2NOCl--->2NO + Cl2
Time(s) [NOCL)(M)
0 0.200
575 0.158
995 0.137
2080 0.102
a) Calculate the rate constant, k, and include units.
b)What is the average rate of reaction between time 0 and 995 s?
Are these data experimental or is it a problem? Any clue as to the order?
it is the problem
a) To calculate the rate constant, k, we can use the integrated rate law for a first-order reaction:
ln([NOCl]t/[NOCl]0) = -kt
Here, [NOCl]t refers to the concentration of NOCl at a given time t, [NOCl]0 is the initial concentration of NOCl, k is the rate constant we are trying to calculate, and t is the time elapsed.
Given the data, we can choose any two data points to substitute into the equation. Let's choose the points at time 0 and time 575 s:
ln(0.200/0.200) = -k * 0
ln(0.158/0.200) = -k * 575
Simplifying the second equation gives us:
ln(0.79) = -k * 575
Now we can solve for the rate constant, k. Take the antilog of both sides to eliminate the natural logarithm:
0.79 = e^(-k * 575)
To isolate k, divide both sides by e^(-k * 575):
0.79 / e^(-k * 575) = 1
Taking the natural logarithm of both sides:
ln(0.79 / e^(-k * 575)) = ln(1)
Using the logarithmic property, we can rewrite the left side as:
ln(0.79) - ln(e^(-k * 575)) = 0
Simplifying further:
ln(0.79) + k * 575 = 0
Now, isolate k:
k * 575 = -ln(0.79)
k = -ln(0.79) / 575
Plugging in the value for ln(0.79) ≈ -0.2336 and evaluating the expression gives us:
k ≈ -0.2336 / 575
Therefore, the rate constant, k, is approximately -4.06 x 10^(-4) s^(-1).
b) The average rate of reaction between time 0 and 995 s can be determined by calculating the change in concentration of NOCl over the change in time:
Average rate = (Δ[NOCl]) / (Δt)
To find the change in concentration, subtract the initial concentration [NOCl]0 from the final concentration [NOCl]995:
Δ[NOCl] = [NOCl]995 - [NOCl]0
Substituting the given values:
Δ[NOCl] = 0.137 - 0.200
Δ[NOCl] = -0.063 M
The change in time is given as Δt = 995 s.
Now, we can calculate the average rate:
Average rate = (-0.063 M) / (995 s)
The units cancel out, leaving us with the average rate in terms of M/s:
Average rate ≈ -6.331 x 10^(-5) M/s
Therefore, the average rate of reaction between time 0 and 995 s is approximately -6.331 x 10^(-5) M/s.