Question

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

n₂	h₂	initial rate of reaction
1.72m	1.37m	3.33×10⁴ m/s
1.55m	3.56m	2.03×10⁵ 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 the order with respect to $\ce{N2}$

Compare the first and second rows where $[\ce{H2}]$ is constant ($1.37M$). The ratio of $[\ce{N2}]$ is $\frac{1.72}{1.55}\approx1.11$, and the ratio of the rates is $\frac{3.33\times 10^{4}}{3.00\times 10^{4}} = 1.11$. Since the ratio of the rates is equal to the ratio of the concentrations of $\ce{N2}$, the order with respect to $\ce{N2}$ is 1.

Step2: Determine the order with respect to $\ce{H2}$

Compare the first and third rows where $[\ce{N2}]$ is constant ($1.55M$). The ratio of $[\ce{H2}]$ is $\frac{3.56}{1.37}\approx2.6$, and the ratio of the rates is $\frac{2.03\times 10^{5}}{3.00\times 10^{4}}\approx6.77$. Since $6.77\approx2.6^{2}$, the order with respect to $\ce{H2}$ is 2.

Step3: Write the rate - law

The rate - law is rate = $k[\ce{N2}][\ce{H2}]^{2}$.

Step4: Calculate the rate constant $k$

Using the first row data ($[\ce{N2}]=1.55M$, $[\ce{H2}]=1.37M$, rate = $3.00\times 10^{4}M/s$), substitute into the rate - law:
$k=\frac{\text{rate}}{[\ce{N2}][\ce{H2}]^{2}}=\frac{3.00\times 10^{4}M/s}{1.55M\times(1.37M)^{2}}$
$k=\frac{3.00\times 10^{4}M/s}{1.55M\times1.8769M^{2}}=\frac{3.00\times 10^{4}M/s}{2.90M^{3}}\approx1.0\times 10^{4}M^{-2}s^{-1}$

Answer:

rate = $k[\ce{N2}][\ce{H2}]^{2}$
$k = 1.0\times 10^{4}M^{-2}s^{-1}$