Rate Determination and Activation Energy

Rate Determination and Activation Energy

 

OBJECTIVES

• To determine the effect of temperature on chemical kinetics.
• React solutions of crystal violet and sodium hydroxide at four different temperatures.
• Measure and record the effect of temperature on the reaction rate and rate constant.
• Calculate the activation energy, E_a, for the reaction.

 

Lecture Topic References

Review the following before performing the experiment:

Chapter Title: Chemical Kinetics
Section Title: The Rate Law:  The Effect of Concentration on Reaction Rate; The Effect of Temperature on Reaction Rate

Tro, N. (2017). Chemistry:  A Molecular Approach. 4^th Edition. Boston: Pearson. (Or latest edition)

CONCEPTS

An important part of the kinetic analysis of a chemical reaction is to determine the activation energy, E_a. Activation energy can be defined as the energy necessary to initiate an otherwise spontaneous chemical reaction so that it will continue to react without the need for additional energy. An example of activation energy is the combustion of paper. The reaction of cellulose and oxygen is spontaneous, but you need to initiate the combustion by adding activation energy from a lit match.

In this experiment you will investigate the reaction of crystal violet with sodium hydroxide. Crystal violet, in aqueous solution, is often used as an indicator in biochemical testing. The reaction of this organic molecule with sodium hydroxide can be simplified by abbreviating 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 the typical behavior of an indicator. You will measure the color change with a Colorimeter (Figure 1). You can assume that absorbance is directly proportional to the concentration of crystal violet according to Beer’s law (A = cb, where A is absorbance; c is concentration in M; light path in cm).

The molar concentration of the sodium hydroxide, NaOH, solution will be much greater than the concentration of crystal violet. This ensures that the reaction, which is first order with respect to crystal violet, will be first order overall (with respect to all reactants) throughout the experiment. You will monitor the reaction at different temperatures, while keeping the initial concentrations of the reactants the same for each trial. In this way, you will observe and measure the effect of temperature change on the rate of the reaction. From this information you will be able to calculate the activation energy, E_a, for the reaction.

 

Figure 1   Colorimeter Schematic Diagram

 

MATERIALS

 

Vernier computer interface or LabQuest

Computer

Colorimeter

Temperature Probe

5 plastic cuvettes

0.10 M sodium hydroxide, NaOH, solution

2.5 × 10^–5 M crystal violet solution

Crystallization dish

ice

two 10 mL graduated cylinders

two scintillation vials

30 mL beaker

watch with a second hand

 

PROCEDURE

Note: You will be preparing a series of water baths during this experiment. Measure the temperature of the water baths in whatever way you wish, but make sure that your measurements are as accurate as possible.

1. Obtain and wear goggles.
2. Calibrate the colorimeter with a blank.
3. Prepare a blank by filling a cuvette 3/4 full with distilled water. To correctly use cuvettes, remember:
   • Wipe the outside of each cuvette with a lint-free tissue (Kimwipes).
   • Handle cuvettes only by the top edge of the ribbed sides (not the clear sides).
   • Dislodge any bubbles by gently tapping the cuvette on a hard surface.
   • Always position the cuvette so the light passes through the clear sides. Cover the cuvette.
4. Connect the Colorimeter to the computer interface. Prepare the computer for data collection by opening the file “35 Activation Energy” from the Advanced Chemistry with Vernier folder of Logger Pro.
5. Open the Colorimeter lid, insert the blank, and close the lid.
6. To calibrate the Colorimeter, press the < or > button on the Colorimeter to select the wavelength of 565 nm (Green). Press the CAL button until the red LED begins to flash and then release the CAL button. When the LED stops flashing, the calibration is complete. Remove the cuvette from the Colorimeter and save it for Step 8.
7. Prepare the NaOH and crystal violet solutions for the first trial.
   1. Use a 10 mL graduated cylinder to obtain 3 mL of 0.10 M NaOH solution. Transfer the solution to a 20 mL white-capped vial. WARNING: Sodium hydroxide solution, NaOH: Causes skin and eye irritation.
   2. Use another 10 mL graduated cylinder to obtain 3 mL of 2.5 × 10–5 M crystal violet solution. Transfer the solution to a second 20 mL white-capped vial. WARNING: Aqueous crystal violet: May be harmful if swallowed. May cause skin irritation and eye damage.
   3. Prepare the water bath using a round crystallization dish.
   4. Cap the two vials tightly and place them in the water bath. Make sure that the level of the solutions inside the vials is below the level of the water bath. The vials containing the solutions should be in the water bath for at least one minute.
8. Conduct the first trial at approximately 25 ^o Be ready to time the reaction.
   1. Check the temperature of the water bath; it should be holding steady at or near 25°C.
   2. Dip the temperature probe in the NaOH inside the vial to make sure it is also holding steady at 25°C (preferably 1 to 2 ^oC lower than this target temperature).  Once this temperature is achieved, pour the NaOH and crystal violet solution into a 30 mL beaker.  Start timing the reaction using the second hand on your watch (you may use your mobile phone, but make sure to clean it after the lab). You will allow the reaction to run for one minute before proceeding to Part c of this step.  Carefully stir the reaction mixture inside a 30 mL beaker with a temperature probe.
   3. After one minute, record the temperature of the reaction mixture.
   4. Fill a clean, dry cuvette about 3/4 full with the reaction mixture. Cover the cuvette and place it inside the Colorimeter. Close the lid on the Colorimeter.
   5. Click . The default settings are 1 sample per second for 200 seconds. You may click to end the data collection early (You may set the time to collect data for  60 seconds). Observe the progress of the reaction.
   6. When data collection is complete, carefully remove the cuvette from the Colorimeter. Dispose of the contents of the beaker and cuvette as directed.
9. You learned from the Concept section of this procedure that the reaction is first order with respect to crystal violet, hence, you can determine the rate constant, k, by plotting a graph of ln Absorbance vs. time.
   1. Choose New Calculated Column from the Data menu.
   2. Enter “ln Absorbance” as the Name, and leave the unit blank.
   3. Enter the correct formula for the column into the Equation edit box by choosing “ln” from the Function list, and selecting “Absorbance” from the Variables list. Click .
   4. Click the y-axis label. Choose ln Absorbance. A graph of ln absorbance vs. time should now be displayed. Change the scale of the graph, if necessary (Click the Autoscale icon on the menu bar).
   5. Click Linear Regression, . Record the slope value in your data table as the rate constant, k. Read the PROCESSING THE DATA section to guide you in interpreting the graph.
   6. Properly label (use Figure 1 for the first graph) and save the graph.
10. To prepare for the next trial, choose Store Latest Run from the Experiment menu.
11. Repeat the necessary steps to complete trials 2–4. The next trials will be at ~20°C, ~15°C, and ~10°C. (Note:  Include all four graphs in your lab report.)

 

PROCESSING THE DATA

As CV⁺ decomposes, its purple color fades away, which makes CV⁺ a perfect indicator of the rate of reaction.  Since the rate of reaction is first-order with respect to the concentration of CV⁺, and the disappearance of purple color CV⁺ (timing until color of CV⁺ dissipates) represents the concentration of CV⁺, which indicates the rate of reaction, collecting and recording the absorbance readings as the reaction proceeds (after one minute of mixing and maintaining the desired temperature setting) can be graphed using the Vernier colorimeter set at 565 nm.  The Absorbance of the mixture in the Colorimeter is directly proportional to the concentration of Crystal Violet (Beer’s Law).  Consequently, Absorbance (A) can be substituted directly for the (CV⁺), so the equation then becomes

                                    In [A]_t = – kt + In [A]₀                                               (Equation 1)

Since the reaction is first order with respect to CV⁺, the integrated rate law for the first order reaction above will be used to obtain the rate constant, k.  As you can see, the above equation shows a linear relationship between the natural log of absorbance and time, t.  Using the general equation of a straight line (y = mx + b) to plot the integrated rate law equation for the first order reaction (Equation 1), a graph of ln [A] vs time can be created, which generated a straight line with a negative slope.

Using the graph of absorbance vs. time, convert the absorbance to In Absorbance on the y-axis, and plot it against the time (60s). If the resulting graph gives a straight line with a negative slope, it confirms that the rate of CV⁺ and OH^– reaction is first order with respect to CV⁺, the negative slope (m) represents the rate constant, k, in the integrated rate law equation.

 

 

In [A]                                                   m = – k

 

In [A]_t = –kt + In [A]₀

y = mx + b

t

Figure 2  Natural Log of Absorbance versus Time (seconds)

Using the negative k from the graph in the integrated rate law equation for the first-order reaction with respect to CV⁺, that is  – (-k).  Therefore, a negative times a negative means the k becomes positive.  Rate constants are supposed to be positive.

Once all the rate constants, k, are graphically determined at four different temperatures, the Arrhenius equation can be manipulated or simplified to allow the graphical determination of activation energy, E_a.

The original Arrhenius Equation shows the other factors that affect the E_a:

K = Ae^{– Ea/RT}                                                        (Equation 2)

 

 

Represents the correct frequency of collision with correct orientation.

Fraction of molecules with enough energy to cross the energy barrier (E_a)

 

 

Manipulated or simplified Arrhenius equation (to obtain the straight line relationship) becomes:

In k =                           (Equation 3)

This requires converting k to In k and t (^oC) to T (Kelvins) and calculating 1/T. Since Equation 3 represents a linear relationship between ln k and 1/T, the data points can be plotted to determine the slope, m.

 

 

 

 

In k

 

 

 

 

 

 

Figure 3  Natural Log of Rate Constant versus the Reciprocal of Absolute Temperature

 

Using Equation 3 and the slope, m, of the trend line, the energy of activation, E_a, can be calculated:

– m

E_a = m x R              (where, R = 8.314 J/k . mol)

If the E_a is low, the energy required to start the reaction is low, hence the time it takes to start the reaction is short.

LAB SAFETY AND WASTE DISPOSAL

Waste Disposal:

Collect and dispose of wastes from Trials I to IV, in the inorganic waste bottle.  Dispose of unused crystal violet in the organic waste bottle, and unused NaOH in the inorganic waste bottle.  All waste bottles are located in the Satellite Accumulation Area (SAA).

Lab Safety: 

Wear the appropriate Personal Protected Equipment (PPE). Read all Safety Data Sheets (SDSs) provided by instructor.  Pay attention to the safety precautions mentioned in the procedure and by the instructor.

Bibliography

Randall, J. and Volz, D. (2017).  Advanced Chemistry with Vernier, 3^rd edition. Rate Determination and Activation Energy. Beaverton, OR:  Vernier Software and Technology.

DATA  AND CALCULATIONS

Trial	Temperature (°C)	Rate constant, k (s–1)
1
2
3
4

DATA ANALYSIS

1. Plot a graph of your data above, using temperature (°C) as the x-axis, and the rate constant, k, as the y-axis.
2. Disconnect your Colorimeter and temperature probe from the interface.
3. Choose New from the File menu. An empty graph and table will be created in Logger Pro.
4. Double click on the x-axis heading on the table, enter a name and unit, then enter the four values for the rate constant from your data table above.

Note:  Attach this graph you created in your lab report as Figure 5 (title the graph properly).  Describe the relationship between rate constant (k) and temperature.

2. Determine the activation energy, Ea, by plotting the natural log of k (ln k) vs. the reciprocal of absolute temperature (1/T). Note: Absolute temperature, T = ^oC + 273.
3. Choose New Calculated Column from the Data menu.
4. Create a column, ln rate constant, k.
5. Create a second column, reciprocal of absolute temperature, 1/(Temperature (^oC) + 273).
6. On the displayed graph, plot ln rate constants (ln k) on the y-axis and the reciprocal of absolute temperature (1/T) on the x-axis by clicking on the respective axes labels. Autoscale the graph if necessary.

Note:  Attach this graph you created in your lab report as Figure 6 (title the graph properly). Describe the relationship between ln k vs. 1/T.

3. Calculate the activation energy, Ea, for the reaction. To do this, first calculate the best fit line equation (linear fit) for the data in Step 2. Record the slope, m, of the linear fit below and use it to calculate the activation energy, Ea, in units of kJ/mol.

   Note: On a plot of ln k vs. 1/T,    Ea = m × R.

4. A well-known approximation in chemistry states that the rate of a reaction often doubles for every 10°C increase in temperature. Use your data to test this rule. (Note: It is not necessarily equal to 2.00; this is just an approximate value, and depends on the activation energy for the reaction.)

CALCULATIONS:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Slope, m : ________________________________________________

Activation Energy, E_a (kJ/mol) : _______________________________

 

 

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