right]$                  ...(ii)

Then by equation (i) and (ii)

              $\mathrm{rate} = \mathrm{k}\text{'} - {\left[\mathrm{NO}\right]}^2 \left[{\mathrm{Br}}_2\right]$

Order of the reaction is 2+1 =3

The rate of reaction in terms of disappearance of the reactant and appearance of product.

H₂(g) + l₂(g) → 2HI(g)

$\mathrm{rate}=\frac{-\mathrm{d}\left[{\mathrm{H}}_2\right]}{\mathrm{dt}}=\frac{-\mathrm{d}\left[{\mathrm{I}}_2\right]}{\mathrm{dt}}=\frac{1}{2}\frac{\mathrm{d}\left(\mathrm{HI}\right)}{\mathrm{dt}}$

The rate of the reaction in terms of disappearance of the reactant and appearance of product.

2NO₂(g) + F₂(g) → 2NO₂ F(g)

$$\begin{gathered} \mathrm{rate}=\frac{-1}{2}\frac{\mathrm{d}\left[{\mathrm{NO}}_2\right]}{\mathrm{dt}} \\ = -\mathrm{d}\frac{\left[{\mathrm{F}}_2\right]}{\mathrm{dt}}=\frac{1}{2}\frac{\mathrm{d}\left[{\mathrm{NO}}_2\mathrm{F}\right]}{\mathrm{dt}} \end{gathered}$$

The rate of the reaction in terms of disappearance of the reactant and appearance of product.

CO(g) + NO₂(g) → CO₂(g) + NO(g)

$$\begin{gathered} \mathrm{rate}=\frac{-\mathrm{d}\left[\mathrm{CO}\right]}{\mathrm{dt}}=\frac{-\mathrm{d}\left[{\mathrm{NO}}_2\right]}{\mathrm{dt}} \\ = \frac{\mathrm{d}\left[{\mathrm{CO}}_2\right]}{\mathrm{dt}}=\frac{\mathrm{d}\left[\mathrm{NO}\right]}{\mathrm{dt}} \end{gathered}$$