## I apologize for the formatting issues. Let's go step-by-step to solve this problem:

A.) To find the rate law, we need to determine the order of the reaction with respect to each reactant. Looking at the given equation:

2 NOCl(g) â†’ 2 NO(g) + Cl2(g)

we can see that the rate is dependent on the concentration of NOCl. The exponent of NOCl in the rate law equation is called the order of the reaction with respect to NOCl.

We can determine the order of the reaction by comparing the initial rates at different concentrations of NOCl. Let's calculate the initial rate for each trial and determine the order:

[NOCl]0 Initial Rate (molecules/cm^3*s)

3.0*10^16 5.98*10^4

2.0*10^16 2.66*10^4

1.0*10^16 6.64*10^3

4.0*10^16 1.06*10^5

If we divide the initial rate of each trial by the initial rate of trial 1, we can find the ratio of the rates for different concentrations:

Trial 1: (5.98*10^4) / (5.98*10^4) = 1

Trial 2: (2.66*10^4) / (5.98*10^4) = 0.444

Trial 3: (6.64*10^3) / (5.98*10^4) = 0.111

Trial 4: (1.06*10^5) / (5.98*10^4) = 1.77

Based on these ratios, we can determine the order of the reaction with respect to NOCl:

Rate = k[NOCl]^x

Where x is the order of the reaction with respect to NOCl, and k is the rate constant.

From the above calculations, it appears that the order with respect to NOCl is approximately 1, as the rate doubles when the initial concentration is doubled. So the rate law for this reaction is:

Rate = k[NOCl]

B.) To calculate the rate constant (k), we can use any of the given trials. Let's use trial 1:

[NOCl]0 = 3.0*10^16 molecules/cm^3

Initial Rate = 5.98*10^4 molecules/cm^3*s

Plugging these values into the rate law equation, we get:

5.98*10^4 = k * (3.0*10^16)

Rearranging the equation to solve for k:

k = (5.98*10^4) / (3.0*10^16)

k â‰ˆ 1.9933*10^-12 molecules/cm^3*s

So, the rate constant for this reaction is approximately 1.9933*10^-12 molecules/cm^3*s.

I hope this helps! Let me know if you have any further questions.