THERMODYNAMICS OF A GAS PHASE REACTION: DISSOCIATION OF N 2 O 4

THERMODYNAMICS OF A GAS PHASE REACTION: DISSOCIATION OF N 2 O 4 OBJECTIVES 1. To measure the equilibrium constant, enthalpy, entropy, and Gibbs free energy change of the reaction N2O4(g) = 2 NO2(g). 2. To gain experience with vacuum equipment. INTRODUCTION The N N bond in N2O4 is sufficiently weak that appreciable dissociation takes place near room temperature. The reaction is N2O4(g) 2 NO2(g) (1) We shall carry out an experiment to determine the partial pressures (in bar) of both monomer (NO2) and dimer (N2O4), from which we can calculate the equilibrium constant for the dissociation of the dimer: (P K = (P NO2 N 2O4 /P ) 2 /P ) (2) The equilibrium composition of the N2O4/NO2 mixture can be determined by several methods. We shall use a simple gravimetric technique. a In this approach, the total mass, mtot of the N2O4/NO2 mixture is measured under conditions of known pressure, temperature, and volume. To calculate the equilibrium constant from mtot we must know the relationship between the total mass of the mixture and the partial pressures of the monomer, PM, and dimer, PD. The total mass of the mixture is just the sum of the mass of the monomer, mm, and the mass of the dimer, md. By using the ideal gas law we can write M MPM V M DPDV m tot = m M + m D = + (3) RT RT where MM and MD are the molar masses of monomer and dimer, respectively. Equation (3) along with Dalton's law, P = PM + PD, provides two equations in two unknowns, from which we a Because NO 2 absorbs visible light (in fact, one of the steps in smog production is photodissociation of NO 2 to NO + O) the composition of the system could also be determined spectrophotometrically. CHM/PHY 340 lab 1

can find PM and PD. The relationship between the equilibrium constant for a gas phase reaction, K, and the standard free energy change, rg (T), for the reaction at a temperature T is given by 1 rg = RT ln K. (4) If K can be determined at several temperatures, then the enthalpy change for the reaction at temperature T can be obtained from the van t Hoff equation: H = R r d ln K d (1/ T) (5) The derivative in eq. (5) is just the slope of a plot of ln K vs. 1/T. If rh is independent of T then the plot should be linear. Once rh and rg are known at 298 K, the standard entropy change for the reaction at 298 K can be evaluated from rg = rh T rs. (6) EXPERIMENTAL METHOD You will use two glass bulbs in this experiment. You will fill one of these bulbs (of known volume V) with the N2O4/NO2 gas mixture so that the pressure is slightly above 1 bar. The bulb is then immersed in a constant temperature bath and vented after temperature equilibration, thereby allowing its total pressure, P, to become equal to the ambient atmospheric pressure. The bulb is then sealed and the mass of its contents (mtot) is determined. The second bulb, of approximately the same volume, is used as a ballast bulb. The ballast bulb is necessary because this experiment is very sensitive to weighing errors. The sample bulb weighs much more than its gaseous contents, so a small percent error in the measurement of the mass of bulb + gas can produce a large percent error in the mass of the gas mixture. The purpose of the ballast bulb is to provide a way to correct for changes in the buoyant force of air during the course of the experiment. The buoyancy correction is an application of Archimedes' principle: the measured weight of an object immersed in a fluid (air) is equal to the true weight of the object minus the weight of displaced fluid. The (upward) buoyant force on the sample bulb is equal to the mass of air displaced by the sample bulb. If the air density changes during the course of the experiment (due to changes in atmospheric T and/or P) the buoyant force will change. By measuring the mass of the ballast bulb whenever you measure the sample bulb's mass, you can CHM/PHY 340 lab 2

detect changes in buoyancy and correct for them. The ballast bulb must be left sealed during the experiment. SAFETY PRECAUTIONS N2O4/NO2 is poisonous and corrosive. Therefore, - Always wear safety glasses during this experiment. Contact lenses are forbidden. - Do all experimental work (except weighing) in a fume hood. - Always THINK before turning a stopcock or disconnecting tubing - will any N2O4 escape into the room? - Use two hands when turning stopcocks. - Never force a stopcock that is hard to turn. - When handling the filled sample bulb, be careful not to drop it. - Protect the vacuum pump from corrosive N2O4 by using a trap filled with liquid nitrogen. PROCEDURE The success of this experiment largely depends on making mass measurements as accurately as possible. The sample bulb will be evacuated and filled using a vacuum line (see Fig. 1). A mechanical pump is connected to the main manifold of the vacuum line through a cold trap that is filled with liquid nitrogen. The purpose of the trap is to condense materials that would damage the pump. The liquid nitrogen is contained in a Dewar flask. Before filling the bulb, be sure to check the level of liquid nitrogen in the Dewar flask and top it off if necessary. The trap is connected to the manifold through a stopcock, M. The manifold has several ports (each coupled via a stopcock) to which the sample bulb and other accessories are attached. 1. Set the thermostat on the water bath to 30 C. Record the volume of the sample bulb (189.3 ml?), the barometric pressure, and the ambient temperature near the balance. 2. Before filling the bulb you must first evacuate the vacuum line. Fill the trap with liquid nitrogen and pump down the manifold. Attach the bulb and the manometer to the manifold, then open stopcocks B, S, and I to pump down the bulb and the manometer line. Do not open the manometer stopcock until the sound of the pump indicates that most of the air has been removed from the system. Continue pumping on the system for a few minutes to remove adsorbed water; it will help to warm the bulb slightly with a heat gun. You should be able to reach a pressure of less than 4 mm Hg. Once you have reached this pressure you may close CHM/PHY 340 lab 3

and remove the manometer. Summary of procedure: Add liquid N2 to trap and turn on pump. Open stopcock M and evacuate main manifold. Carefully attach sample bulb to vacuum system. Attach manometer to N2O4 inlet tube. Open stopcocks S, B, and I and evacuate bulb to a pressure of < 4 mm Hg. Warm slightly with heat gun. Pump for a few minutes to remove water. Close stopcocks S, B, and I. Remove manometer. 3. Close the sample bulb and remove it from the vacuum line. Rinse the outside of the bulb with acetone or methanol and carefully wipe it to remove dirt and/or moisture. (Don't touch it with your fingers before you weigh it!) Allow the sample bulb to sit for 5 minutes to come to room temperature, then determine its mass on an analytical balance. Also measure the mass of the ballast bulb. The bulbs must sit upright on the balance pan, so set each bulb on a small cork ring. Both bulbs should be weighed several times to determine the reproducibility of the measurement. 4. Reattach the sample bulb to the vacuum line. Also attach the N2O4 cylinder. Open stopcocks S, B, and I to evacuate the sample bulb connection and the N2O4 inlet line. Proceed to the next step when the pump has been making its "low pressure" sound for several minutes. 5. Fill the bulb using the following procedure: a. Close the manifold stopcock (M) and open the N2O4 cylinder valves to fill the manifold and the bulb. b b. Be sure the Dewar is full of liquid nitrogen. Flush the bulb once by first closing the N2O4 regulator valve (R) and then opening stopcock M. c. Refill the bulb as in step 5a, then bring the bulb in contact with an ice water bath for a few seconds until a dime-sized puddle of liquid N2O4 has condensed onto the bottom of the bulb. Close the bulb stopcock (B). d. Close the N2O4 tank valve (T). Slowly open stopcock M, and pump the contents of the manifold, the sample inlet tube, and the N2O4 inlet tube, into the trap. b Normally when filling a vacuum line with gas from a cylinder, one must be very careful not to pressurize the line too much. With N 2 O 4 you needn t worry about the gas pressure becoming too high, because N 2 O 4 has a normal boiling point of 21 o C. Therefore, the pressure of N 2 O 4 gas in a room temperature cylinder is very close to 1 bar. CHM/PHY 340 lab 4

e. Close stopcocks S and I and the N2O4 regulator valve (R). f. Weigh the bulb to make sure you have added at least 0.55 grams of N2O4. g. Top off the Dewar flask with liquid nitrogen. You must check the level and top it off periodically throughout the remainder of the experiment. 6. Place the filled bulb in the 30 C temperature bath so that only the neck and stopcock are out of the water. It is important to prevent any water from getting into the bulb or the stopcock. Record the actual bath temperature. After a couple of minutes, open the bulb s stopcock briefly every 30 seconds until the brown vapor no longer emerges from the opening. When the pressure inside the bulb has reached the ambient pressure, remove the bulb from the bath. Turn the thermostat to the next temperature so you don't waste any time. Rinse the bulb with acetone or methanol, and carefully wipe the outside of the bulb. Allow about 5 minutes for the bulb to come to room temperature, then weigh the sample and ballast bulbs. c Repeat the measurements to establish reproducibility. Check your results before going on to step 7; at 30 C you should find K 0.22. 7. Place the bulb in a 45 C water bath and follow the procedure in step 6. Repeat for bath temperatures of 60 and 75 C. 8. Record the barometric pressure and ambient temperature at the end of the experiment. 9. After the final weighing, attach the bulb to the vacuum line and pump out the gas. Shut the stopcock and remove the bulb. Ask me to help you shut down the vacuum line. DATA ANALYSIS 1. Determine the masses of the N2O4/NO2 mixture at each temperature studied. Use the ballast bulb masses to determine the buoyancy correction for each measurement, and determine the corrected N2O4/NO2 masses. 2. Use your data to calculate the value of K at the 4 temperatures. 3. Graph ln K vs. 1/T, and determine rh from a linear regression of the data.. Report the uncertainty in rh. 4. Find rs at 298 K using your linear regression equation. (To do this, combine equations 6 and 8 with the regression equation, which is of the form ln K = m/t + b.) Also determine the uncertainty in this value. From your values of rs and rh, find rg at 298 K, and estimate the uncertainty in this value. Find K at 298 K. 5. Compare your values of rh298, rg298, and rs298 to literature values. c The bulbs must be at room temperature to prevent weighing errors. CHM/PHY 340 lab 5

DISCUSSION Some things to include: Do the algebraic signs of rh and rs for reaction 1 seem reasonable, i.e. do they make sense chemically? Explain. Is the buoyancy correction necessary? Use the ideal gas law for air (Mair = 29 g/mol) to show that the mass of the displaced air would change by about 1 mg if T and P change by 1 K and 1 torr, respectively, for a bulb volume of 190 ml. In light of this, comment on whether the buoyancy corrections are important in your experiment. Linearity of ln K vs. 1/T. Assuming that the value of rcp is temperature-independent, by how much is rh expected to change between the lowest and highest temperatures of your experiment? In light of this, would you be able to detect the corresponding change in the slope of your ln K vs. 1/T data? Comparison to previous work. Read a journal article about the determination of the equilibrium constant for N2O4 dissociation. 2,3,4,5 Describe the method used by the authors to determine the equilibrium constant. Compare their results to yours. REFERENCES 1 Atkins, P. "Physical Chemistry"; W. H. Freeman: New York, 1998; ch. 9. 2 Verhoek, F. H.; Daniels, F. J. Amer. Chem. Soc. 1931, 53, 1250 3 Hisatsune, I. C. J. Phys. Chem. 1961, 65, 2249. 4 Vosper, A. J. J. Chem. Soc. (A) 1970, 625 (copy available from the instructor). 5 Shen, Q.; Hedberg, K. J. Phys. Chem. 1998, 102, 6470. CHM/PHY 340 lab 6

FIGURE 1. Vacuum Line vent to pump cold trap sample bulb manometer N 2 O 4 cylinder CHM/PHY 340 lab 7