LIGHTSTICK KINETICS LAB KIN 1.COMP INTRODUCTION The rate of a chemical reaction is generally expressed by the rate law: Rate = k[a] a [B] b where [A] and [B] are the concentrations of the reactants in mol/l, a and b are experimentally determined exponents in the rate equation, and k is the experimentally determined rate constant that is reaction and temperature dependent. Temperature exerts a significant effect on the rate of a chemical reaction. Increasing the temperature increases the average speed of the molecules, thereby increasing the collision rate between the reacting molecules. Increasing the temperature also increases the fraction of the reacting molecules with energy greater than the energy of activation. The relationship between the rate constant, k, and the temperature, T, is expressed by the Arrhenius equation: k = Ae -Ea/RT A is the pre-exponential factor, which includes the collision frequency and the fraction of molecules that collide with the correct orientation. E a is the energy of activation, the minimum energy the colliding molecules must possess to have a successful reaction. R is the ideal gas constant in energy units, 8.1344 J/mol K. T is the temperature in Kelvin. The exponential term e -Ea/RT expresses the fraction of the reacting molecules with energy greater than the energy of activation. As E a increases, the exponent becomes more negative and the fraction of the reacting molecules with energy greater than the energy of activation decreases. Therefore, as E a increases, the rate constant becomes smaller and the rate of reaction decreases. As T increases, the exponent becomes less negative and the fraction of the reacting molecules with energy greater than the energy of activation increases, resulting in the rate constant becoming larger and the rate of reaction increasing. Taking the natural logarithm of both sides of the Arrhenius equation gives Ea 1 ln k = + R T which fits into the format of an equation for a straight line y = m x + b Reference: Shoemaker, W.; Sipe, J. Lightstick Kinetics: A study of the reaction-rate of a commercial chemiluminescent system with respect to temperature. Presented at the National Science Teachers Convention, Philadelphia, PA, March 2003. KIN1.COMP-1 ln A
A graph of ln k verses 1/T, with the temperature in Kelvin gives a straight line with a slope of E a /R. The value of E a is determined from the slope of the line. In this experiment, the energy of activation for the long-term, light-producing reaction in a lightstick will be determined by monitoring the light intensity of the lightstick as a function of temperature. The light-producing reaction follows first order kinetics, where [X] is the reactant concentration. Rate = k[x] Substituting from the Arrhenius equation gives: Rate = A[X]e -Ea/RT The light intensity, I, at a fixed point from the lightstick should be proportional to the rate of the chemiluminescence reaction. Providing a proportionality constant, c, gives the equation: Rate = c I Substituting for the rate in the previous equation: c I = A[X]e -Ea/RT Dividing both sides of the equation by c gives: I = A[X]e c E a / RT Taking the natural logarithm of both sides of the equation gives: [ Ea ] 1 ln I = + R T ln A[X] c A graph of ln I verses 1/T with the temperature in Kelvin gives a straight line with a slope of E a /R. The value of E a is determined from the slope of the linear regression line. PURPOSE The purpose of this experiment is to study the reaction rate of a chemical reaction with respect to temperature and determine the energy of activation of the chemiluminescent, light producing, reaction utilized within lightsticks. KIN1.COMP-2
EQUIPMENT/MATERIALS Laptop computer with Logger Pro Water bath (45 o C) LabPro with AC adapter Disposable Pipette LabPro computer cable 18x150 mm test tube Light sticks Pre-drilled film canister Vernier Light Sensor Pre-drilled wood block Vernier Temperature Probe Scissors Disposable gloves SAFETY Always wear an apron and goggles in the lab. Gloves should be worn because the dye in the lightstick will stain. PROCEDURE 1. Get a wooden block and set up according to Figure 1. Place the 18 x 150 mm test tube in the top hole. Insert the temperature probe through the hole in the film canister and then insert it into the test tube, making sure that the film canister shields the reaction from any incoming light. Place the light sensor into the horizontal hole of the wood block. 2. Snap the lightstick and shake the contents well. Wait 10 min. for the short-term lightemitting reaction to finish so only the light from the long-term reaction is being measured. Continue with steps 3, 4, and 5 while you wait. Film Canister Temperature Probe Test tube Light Sensor Computer LabPro Wood Block Figure 1 KIN1.COMP-3
3. Prepare a 50 C water bath. 4. Prepare the sensors for data collection. Connect the light sensor to CHN-1 and the temperature probe to CHN-2 of the LabPro. Be sure the light sensor is set at 0-600 lux. 5. Cut off the top of the lightstick with a pair of scissors and transfer approximately 5 ml of the contents into the test tube using a pipette. 6. Place the test tube with contents and temperature probe in the water bath until the meter reads 50 C. 7. Remove the test tube assembly from the water bath and dry it quickly. 8. Set up the wood block, test tube, and light sensor assembly and begin data collection by clicking Collect. Samples will be taken every 30 seconds for 10 minutes. DATA ANALYSIS: 1. Double Click on the X heading in the data table. 2. In the name box, type time 3. In the units box, type sec 4. Select Sig Figs and enter a value of 3 for rounding. Click OK. 5. Double Click on the Y heading in the data table. 6. In the name box, type intensity 7. In the units box, type lux 8. Select Sig Figs and enter a value of 3 for rounding. Click OK. 9. From the pull-down menus select Data New Column Manually Entered 10. In the new column name box enter Temperature 11. In the new column unit box enter Celsius. Click OK. 12. Remove any unwanted data sets by single clicking on the row number and selecting Edit Delete Data Row from the pull-down menus. Click OK. 13. From the pull-down menus select Data New Column Calculated 14. In the new column name box enter Abs. Temp 15. In the new column unit box enter K KIN1.COMP-4
16. Place the cursor in the new column formula box. Select Temperature from the columns button then type +273 Click OK. 17. From the pull-down menus select Data New Column Calculated 18. In the new column name box enter ln intensity 19. In the new column unit box enter lux 20. Place the cursor in the new column formula box. Click the ln button then select intensity from the columns button. Click OK. 21. From the pull-down menus select Data New Column Calculated 22. In the new column name box enter 1/ Abs.Temp 23. In the new column unit box enter 1/K 24. Place the cursor in the new column formula box. Type 1/ Click on the columns button and select Abs. Temp. Click OK. 25. Double Click on each new heading that you created and select significant figures and enter a value of 3 for rounding. Click OK. 26. In the graph window, double Click on the X (horizontal) axis. Click on the connecting lines button to remove the function. Click on More X-axis options. Choose to plot 1/Abs. Temp. Select Autoscale Click OK. 27. Click on More Y-axis options. Choose to plot ln intensity. If any other selections are highlighted, remove them by clicking on them. Select Autoscale Click OK. 28. Click OK. 29. Click on the data point in the upper left of the graph window, hold down the mouse button and drag to the data point in the lower right of the graph window, then release the mouse button. 30. From the pull-down menus, choose Analyze Regression. A regression box containing slope (M), intercept (B), and a correlation value (COR) will appear. 31. To print your graph, click anywhere on the graph window, then select File Print Selected Display 32. To print your data table you must first drag the edges of the data table window so that the entire table appears on the computer screen. Then select File Print Selected Display KIN1.COMP-5
33. According to our substituted Arrhenius equation the slope should be equal to E a /R where R has a value of 8.3144 J/mole K, thus allowing us to calculate the value of E a in units of J/mole. 34. Given the actual value in kj/mole, a percent error calculation can be performed. KIN1.COMP-6
PRE-LAB ANALYSIS Name Name Period Class Date LIGHTSTICK KINETICS 1. The following data was collected for the first order reaction: 2 N 2 O 5 (g) 2 N 2 O 4 (g) + O 2 (g) Determine graphically the energy of activation for the reaction. Show your calculations. Temp. ( C) Rate Constant, k (sec -1 ) ln k Temp. (K) 1/Temperature (K -1 ) 0.0 7.87 X 10 3 25.0 3.46 X 10 5 45.0 4.98 X 10 6 65.0 4.87 X 10 7 Slope of the regression line (M) Y intercept (B) Correlation factor (COR) E a (kj/mol) KIN1.COMP-7
2. Calculate the rate constant at 35.0 C. Show your calculations. 3. At what temperature ( C) will the rate constant be 8.00 X 10 6 sec -1? Show your calculations. KIN1.COMP-8
DATA SHEET Name Name Period Class Date LIGHTSTICK KINETICS Attach your graphs and data tables to this lab report. Slope of the regression line (M) Y-intercept (B) Correlation factor (COR) Experimental value for E a (kj/mol) Accepted value for E a (kj/mol) Percent Error CALCULATIONS: (Include a sample of each type of calculation performed by LoggerPro) QUESTION: 1. How did the light intensity vary with temperature? Why does this happen? KIN1.COMP-9