Question

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

h₂	i₂	initial rate of reaction
0.947m	2.35m	3.58×10⁵ m/s
3.09m	0.525m	2.61×10⁵ m/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 reaction order with respect to $I_2$

Compare the first and second rows where $[H_2]$ is constant. $\frac{[I_2]_2}{[I_2]_1}=\frac{2.35M}{0.525M}\approx4.48$, $\frac{\text{rate}_2}{\text{rate}_1}=\frac{3.58\times 10^{5}M/s}{8.00\times 10^{4}M/s}= 4.475\approx4$. So the reaction is first - order with respect to $I_2$.

Step2: Determine reaction order with respect to $H_2$

Compare the first and third rows where $[I_2]$ is constant. $\frac{[H_2]_3}{[H_2]_1}=\frac{3.09M}{0.947M}\approx3.26$, $\frac{\text{rate}_3}{\text{rate}_1}=\frac{2.61\times 10^{5}M/s}{8.00\times 10^{4}M/s}=3.2625\approx3.26$. So the reaction is first - order with respect to $H_2$.

Step3: Write the rate law

The rate law is $\text{rate}=k[H_2][I_2]$.

Step4: Calculate the rate constant $k$

Using the first row of data: $k = \frac{\text{rate}}{[H_2][I_2]}$. Substitute $\text{rate}=8.00\times 10^{4}M/s$, $[H_2]=0.947M$ and $[I_2]=0.525M$. $k=\frac{8.00\times 10^{4}M/s}{0.947M\times0.525M}\approx1.6\times 10^{5}M^{-1}s^{-1}$.

Answer:

rate = $k[H_2][I_2]$
$k = 1.6\times 10^{5}M^{-1}s^{-1}$