Determination of R: The Gas Law Constant Objective: To gain a feeling for how well real gases obey the ideal gas law and how to determine the ideal gas law constant, R. Apparatus Balance Bunsen burner and hose Test tube 250 mL beaker 8 oz wide mouth bottle Rubber stoppers Pinch clamp Clamp Barometer (or readings) Glass tubing Rubber tubing Thermometer Ring stand Chemicals Potassium Chlorate (KClO3) Manganese (IV) Oxide (MnO2) Introduction: Most gases obey the ideal gas equation, PV=nRT, quite well under ordinary conditions, that is, at room temperature and atmospheric pressure. Small deviations from this law are observed, however, because real gas molecules are finite in size and exhibit mutual attractive forces. The van der Waals equation, Where a and b are constants characteristic of a given gas, takes into account these two causes for deviation and is applicable over a much wider range of temperatures and pressures than the ideal gas equation. The term nb in the expression (V-nb) is a correction for the finite volume of the molecules; the correction to the pressure by the term n2a/V2 takes into account the intermolecular attractions. In this experiment you will determine the numerical value of the gas law constant, R, in its common units of L-atm/mol-K. This will be done using both the ideal gas law and the van der Waals equation together with measured values of pressure, P, temperature, T, volume, V and number of moles, n, of an enclosed sample of oxygen. Then you will perform an error analysis on the experimentally determined constant. The oxygen will be prepared by the decomposition of potassium chlorate, using manganese (IV) oxide as a catalyst: If the KClO3 is accurately weighed before and after the oxygen has been driven off, the weight of the oxygen can be obtained by difference. The oxygen can be collected by displacing water from a bottle, and the volume of the gas can be determined from the volume of water displaced. The pressure of the gas may be obtained though the use of Dalton’s law of partial pressures, the vapor pressure of water, and atmospheric pressure. Dalton’s law states that the pressure of a mixture of gases in a container is equal to the sum of the pressures that each gas would exert if it were present alone. Patmospheric = PO2 + PH2O vapor SAFETY WARNING!!!! KClO3 is very dangerous to work with. Be careful not to apply too much friction when scooping out the powder. KClO3 is a strong oxidizing agent and will react readily when heated with certain easily oxidizable substances such as grease and rubber. DO NOT HAVE KClO3 and MnO2 come in contact with the rubber stopper or a severe explosion may occur. Make certain that the clamp holding the test tube is secure so that the test tube cannot move. Procedures: 1. Add a small amount of MnO2 (about 0.02 g) and approximately 0.3 g of KClO3 to a test tube and accurately weigh to the nearest 0.001 grams. Please also pre-weigh a dry beaker (it will be used to collect the water displaced by the experiment). 2. Add ~200 mL of distilled water into the bottle. 3. Assemble the apparatus as illustrated in the figure, but do not attach the test tube. Be sure that tube B does not extend below the water level in the bottle. 4. Attached a rubber bulb to tube B and apply pressure through it so that water may travel into tube A. Close the clamp when tube A is filled. 5. Mix the solids in the test tube by rotating the tube, being certain that none of the mixture is lost from the tube, and attach tube B as shown in the figure. AGAIN, read the safety warning about KClO3 and rubber stoppers. 6. Fill the beaker about half full of water, insert tube A in it and open the pinch clamp. Lift the beaker until the levels of water in the bottle and the beaker are identical. Then close the clamp, discard the water in the beaker, and dry the beaker. The purpose of equalizing the levels is to produce atmospheric pressure inside the bottle and test tube. 7. Set the beaker with tube A in it on the bench and open the pinch clamp. A little water will flow into the beaker, but if the system is airtight and has no leaks, the flow will soon stop and tube A will remain filled with water. If this is not the case, check the apparatus for leaks and start over. Leave in the beaker the water that has flowed into it; at the end of the experiment, the water levels will be adjusted and this water will flow back into the bottle. 8. Heat the lower part of the test tube gently (be certain that the pinch clamp is open) so that a slow, but steady stream of gas is produced, as evidenced by the flow of water into the beaker. When the rate of gas evolution slows considerably, increase the rate of heating, and heat until no more oxygen is evolved. Allow the apparatus to cool to room temperature, making certain that the end of the glass tube is in the beaker is always below the surface of the water. Some of the water will flow back into the bottle, which is normal. Equalize the water levels in the beaker and the bottle as before and close the clamp. 9. Weigh the beaker with the water and get a temperature of the water. Using the temperature, match the density and calculate the volume of water that was displaced with the chart. This is the volume of oxygen produced. If your temperature is 24.5oC round up to 25.0oC or if it is 24.3oC round down to 24.0oC. Record barometric pressure. The vapor pressure of water can be found by the temperature of the water from the chart. 10. Remove the test tube from the apparatus and accurately weight the tube and contents. The difference in mass between this and the original mass of the tube and contents is the mass of the oxygen produced. 11. Waste Disposal: Please do not throw any of the contents in a waste bin. Return the tube to Mr. Yip for proper disposal. Data Mass of test tube + KClO3 + MnO2 Mass of test tube + contents after reaction Mass of oxygen produced Mass of beaker Mass of beaker + displaced water Mass of water Temperature of water Density of water Volume of water = Volume of O2 gas Barometric pressure Vapor pressure of water Pressure of O2 gas Calculations Calculate the gas law constant, R, from your data using the ideal gas equation. Calculate the gas law constant, R, using the van der Waals equation. o For O2, a = 1.360 L2atm/mol2 and b = 31.83 cm3/mol o Be sure to keep your units straight. Error analysis: Determine the maximum and minimum value of R consistent with the experimental reliability of your data from the ideal gas law: Assume that the reliabilities for the various measure quantities in this experiment are as follows: P = 0.1 mmHg V = 0.0001 L T = 1oC m = 0.0001 g o To determine the maximum value of R, use the maximum values that the pressure and volume may have and the minimum values that the mass and temperature may have. Similarly, calculate the minimum value of R from the minimum values of P and V and the maximum values for m and T. Determine the average value of R and assign an uncertainty range to this average value. o Example: Assume that the measured quantities were as follows: P = 705.5 torr, T = 20oC. V = 242.9 mL, and m = 0.3002 g. What would be the maximum and minimum values of R, the average value of R, and the uncertainty range to be assigned to this average value? Solution: First put the measured quantities into proper units as follows: 705.5 torr = 0.928 atm 760 torr V = 242.9 mL = 0.2429 L P= m = 0.3002 g T = (20o C + 273) K = 293 K Therefore (705.6 torr/(760 torr/atm))(0.2430 L)(32.00 g/mol) (0.3001 g)(292 K) = 0.0823 L-atm/mol-K Maximum R = (705.4 torr/(760 torr/atm))(0.2428 L)(32.00 g/mol) (0.3003g)(294K) = 0.0816 L-atm/mol-K Minimum R = The average value for R is therefore, 0.0823 + 0.0816 Average = L-atm/mol-K 2 = 0.0820 L-atm/mol-K Since the maximum and minimum values of R differe from the average by 0.0004, R is written as R = 0.0820 0.0004 L-atm/mol-K Questions 1. Write a paragraph about some of the sources of error in your experiment. Indicate the ones that you feel are the most important. 2. Which gas would you expect to deviate more from ideality, H2 or HBr? Please explain your answer. 3. How might the solubility of O2 in water affect the value of R you determined? Please explain. 4. You have a 0.5576 gram mixture of KClO3 and a non-reactive compound. You place the compound in our experimental setup and get the following results. mass of O2 = 0.08420 g a. If the mixture were pure KClO3, what is the theoretical yield of O2 that would be produced? b. What is the mass percent of KClO3 in the mixture? Grading Rubric Prelab (10 points) Data table (5 points) Calculations (20 points) Questions (10 points) NAME _________________________________ DATE _________________________________ Prelab - Determination of R: The Gas Law Constant 1. Under what conditions of temperature and pressure would you expect gases to obey the ideal gas equation? 2. Why do you equalize the water levels in the bottle and the beaker? 3. Why is the corrective term to the volume subtracted and not added to the volume of the van der Waals equation? 4. Given the following data from Mr. Yip’s freshman college lab experience. Weight of the Test Tube + KClO3 + MnO2 Weight of Test Tube + Contents After Reaction: Weight of 125 mL flask + water Weight of 125 mL flask Weight of Water Temperature of Water Barometric Pressure: 21.5854 g 21.5012 g 198.8 g 131.6 g 67.2 g 25 O C 763 mm Hg Solve for the R constant on the back of the paper. Please SHOW ALL UNITS AND WORK!!!!