Feb 19, 2016

$R = k \left[C l {O}_{2}\right] {\left[O {H}^{-}\right]}^{2}$
$k = 1147.2 {M}^{- 2}$
The rate constant k changed only when Temperature changed.

#### Explanation:

(a) The general expression of the reaction rate is:

$R = k {\left[C l {O}_{2}\right]}^{n} {\left[O {H}^{-}\right]}^{m}$

To determine the order of each reactant we will follow the following method.

We will choose two data entries where one of the concentrations is unchanged, then divide the rates of each entry by each other:

First to determine m :

$\frac{{R}_{1}}{{R}_{2}} = \frac{k {\left[C l {O}_{2}\right]}_{1}^{n} {\left[O {H}^{-}\right]}_{1}^{m}}{k {\left[C l {O}_{2}\right]}_{2}^{n} {\left[O {H}^{-}\right]}_{2}^{m}}$

$\implies \frac{2.33 \times {10}^{- 4}}{9.34 \times {10}^{- 4}} = \frac{\cancel{k} \times \cancel{{\left(1.30 \times {10}^{- 3}\right)}^{n}} \times {\left(1.25 \times {10}^{- 2}\right)}^{m}}{\cancel{k} \times \cancel{{\left(1.30 \times {10}^{- 3}\right)}^{n}} \times {\left(2.50 \times {10}^{- 2}\right)}^{m}}$

$\implies 0.25 = {\left(0.50\right)}^{m} \implies m = 2$

Now to determine n :

$\frac{{R}_{2}}{{R}_{3}} = \frac{k {\left[C l {O}_{2}\right]}_{2}^{n} {\left[O {H}^{-}\right]}_{2}^{m}}{k {\left[C l {O}_{2}\right]}_{3}^{n} {\left[O {H}^{-}\right]}_{3}^{m}}$

$\implies \frac{9.34 \times {10}^{- 4}}{1.87 \times {10}^{- 3}} = \frac{\cancel{k} \times {\left(1.30 \times {10}^{- 3}\right)}^{n} \times \cancel{{\left(2.50 \times {10}^{- 2}\right)}^{m}}}{\cancel{k} \times {\left(2.60 \times {10}^{- 3}\right)}^{n} \times \cancel{{\left(2.50 \times {10}^{- 2}\right)}^{m}}}$

$\implies 0.5 = {\left(0.50\right)}^{n} \implies n = 1$

Therefore, the reaction rate expression is: $R = k \left[C l {O}_{2}\right] {\left[O {H}^{-}\right]}^{2}$

(b) to calculate the value of the reaction rate constant we can choose any of the entries as follows:

$R = k \left[C l {O}_{2}\right] {\left[O {H}^{-}\right]}^{2} \implies 2.33 \times {10}^{- 4} = k \times 1.30 \times {10}^{- 3} \times {\left(1.25 \times {10}^{- 2}\right)}^{2}$

$\implies k = 1147.2 {M}^{- 2}$

(c) The rate constant k changed only when Temperature changed.

Here is a video that will further explain how to determine the rate order of a reaction rate:
Chemical Kinetics | Determining the Form of the Rate Order.