Question

Chlorine oxide (ClO), which plays an important role in the depletion of ozone, decays rapidly according to the equation

2ClO(g) → Cl₂(g) + O₂(g)

From the following data, determine the reaction order and calculate the rate constant of the reaction.

Time (s)	[ClO] (M)
2.57 × 10−3	8.49 × 10−6
3.20 × 10−3	7.26 × 10−6
3.83 × 10−3	6.34 × 10−6
4.46 × 10−3	5.62 × 10−6
5.09 × 10−3	5.06 × 10−6

1) What is the order of reaction? (0,1, or 2)?

2) What is the rate constant? (k = ?) (Enter your answer in scientific notation.)

Answer 1

1)

For a zero order reaction, the integrated rate law is written as

Hence, plotting concentration [A] vs time t should yield a straight line if the reaction is indeed zero order.

Similarly, for a first order reaction, the integrated rate law is written as

Hence, plotting ln[A] vs time should yield a straight line if the reaction is indeed first order.

Again, for a second order reaction, the integrated rate law is written as

Hence, plotting 1/[A] vs t should yield a straight line if the reaction is indeed second order.

Now, for the given data, we can tabulate the data points needed to plot the graphs for the test of order of the reaction as follows:

Now, we can plot [ClO] vs time to check if the reaction is zero order:

Note that the plot of [ClO] vs time is clearly not a straight line. Hence, our reaction is not a zero order reaction.

Now, we can plot ln[ClO] vs time as follows:

Clearly, the above plot is also not a straight line, hence, the reaction is not a first order reaction.

Now, we can plot 1/[ClO] vs t as follows:

Note that the above plot of 1/[ClO] vs time is a perfect straight line with R² value of 1.

Hence, the order of our reaction must be 2.

2)

Remember that for a second order reaction, the integrated rate law is

Where k is the rate constant.

Now, the plot of 1/[ClO] in y axis vs time t in x axis has resulted in a straight line with slope k.

Hence, the rate constant of the reaction is the slope of the plot of 1/[ClO] vs time.

The equation of the line for the plot from linear fit is

Where y is 1/[ClO] in M^-1

x is time in seconds (s).

Hence, the unit of the slope will be M^-1 s^-1.

Hence,