The rate law is defined as the rate of a chemical reaction, which is dependent on the concentration of the reactants.
It can be calculated by the formula:
[tex]\text v_o &= \text k [\text A]^x [\text B]^y[/tex]
where,
In the given reaction:
[tex]\begin{aligned}2\;\text{ClO}_2\left(aq \right )+2\text{OH}^-\left(aq \right )\rightarrow\text{ClO}_3^-\left(aq \right )+\text{ClO}_2^-+\text{H}_2\text{O} \end{aligned}[/tex]
Using the rate law formula, we get:
Rate = K [Cl]ⁿ [OH⁻]ⁿ
0.0248 = K [0.060]ⁿ [0.030 ]ⁿ ........(1)
0.00276 = K [0.020]ⁿ [0.030 ]ⁿ .........(2)
0.00828 = K [0.020]ⁿ [0.090]ⁿ ..........(3)
Dividing (1) equation by (2), we get:
[tex]\begin {aligned} \dfrac {0.0248}{0.00276}&= \dfrac{\text K (0.06)^n (0.03)^n} {\text K (0.02)^n (0.03)^n}\\\\9 &= \dfrac{0.06}{0.02}^n\\\\3 ^2 &= 3 ^ m\\\text m &=2\\\end {aligned}[/tex]
Dividing the equation (2) by (3), we get:
[tex]\begin {aligned} \dfrac {0.00276}{0.00828 }&= \dfrac{\text K (0.02)^n (0.03)^n} {\text K (0.02)^n (0.09)^n}\\\\\dfrac{1}{3} &= \dfrac{0.03}{0.09}^n\\\\ \dfrac{1}{3} ^1 &= \dfrac{1}{3} ^n\\\\\text n &=2\\\end {aligned}[/tex]
Based on the rate law:
a. Rate = K [ClO₂]²⁻ [OH⁻]¹
b. 0.0248 = K [0.06]² [0.03]¹
K = [tex]\dfrac {0.0248}{(0.06)^2 \times 0.03}[/tex] = 229.63 m⁻²s⁻¹
c. Rate = K [ClO]₂ [OH⁻]ⁿ
Rate = 229.62 x (0.2)² (0.05)¹
Therefore, the rate of the reaction is 0.45926 m/sec.
To know more about the rate law of the reaction, refer to the following link:
https://brainly.com/question/14779101
