In the lab, we can determine the order of reaction and the rate constant by plotting the concentration vs time data. For example, the concentration of C₄H₉Cl was determined at 50 second and 100 second time intervals as the reaction proceeded. The balanced chemical equation is below.

C₄H₉Cl (l) + H₂O (l) → C₄H₉OH (l) + HCl (aq)

The following concentration/time data was collected in the lab.

The data was plotted as concentration of butyl chloride vs. time in seconds.

From the plot above, we can see this is not a zero order reaction. A plot of concentration vs. time would give a straight line. We can plot ln[C₄H₉Cl] vs. time as well as 1/[C₄H₉Cl] vs. time. The data is shown below.

Below, 1/[C₄H₉Cl] vs. time was plotted. The plot is not linear, therefore, it is not a second order reaction.

Below, ln[C₄H₉Cl] vs. time is plotted. The plot is linear, and the reaction is first order in C₄H₉Cl.

The rate constant is equal to the negative of the slope. The slope is -0.00201, and k = 0.00201 s^-1.

To find the slope of the line, you can do a linear regression in Excel and display the equation on the plot. If you do not have access to Excel, you can find the slope, \(\displaystyle \frac{\Delta y}{\Delta x}\), using two points on the line that are further away from one another. Then use the point slope formula to find the equation of the line.

First, find the slope:

y₂ – y₁ = m (x₂ – x₁)

Solve for the slope, m.

\(\displaystyle m\;=\;\frac{y_2\;-\;y_1}{x_2\;-\;x_1}\)
 

Next we can use one of the points on the line to determine the equation for the line.

Y – Y₁ = m (x – x₁)

Worksheet: Time Concentration Data: Plots

Exercises

Exercise 1. The following reaction

C₂H₄ (g) + O₃ (g) → C₂H₄O (g) + O₂ (g)

has the time-concentration data in the table below. Use the information to answer the questions.

Check Solution to Exercise 1

Exercise 2. Consider the reaction and the concentration/time data below to answer the questions.

2 N₂O₅ (g) → 4 NO₂ (g) + O₂ (g)

Check Solution to Exercise 2

Exercise 3. Consider the following reaction and concentration/time data obtained from the lab to answer the questions.

2 NOBr (g) → 2 NO (g) + Br₂ (g)

Check Solution to Exercise 3

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