Question

some measurements of the initial rate of a certain reaction are given in the table below.

h₂	i₂	initial rate of reaction
1.47m	0.699m	0.551m/s
0.161m	0.699m	0.0603m/s
1.47m	0.107m	0.0843m/s

use this information to write a rate law for this reaction, and calculate the value of the rate constant k. round your value for the rate constant to 2 significant digits. also be sure your answer has the correct unit symbol.
rate = k
k =

Explanation:

Step1: Determine the order with respect to $H_2$

Compare the first and second rows where $[I_2]$ is constant. $\frac{\text{rate}_2}{\text{rate}_1}=\frac{0.0603}{0.551}$, and $\frac{[H_2]_2}{[H_2]_1}=\frac{0.161}{1.47}$. $(\frac{0.161}{1.47})^n=\frac{0.0603}{0.551}$, solving for $n$ gives $n = 1$.

Step2: Determine the order with respect to $I_2$

Compare the first and third rows where $[H_2]$ is constant. $\frac{\text{rate}_3}{\text{rate}_1}=\frac{0.0843}{0.551}$, and $\frac{[I_2]_3}{[I_2]_1}=\frac{0.107}{0.699}$. $(\frac{0.107}{0.699})^m=\frac{0.0843}{0.551}$, solving for $m$ gives $m = 1$.

Step3: Write the rate - law

The rate - law is rate = $k[H_2][I_2]$.

Step4: Calculate the rate constant $k$

Using the first row data: $k=\frac{\text{rate}}{[H_2][I_2]}$. Substitute rate = $0.551M/s$, $[H_2]=1.47M$ and $[I_2]=0.699M$. $k=\frac{0.551}{1.47\times0.699}\ M^{-1}s^{-1}\approx0.53\ M^{-1}s^{-1}$

Answer:

rate = $k[H_2][I_2]$
$k = 0.53\ M^{-1}s^{-1}$