Rate Determination
and Activation Energy

An important part of the kinetic analysis of a chemical reactionis to determine the activation energy, E_a.Activation energy can be defined as the energy necessary toinitiate an otherwise spontaneous chemical reaction so that it willcontinue to react without the need for additional energy. Anexample of activation energy is the combustion of paper. Thereaction of cellulose and oxygen is spontaneous, but you need toinitiate the combustion by adding activation energy from a litmatch.

In this experiment you will investigate the reaction of crystalviolet with sodium hydroxide. Crystal violet, in aqueous solution,is often used as an indicator in biochemical testing. The reactionof this organic molecule with sodium hydroxide can be simplified byabbreviating the chemical formula for crystal violet as CV.

CV⁺(aq) + OH^–(aq) ? CVOH(aq)

As the reaction proceeds, the violet-colored CV⁺reactant will slowly change to a colorless product, following thetypical behavior of an indicator. The color change will beprecisely measured by a Vernier Colorimeter (see Figure 1) set at565 nm wavelength. You can assume that absorbance is directlyproportional to the concentration of crystal violet according toBeer’s law.

The molar concentration of the sodium hydroxide, NaOH, solutionwill be much greater than the concentration of crystal violet. Thisensures that the reaction, which is first order with respect tocrystal violet, will be first order overall (with respectto all reactants) throughout the experiment. You will monitor thereaction at different temperatures, while keeping the initialconcentrations of the reactants the same for each trial. In thisway, you will observe and measure the effect of temperature changeon the rate of the reaction. From this information you will be ableto calculate the activation energy, E_a, for thereaction.

OBJECTIVES

In this experiment, you will

React solutions of crystal violet and sodium hydroxide at fourdifferent temperatures.

Measure and record the effect of temperature on the reactionrate and rate constant.

Calculate the activation energy, E_a, for thereaction.

Figure 1

Figure1

MATERIALS

LabPro or CBL 2 interface	1 liter beaker
computer or handheld	ice
Vernier Colorimeter	two 10 mL graduated cylinders
Temperature Probe	two 100 mL beakers
5 plastic cuvettes	50 mL beaker
0.10 M sodium hydroxide, NaOH, solution	watch with a second hand
2.5 × 10–5 M crystal violet solution

PROCEDURE

1. Obtain and weargoggles.

2. Set up the datacollection system. Connect a LabPro or CBL 2 to the computer orhandheld with the proper interface cable.

a. Connect a Colorimeter toChannel 1 of the interface. Connect a Temperature Probe to Channel2.

b. Start the data collectionprogram.

c. Set up the time graph for 3seconds per sample and 20 samples.

d.Follow the appropriate steps to calibrate the Colorimeter.

3. Ready the NaOH andcrystal violet solutions.

a.Use a 10 mL graduated cylinder to obtain 10.0 mL of 0.10 MNaOH solution. Transfer the solution to a 100 mL beaker.CAUTION: Sodium hydroxide solution is caustic.Avoid spilling it on your skin or clothing.

b.Use another 10 mL graduated cylinder to obtain 10.0 mL of 2.5× 10^–5 M crystal violet solution. Transfer the solutionto a second 100 mL beaker. CAUTION: Crystalviolet is a biological stain. Avoid spilling it on your skin orclothing.

4. You are now readyto perform a trial. The four trials will be at ~10°C, ~15°C, ~20°C,and ~25°C.

a.Prepare a water bath that is ~10°C in a 1 liter beaker.

b.Lower the respective 100 mL beakers containing 10 mL of NaOHand 10 mL of crystal violet solutions into the water bath.

c.When you are certain the reactants have cooled to thetemperature of the water bath, pour the contents of both beakersinto the 50 mL beaker.

d.Gently stir the contents of the 50 mL beaker with theTemperature Probe. After one minute, record the temperature of themixture.

e.Fill a clean, dry cuvette about ¾ full with the reactionmixture. Place the cuvette in the Colorimeter. Close the lid on theColorimeter.

f.Begin data collection.

g.When the data collection is complete, carefully remove thecuvette from the Colorimeter. Dispose of the contents of the beakerand cuvette as directed.

h.Create a new calculated column of natural log (ln) ofabsorbance, using your data-collection program. Display a graph ofln absorbance vs. time.

i.On the plot of ln absorbance vs. time for your latesttrial, fit the data with a linear regression curve. From thislinear fit, record the value of the rate constant, k, inyour data table.

5. Repeat Steps 3-4,using a water bath at ~15°C. Add warm water to the last water bathto bring it up to this temperature.

6. Repeat Steps 3-4,using a water bath at ~20°C. Add warm water to the last water bathto bring it up to this temperature.

7. Repeat Steps 3-4,using a water bath at ~25°C. Add warm water to the last water bathto bring it up to this temperature.

8. Print a graph ofln absorbance vs. time, with all four trials displayed onthe graph.

DATA TABLE

Trial	Temperature (°C)	Rate constant, k (s–1)
1	118c	-o.002532
2	14.8C	-0.002062
3	20.2C	-0.004048
4	21.3	-0.004513

DATA ANALYSIS

1. Create a graph ofyour data above, plotting Temperature (°C) on the x axis, and therate constant, k, on the y axis. Use the manual-entrycapability of your data-collection program to enter thesevalues.

2. In order todetermine the activation energy, E_a, you willfirst need to plot the natural log of k vs. thereciprocal of absolute temperature.

a. From the rate constant,k, data you entered in Step 1, create a calculated column,ln rate constant, k.

b. Create a second column, reciprocal ofabsolute (Kelvin) temperature, by creating a new calculated column,1/(Temperature (°C) + 273).

c.Display a graph ln k vs. 1/absolutetemperature.

3. Calculate theactivation energy, E_a, for the reaction. To dothis, first perform a linear fit on the graph you created in Step 2above. Use the slope, m, of the linear fit to calculatethe activation energy, E_a, in units of kJ/mol.Note: On a plot of ln k vs. 1/absolutetemperature, E_a = m × R.

4. A well-knownapproximation in chemistry states that the rate of a reaction oftendoubles for every 10°C increase in temperature. Use your data totest this rule. Calculate the ratio of the rate constant at ~20°Cto the rate constant at ~10°C. Then calculate the ratio of the rateconstant at ~25°C to the rate constant at ~15°C. How close werethese values to a ratio of 2? (Note: It is notnecessarily equal to 2.00; this is just an approximate value, anddepends on the activation energy for the reaction.)

5. Using the rateconstant and precise temperature value for the trial that was doneat room temperature (~20°C), as well as the E_avalue you obtained in Step 3 above, calculate what the rateconstant would be at 40°C.