Question

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

n₂	h₂	initial rate of reaction
0.363m	6.65m	233.m/s
1.53m	1.37m	853.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 order with respect to $H_2$

Keep $[N_2]$ constant (first two rows where $[N_2]= 0.363M$). $\frac{[H_2]_2}{[H_2]_1}=\frac{6.65M}{1.37M}\approx4.85$, $\frac{\text{rate}_2}{\text{rate}_1}=\frac{233M/s}{48.0M/s}\approx4.85$. Since the ratio of rates is equal to the ratio of $[H_2]$, the order with respect to $H_2$ is 1.

Step2: Determine order with respect to $N_2$

Keep $[H_2]$ constant (first and third rows where $[H_2]=1.37M$). $\frac{[N_2]_3}{[N_2]_1}=\frac{1.53M}{0.363M}\approx4.22$, $\frac{\text{rate}_3}{\text{rate}_1}=\frac{853M/s}{48.0M/s}\approx17.77$. Since $4.22^2\approx17.77$, the order with respect to $N_2$ is 2.

Step3: Write the rate - law

The rate - law is rate = $k[N_2]^2[H_2]^1$.

Step4: Calculate the rate constant $k$

Using the first row of data ($[N_2]=0.363M$, $[H_2]=1.37M$, rate = $48.0M/s$) and the rate - law rate = $k[N_2]^2[H_2]$. We can solve for $k$: $k=\frac{\text{rate}}{[N_2]^2[H_2]}$. Substitute the values: $k=\frac{48.0M/s}{(0.363M)^2\times1.37M}$. $k=\frac{48.0M/s}{0.131769M^2\times1.37M}=\frac{48.0M/s}{0.18052353M^3}\approx270M^{-2}s^{-1}$.

Answer:

rate = $k[N_2]^2[H_2]$
$k = 270M^{-2}s^{-1}$