Determining Order and Rate Constant for Ozone Reaction at 298 K

[plexus0208]

Homework Statement

In a reaction between ozone and an organic species, the observed rate was found to depend only on the concentration of ozone at 298 K. Using the data below, determine the order of this reaction and the rate constant (include units).
Time (s) |Ozone conc (molecules/cm3)
0 | 4.311×1015
50 | 2.890×1015
100 | 2.036×1015
150 | 1.435×1015
200 | 0.995×1015
250 | 0.689×1015

Homework Equations

The Attempt at a Solution

Is it first order? I plotted the graph of ln[O3] vs. time on excel and that was a straight line.
Also to find k, do I use ln[A]_t = ln[A]_o - kt? If I use this equation, which value do I use for [A]_t?--because the value of k differs slightly for different values.

 

[windwitch]

When contemplating whether the reaction is first order or not, I would advise taking a graphical approach. Try to imagine what a graph would look like if the line had an equation of a first order reaction versus a second order reaction. Perhaps you may even want to try looking at the graphic behaviour of higher order reactions although the first two may suffice.

Now, when you are determining the value of [A]t, you have to understand that any point on the line works. "HOWEVER," you must use a point on the graph that you have created. Don't forget that when you are creating a line of best fit, you are assuming only the points on that line are relevant, not the points away from the line that helped form it.

 

[Blueshift5]

Based on the provided data, it appears that the reaction between ozone and the organic species is first order. This can be confirmed by plotting the natural log of the ozone concentration versus time, as you have done. The resulting straight line indicates a first order reaction.

To find the rate constant (k), you can use the equation ln[A]t = ln[A]o - kt, where [A]t is the ozone concentration at a specific time and [A]o is the initial ozone concentration. In this case, you can use any of the given values for [A]t, as long as you use the corresponding time value. For example, if you use the first data point (time = 0 s, [A]t = 4.311×1015 molecules/cm3), you can solve for k using the equation. Then, if you use the second data point (time = 50 s, [A]t = 2.890×1015 molecules/cm3), you should get the same value for k. This can help confirm the first order reaction and the validity of your data. The units for k will depend on the units used for time and concentration in the given data.