Resonance Energy of Benzene

Transcription

1 Resonance Energy of Benzene Purpose The purpose of this experiment is to evaluate the resonance energy of benzene by calorimetry. The heat of combustion of a compound will be measured with a bomb calorimeter. That measurement, plus literature values of combustion and vaporization enthalpies, will lead to an experimental value of the resonance energy. Background The molecule trans,trans,cis-1,5,9-cyclododecatriene ("CDDT") is a 12-membered hydrocarbon. Labels "E,E,Z" are sometimes used in place of "trans, trans, cis". CDDT contains three double bonds in a ring. These bonds are not resonance stabilized. CDDT can split into benzene and cyclohexane according to the following hypothetical reaction: C 12 H 18 (gas) C 6 H 6 (gas) + C 6 H 12 (gas) (1) The heat of reaction (Δ rxn H) is related to the resonance energy (ΔU) of benzene because the number of bonds of each type (C-C, C=C, C-H) is the same on both sides of the reaction. 1 Notice that all three of the compounds in reaction 1 are liquids under standard conditions at 25 C. The resonance energy is determined from reaction 1 in the gas phase where intermolecular interactions are negligible. A bomb calorimeter will be used to measure the heat of combustion of liquid CDDT. Combustion in the bomb calorimeter occurs under constant volume, so heat equals energy. The ideal gas law suffices to correct energy, ΔU, to enthalpy, ΔH: ΔH = ΔU + Δ(PV) = U + ( n gas )RT (2) CDDTbomb.odt 1

2 Our bomb calorimeter is an isoperibol calorimeter. Combustion occurs in the bomb, which sits in a water-filled bucket. A water-filled calorimeter jacket surrounds the bucket. The calorimeter jacket is held at a constant temperature while heat from the burning sample causes the bomb and bucket temperature to rise. The temperature difference between the bucket and the jacket causes a small heat flow. The calorimeter automatically calculates and accounts for the heat lost to or gained from the calorimeter jacket. The reaction for combustion of CDDT under standard conditions is C 12 H 18 (l) + (33/2)O 2 (g) 12 CO 2 (g) + 9 H 2 O(l) (3) The change in PV, Δ(PV) = Δn gas RT = (12-33/2)RT = -4.5RT. Substitute R= J mol - 1 K -1 and T=298.15K to get a numerical value for Δ(PV) for combustion of CDDT. The enthalpy of vaporization of CDDT is kj/mol. 3,4 The resonance energy of benzene can be defined as the negative ΔU of reaction 1, with reactants and products in the gas phase. 5 After you calculate Δ 1 H, convert it to Δ 1 U and resonance energy. Reagents and Supplies benzoic acid pellets (approximately 1g each) for standardizing the bomb calorimeter. Run two times. trans,trans,cis-1,5,9-cyclododecatriene ("CDDT") weigh precisely about 0.5 g. Run twice. In the lab (or get from the stockroom if they are not in the lab): 2L volumetric flask 1 ml pipet and bulb gloves for handling CDDT CDDTbomb.odt 2

3 Bomb Calorimetry Procedure for the Parr 1261 calorimeter Use a pellet of benzoic acid to do a standardization run and determine the "energy equivalent" (EE) of the calorimeter. It should be about 2400 calories per degree. The EE value for a standardization is stored in the calorimeter's memory. By default, the calorimeter uses the last 10 values stored to calculate heats for determination runs. In this experiment, however, you will calculate the EE value yourself from the temperature rise and the known energy of combustion of benzoic acid. (Instructions are below.) Make two standardization runs with benzoic acid. Use liquid CDDT to determine the heat of combustion of CDDT. Because the bomb operates at constant volume, the heat observed equals ΔU. Make two runs with CDDT and average the results. Detailed instructions follow. I. Equilibrate the Calorimeter Operating the Bomb Calorimeter 1. Turn on calorimeter using the power switch on the back. Turn the water faucet on slightly; this supplies a slow flow of cooling water to the bomb. Press the F1 key on the calorimeter to start the water pump and heater. You will hear them and can also look at the back of the instrument to check that the heater light is on. Allow 20 minutes for the controller to warm up and the jacket temperature to stabilize. The STANDBY light will turn on when the jacket temperature has reached the setpoint, 25º C. 2. Fill the calorimeter bucket with exactly 2 liters of distilled water measured by a 2L volumetric flask. Close the top of the calorimeter. II. Weigh the Sample 1. Cut a 10 cm piece of fuse wire and weigh it. 2. For a "calibration", weigh a pre-made pellet of benzoic acid. 3. For each "determination" run, use g liquid CDDT. Record the mass precisely. III. Attaching the Fuse Set the bomb head on the support stand and fasten a 10 cm length of fuse wire between the two electrodes. To attach the fuse to quick-grip electrodes, insert the ends of the wire into the eyelet at the end of each stem and push the cap downward to pinch the wire into place. Figure 1. support stand and fuse wire. CDDTbomb.odt 3

4 Place the fuel capsule with its weighed sample in the electrode loop and bend the wire downward toward the surface of the charge. When using a sample that is a pellet, bend the wire so that the loop bears against the top of the pellet. The wire should not touch any liquid sample, however, but should be positioned just slightly above it. Pipet exactly 1 ml of distilled water into the bomb. This is to absorb and retain acidic byproducts that may form during combustion. IV Close the Bomb Care must be taken not to disturb the sample when moving the bomb head from the support stand to the bomb cylinder. Check the sealing ring to be sure that it is in good condition and moisten it with a bit of water so that it will slide freely into the cylinder; then slide the head into the cylinder and push it down as far as it will go. For easy insertion, push the head straight down without twisting and leave the gas release valve open during this operation. Set the screw cap on the cylinder and turn it down firmly by hand to a solid stop. When properly closed, no threads on the cylinder should be exposed. If the screw cap tends to bind to the cylinder at this point, indicating that it might be difficult to open the bomb after it has been fired, turn the screw cap back slightly - but only a few degrees - enough to release the binding, since the bottom thread must remain fully engaged. Hand tightening suffices. Do not use a wrench on the screw cap. V Fill the Bomb with Oxygen 1. Close the gas relief valve on the bomb. 2. Open main valve on oxygen tank. Gas pressure in tank should be at 2000 psi and the regulated gas pressure should be 450 psi. 3. Attach gas line to gas inlet valve 4. Push O 2 Fill key on the calorimeter. A pressure lower than 420 psi will cause a low pressure warning. VI Operate the Calorimeter 1. Set the bucket in the calorimeter, as follows. Attach the lifting handle to the two holes in the side of the screw cap and partially lower the bomb in the water. Handle the bomb carefully during this operation so that the sample will not be disturbed. Push the two ignition lead wires into the terminal sockets on the bomb head. Orient the wires away from the stirrer shaft so they do not become tangled in the stirring CDDTbomb.odt 4

5 mechanism. Lower the bomb completely into water with its feet spanning the circular boss in the bottom of the bucket. Remove the lifting handle from the bomb (not from the bucket) and shake any drops of water back into the bucket. 2. Close the calorimeter cover. This lowers the stirrer and thermistor probe into the bucket. 3. Check the LED display to see whether the calorimeter is prepared to do a standardization (i.e., benzoic acid) or a determination. In the former case, "STD" will be lit; in the latter, "DETR". Benzoic acid is for standardization but CDDT combustion is a determination, and it is important that the calorimeter display match the type of run you are doing. Use Shift-F2 if necessary to change the type of run. Push START to initiate the test. 4. The calorimeter may automatically supply a six-digit Sample Identification Number. If not, it will wait for you to enter a sample id: up to six digits of your choice. Press "ENTER." 5. The calorimeter will prompt for the sample weight by flashing the WEIGHT light. Type the mass, in grams, and press "ENTER." 6. The calorimeter will now take over and conduct the test. During the time it is establishing the initial equilibrium, it will light the PREPERIOD light. Just before it fires the bomb, it will sound a series of short beeps to warn the user to move away from the calorimeter. 7. CAUTION: Do not have the head, hands, or any part of the body over the calorimeter when the bomb is being fired. Continue to stand clear for 30 seconds after firing. 8. Once the bomb has been fired, the POST light will come on. The calorimeter will check to make certain that a temperature rise occurs and will then look for the final equilibrium conditions, or if it fails to detect a temperature rise within the allotted time, the calorimeter will terminate the test and advise the user of the error. 9. At the conclusion of the test, the calorimeter will signal the user with a long beep. Press the DONE key to store the test result in the memory of the calorimeter. The calorimeter will automatically print out a preliminary report. 10. Open the cover and remove the bomb and bucket. Remove the bomb from the bucket and open the knurled valve knob on the bomb head to release the residual gas pressure before attempting to remove the cap. This release should proceed slowly over a period of not less than one minute to avoid entrainment losses. After all pressure has been released, unscrew the cap; lift the head out of the cylinder and place it on the support stand. CDDTbomb.odt 5

6 Examine the interior of the bomb for soot or other evidence of incomplete combustion. If such evidence is found, the test will have to be discarded. 11. Wash all interior surfaces of the bomb with water and dry thoroughly for the next run. Pour the bucket of water back into the 2L volumetric flask and refill the flask to the mark. Dry the bucket. 12. Remove all unburned pieces of fuse wire from the bomb electrodes and weigh them to obtain the fuse wire correction in calories (1400 cal/g or kj/g). 13. Now that you have the fuse correction you can print out your final report. Press the RPT key and the calorimeter will prompt you for a sample ID. Key in the ID number of the sample and hit ENTER. You will be prompted for a fuse correction. Key in the number of calories calculated previously and hit ENTER. Now you will be prompted for an acid correction. Hit ENTER to accept the default. In the case of a determination, you will be prompted for a sulfur correction. Again, you can hit ENTER to accept the default. 14. When you are done with all of your runs and have printed all of your final reports you need to erase your information. Press SHIFT and then F1 and you will be prompted for a Sample ID. Key in your Sample ID and hit ENTER. Again, you will be prompted for a Sample ID and you can key in your second and press ENTER. Once you have erased all samples, press DONE. 15. If no one else is using the calorimeter, you should turn it off. Press F1, which will stop the water pump. Turn off the water faucet. Turn off the power switch on the back of the bomb. CDDTbomb.odt 6

7 Table 2. Sample Calorimeter Reports CALORIMETRY PRELIMINARY REPORT 04/01/09 12:34:55 STANDARDIZATION SAMPLE ID CAL ID 1 WEIGHT.9860 FUSE ACID 10 SULFUR 0.00 INIT. TEMP TEMP. RISE SPIKE WGHT. EE VALUE GROSS HEAT CAL/G DYNAMIC MODE CALORIMETRY FINAL REPORT 04/01/09 13:30:36 STANDARDIZATION SAMPLE ID CAL ID 1 WEIGHT (grams) FUSE (cal) 15.0 ACID 10 SULFUR 0.00 INIT. TEMP TEMP. RISE SPIKE WGHT. EE VALUE GROSS HEAT CAL/G DYNAMIC MODE CALORIMETRY PRELIMINARY REPORT 04/01/09 17:00:51 DETERMINATION SAMPLE ID CAL ID 1 WEIGHT.431 FUSE 14.8 ACID 10 SULFUR 0.00 INIT. TEMP TEMP. RISE SPIKE WGHT. EE VALUE GROSS HEAT CAL/G DYNAMIC MODE CALORIMETRY FINAL REPORT 04/01/09 17:37:52 DETERMINATION SAMPLE ID CAL ID 1 WEIGHT (grams).425 FUSE (cal) 13.4 ACID 10 SULFUR 0.00 INIT. TEMP TEMP. RISE SPIKE WGHT. EE VALUE GROSS HEAT CAL/G DYNAMIC MODE CDDTbomb.odt 7

8 Calculations In order to calculate the heat capacity, C, of the bomb calorimeter use results from the standardization run. The standardization run burns benzoic acid. C 6 H 5 COOH(s) + (15/2)O 2 (g) 7CO 2 (g) + 3H 2 O(l) The heat of combustion of the benzoic acid pellets used in this experiment is reported by the supplier, Parr Instrument Company, to be kj/g. That is equivalent to Δ c U = kj/mol. The heat released by combustion of the pellet, Q ba, may be calculated either as kj/g m ba or -Δ c U n ba, where m ba stands for the mass of benzoic acid, n ba for the moles. For a pellet of mass g, for example, Q ba = kj. Q ba = kj/g m ba Calculate the fuse correction. Fuse correction = 5.858kJ/g grams of fuse burned. For example, g kj/g = kj. Calculate the heat capacity of the bomb. C = [ Q ba + fuse correction] / (Temp. rise) where "Temp. rise" is the temperature rise, read from either the preliminary or final standardization report. For example, with the fuse correction Q ba given above, and with a temperature rise of K, C = kj/k. You will have preformed two standardization runs. Each gives a value of the heat capacity. Calculate the average and use the average C in all further calculations. For each of the two determination runs calculate the fuse correction. Convert the mass of cddt to moles. n cddt = (mass cddt) / ( molecular mass cddt) = (grams cddt)/ g/mol. For example, g / g/mol = mol. Calculate the enthalpy of combustion of liquid cddt. Δ c U(cddt,liquid) = - [(Temp rise) C - (grams fuse burned) 5.858kJ/g] / n cddt For example, using the data on the first of the two sample determination reports, and with an average C (just an example) of kj/k, CDDTbomb.odt 8

9 Δ c U(cddt,liquid) = -[( K) kj/k kj] / mol = kj/mol. Average the cddt combustion energies from the two runs. Convert from Δ c U(cddt,liquid) to Δ c H(cddt,liquid) as discussed earlier. Use T = 298K. Δ c H(cddt,liquid) = Δ c U(cddt,liquid) -4.5RT The enthalpy of vaporization of cddt is kj/mol. 3,4 The enthalpy of combustion of gaseous cddt can be calculated with the aid of the enthalpy of vaporization. Δ c H(cddt,gas) = Δ c H(cddt,liquid) - Δ vap H(cddt,liquid) Calculate the enthalpy of formation of gaseous cddt from its combustion enthalpy and the formation enthalpies of gaseous carbon dioxide and liquid water. From the stoichiometry of reaction 3, the combustion reaction, Δ f H o (cddt,gas) = 12Δ f H o (CO 2,gas) + 9Δ f H o (H 2 O,liquid) - Δ c H(cddt,gas) Look up literature values of the enthalpy of formation of gaseous benzene and gaseous cyclohexane. Using those and your Δ f H o (cddt,gas), calculate the standard enthalpy of reaction 1. Then convert ΔH for reaction 1 to ΔU, using Δ rxn1 U = ΔH - Δn gas RT, where Δn gas is the change in the number of moles of gas in reaction 1 (i.e., Δn gas =2-1) and T = 298K. Finally, Resonance Energy = U res = -Δ rxn1 U You may find a literature value of the resonance energy of benzene in books and on the web. Linus Pauling's early paper 6, and the textbook Organic Chemistry by McMurry 7, for example, discuss resonance energy. Yirong Mo and Paul von Ragué Schleyer 8 discuss the traditional value (their reaction 3) and more modern evaluations. CDDTbomb.odt 9

10 Experimental uncertainty in resonance energy The experimental uncertainty in resonance energy, U res, can be estimated based on uncertainties in the largest contributions to Δ rxn1 U. Assume that literature values of formation enthalpies are essentially exact. Fuse corrections and Δ(PV) corrections are small, so they contribute little to uncertainty in U res. The absolute uncertainty (i.e., not the percent uncertainty) in U res is approximately the same as the absolute uncertainty in the combustion enthalpy of liquid CDDT. Δ c H(CDDT) - ΔT C / n CDDT where n CDDT represents moles of CDDT in a sample. Uncertainties in ΔT, C and n CDDT may be estimated as follows. Moles is proportional to molecular mass (which is known essentially exactly) so relative uncertainty (i.e., percent uncertainty) in n CDDT is the same as relative uncertainty in mass of CDDT, which is determined primarily by the scale on which the mass was taken. σ ncddt /n CDDT = σ mcddt /m CDDT, where m CDDT is the mass of CDDT. The mass of CDDT will be measured to approximately 10-3 or 10-4 g, depending on the balance used. Suppose, for example, that σ mcddt = grams and m CDDT = 0.5 grams. Then σ ncddt /n CDDT = σ mass /m CDDT / 0.5 = The uncertainty in C, the heat capacity of the bomb, is approximately the difference between the two values of C that were measured. If, for example, the values of C measured were and kj/k, then σ C 0.04 kj/k and σ C /C = 0.04/10 = The uncertainty of ΔT may be taken to be ±1 in the last digit shown on the print-out, assuming that all printed digits are significant. The Parr calorimeter prints temperature rise to five decimal places, so σ ΔT /(ΔT) T / 2T = which is insignificant compared to uncertainties in moles and heat capacity. Combining uncertainties in C and n CDDT, neglecting σ ΔT, the uncertainty in Δ C H(CDDT) is σ ΔH / (Δ c H) [ (σ C /C) 2 + (σ mcddt /m CDDT ) 2 ] 1/2. The absolute uncertainty in U res is the same as the absolute uncertainty in Δ C H(CDDT). σ Ures = Δ C H(CDDT) [ (σ C /C) 2 + (σ mcddt /m CDDT ) 2 ] 1/2 Using the example uncertainties above suggests σ Ures = (7300kJ/mol) [ ( ) 2 +( ) 2 ] 1/2 = 30 kj/mol. Your experimental uncertainty may differ from that estimate. Calculate σ Ures based on your heat capacities and CDDT masses, as a basis for deciding whether the U res you calculate does or does not agree with a literature value within experimental uncertainty. CDDTbomb.odt 10

11 References 1. Pickering, M. A novel bomb calorimetric determination of the resonance energy of benzene. Journal of Chemical Education 1982, 59(4), Engel, T.; Reid, P. Physical Chemistry, 3rd edition; Pearson Education: Boston; See section 8.6 for the Clausius-Clapeyron equation. 3. Rauh, Von H.-J.; Geyer, W.; Schmidt, H.; Geiseler, G. Bildungsenthalpien und Mesomerieenergien von π-bindungssystemen. 5. Mitteilung: Bildungsenthalpien von Oligomeren des Butadiens. Zeitschrift fur Physikalische Chemie 1973, 253, NIST web book. Data downloaded 3 December 2012 from 5. Halpern, A.M. Experimental Physical Chemistry, 2nd ed; Prentice-Hall: Upper Saddle River, NJ, 1997; Experiment Pauling, Linus; Sherman, J. The Nature of the Chemical Bond. VI. The calculation from thermochemical data of the energy of resonance of molecules among several electronic structures, Journal of Chemical Physics, 1(8), , McMurry, John, Organic Chemistry, Sixth edition; Brooks/Cole - Thomson Learning: Belmont, California; 2004; pages Mo, Yirong; von Ragué Schleyer, Paul, An Energetic Measure of Aromaticity and Antiaromaticity Based on the Pauling Wheland Resonance Energies, Chemistry A European Journal 2006, 12(7), CDDTbomb.odt 11