Question

Hello I am doing a few practice problems for an upcoming exam and would appreciate the help!

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)
1.33 × 10−3	8.97 × 10−6
2.13 × 10−3	7.07 × 10−6
2.93 × 10−3	5.83 × 10−6
3.73 × 10−3	4.96 × 10−6
4.53 × 10−3	4.32 × 10−6

So I got that the reaction rate=2, however what would the rate constant be?

Thank you

Answer 1

As you said

Rate is of second order

Which can be found by drawing a graph between 1/[ClO] and time. It is straight line. Indicating the order = 2

We have:

Time	[ClO} (M)	1/[ClO]
1.33 *10−3	8.97 *10−6	1.12*105
2.13 * 10−3	7.07 * 10−6	1.41*105
2.93 * 10−3	5.83* 10−6	1.72*105
3.73 *10−3	4.96 * 10−6	2.02*105
4.53 * 10−3	4.32 * 10−6	2.31*105

Now second order reaction we have

1/[ClO ] = 1/[ClO]_o + kt

comparing it with y = mx+ c

m = k = slope = y₂-y₁ / x₂-x₁  = (2.31*10⁵) - (1.12*10⁵) / ( 4.53 * 10⁻³) - (1.33 *10⁻³)

k ( rate constant) = 3.75 *10⁷ M^-1s^-1

Any two values with their corresponding times can be taken