Gas Laws Introduction In 1662 Robert Boyle found that, at constant temperature, the pressure of a gas and its volume are inversely proportional such that P x V = constant. This relationship is known as Boyle s Law. In 1787 Jacques Charles observed the linear relationship between temperature and volume at constant pressure. In the mid 1800 s after the Kelvin or absolute temperature scale was formulated, Charles Law was worded to state that at constant pressure the temperature (in K) and volume of a gas are directly proportional such that T V = constant These laws apply perfectly only to ideal gases as defined by the kinetic-molecular theory, kmt. Briefly, 1. Gas molecules are in constant, random motion. They move in straight lines until they collide with another molecule or the walls of the container. 2. The average kinetic energy of molecules is proportional to the temperature in Kelvin units. 3. All collisions of gas molecules are perfectly elastic the gas sample does not lose energy because of these collisions. 4. Gas molecules have negligible volume, and the space between them is large. 5. There are no attractive forces between gas molecules. They don t stick to each other. One characteristic of a gas is that it exerts pressure on the walls of its container. With the kineticmolecular theory, we can understand pressure as the result of collisions of the gas molecules with the walls of the container. The amount of pressure is related to the number of collisions per unit time and the strength of the collision (a result of the mass of the molecules and how fast they are moving). Why should you care? Gases and effective gas exchange (O 2 in, CO 2 out) are quite important in maintaining your body in a healthy state. Gas exchange is also important in some medical diagnostic and treatment procedures. If you develop a reasonable understanding of the kinetic molecular theory, you will be in a position to understand respiratory physiology much better. In this lab you will use two gas laws that allow you to make predictions about the behavior of gases. True ideal gases do not exist. Air behaves very much like an ideal gas, however, being a mixture of several nonpolar gases N 2, O 2, and Ar. These gases have only very weak intermolecular attractive forces called London forces. Water vapor, on the other hand, does not behave very much like an ideal gas, having relatively strong intermolecular attractive forces between molecules. Recall that the water molecule is quite polar and can undergo hydrogen bonding also. Boyle s Law Boyle's law states that the volume of a fixed quantity of gas at constant temperature is inversely proportional to its pressure, such that P x V = constant. In other words, if you have the same quantity of gas at the same temperature and you continually increase the pressure on that gas sample, its volume will decrease by the same ratio. If you double the pressure, the volume will 1
decrease by 1/2. If you use four times the pressure the volume will decrease to 1/4 of what it was. This means that the product of P V will be a constant. To investigate Boyle s law, a sample of air in a large syringe is used. The syringe is mounted vertically (tip down) in a wooden block with another wooden block mounted on the end of the plunger. You will see that by adding weights to the top of a plunger, the volume of gas in the syringe will decrease. Boyle's law predicts that the pressure of the gas should also change. When a weight is placed on top of the plunger, the plunger moves down farther into the syringe. The plunger stops moving when the pressure of the gas in the syringe is equal to the pressure exerted by the total mass (the atmosphere + added weight) pushing down on the syringe. Pressure (P) is defined as force (F) per unit area (A) and the force on an object is mass (m) times the acceleration of gravity (g, 9.81 m/s 2 ). The pressure of the gas is directly proportional to the mass supported by the gas, so our pressure will be recorded in kg. Pressure Force Area F A m A g (1) The mass supported by the gas in the syringe is equal to the sum of the mass of the atmosphere (m atm ) and the mass of the weight (m weight ): pressure of gas = m atm + m weight (2) The mass of the atmosphere is calculated from the atmospheric pressure and the cross-sectional area of the syringe. The atmospheric pressure is measured using a barometer in the lab. Your instructor will supply the value for the mass atm for you to use in calculating the total gas pressure. The barometer (see Figure 1) consists of a glass tube sealed at one end, which has been filled with mercury and then inverted into a reservoir of mercury. The mercury does not "fall out" of the glass tube completely because the reservoir into which the tube has been inverted is open to the atmosphere. The pressure of the atmosphere is sufficient to hold most of the mercury in the inverted tube. However, as the pressure of the atmosphere changes from day to day with the weather, the exact height to which the mercury level is held in the tube varies. The height of the mercury in the tube is taken as a direct measurement of the atmospheric pressure at any time and is quoted in units of "millimeters of mercury". The average pressure of the atmosphere can support a column of mercury to a level of approximately 760 mm. During periods of clear weather ("high" pressure), the mercury level in the barometer will be above 760 mm; during periods of stormy weather ("low" pressure), the mercury level will be below 760 mm. Radio and televisions usually report the barometric pressure in inches of mercury; 760 mm is approximately equivalent to 30 inches. 2
inches cm Scale Top of Hg column 30 10 5 0 77 76 Vernier 75 74 2 1 Figure 1. The mercury barometer. One standard atmosphere supports a column of mercury to a height of 760 mm. The vernier scale in (b) permits reading the pressure to a fraction of a millimeter. The reading for this particular measurement is 744.7 mm Hg. Note how the zero on the vernier scale is between the fourth and fifth mark after 74 (so that gives 744, see arrow #1), and then notice that the 7 th line on the vernier scale matches up exactly with a line on the scale (see arrow #2), this allows you to read to the tenths place. 29 73 Thermometer (b) Mercury reservoir 3
Boyle s Law Procedure 1. Remove the cap from the tip of the syringe and draw in about 30 ml of air. Replace the cap. 2. Read the volume of gas in the syringe to 0.1 ml. To get a reproducible volume reading, push down slightly on the plunger and let it rise. Repeat until the volume measurements agree. Your first set of measurements will be taken when no mass has been added to the plunger, so the first column will read 0.0 kg. Add weights to the plunger 0.5 kg at a time until the total mass is 5.0 kg. Record your measurements on the spreadsheet template. 3. Read the atmospheric pressure from the barometer in the lab. Boyle s Law Calculations 1. Complete your data sheet by filling in the Pressure column. Add the mass (kg) of the atmosphere to the mass (kg) of the weights you added to get the total mass (kg) supported by the column of air in the syringe. 2. Now multiply your pressure (kg) by your volume of air (ml), rounding off to the correct number of significant figures. This is important! 3. What do you notice about all of your P V values? Charles Law Procedure 1. Fit a dry 250-mL Erlenmeyer flask with a one-hole stopper with an outlet tube. (The experiment will fail if water is inside the flask. The flask must be perfectly dry.) 2. Prepare a set-up as shown in Figure 2, but use a hotplate instead of a Bunsen burner. 3. Clamp the Erlenmeyer flask up around the rim and rubber stopper so that it will extend as far into the beaker as possible. 4. Set up a 400-mL beaker on the bench-top next to the hotplate and fill this beaker with water. Place the end of the outlet tube under the water and keep immersed during the entire experiment. 1-L 5. Place the 1-L beaker on the hotplate and clamp the Erlenmeyer flask as far down into the beaker as possible. Fill the 1-L beaker with tap water (as full as possible) and add 3-4 boiling stones. 6. Heat the water to boiling and boil gently until air has stopped bubbling from the outlet tubing. Record the temperature of the boiling water, T 1. 400 ml Figure 2. Set up for Charles' Law 4
7. Turn off the burner and carefully remove the Erlenmeyer flask from the 1-L beaker, keeping the end of the tubing under water in the other beaker! Let the Erlenmeyer flask come to room temperature sitting on the bench-top. Water will be drawn into the flask as the flask cools. 8. When the flask has cooled to room temperature and no more water is being drawn into the flask, be sure the water level in the beaker and in the Erlenmeyer flask are at equal heights before removing the rubber stopper. With a graduated cylinder, measure the volume of water in the flask. Record this volume of water and subtract it from the total volume of the flask (step 9) to get the volume of air in the flask at room temperature (the result of the subtraction is V 2 ). Record the room temperature, T 2. 9. Determine the volume of the flask by first filling it full of water and then inserting the rubber stopper back in the flask. Measure the volume of water in the flask, using the 100 ml graduated cylinders from your drawer. Because the volume will be greater than 100 ml, you will need to fill the cylinder more than once. This corresponds to the volume of air in the flask at the boiling water temperature, V 1. Recap: T 1 is the temperature of the boiling water, V 1 is the TOTAL volume of the flask. T 2 is room temperature, V 2 is the amount of air in the flask after it has cooled down to room temperature. Charles Law Calculations Calculate the volume of air that should have been present in the flask at room temperature using V 2 V 1 T 2 T 1 This is your theoretical or true value. Compare this to your actual, experimental value for air and find the % error. Keep track of your sig. fig.! 5
Pre-lab questions 1. What is the pressure of the gas in the syringe when no weights are placed on top? 2. How do you find the pressure of the gas in the syringe during the experiment? 3. In a mercury barometer what keeps the column of mercury at a height of approximately 760 mm on an average day at sea level? 4. Considering the Charles Law experiment: a. What specific molecules make up the gas in the Erlenmeyer flask when you begin the experiment? b. What is the pressure of these molecules before you begin the experiment? c. What are these molecules doing inside the closed flask at room temperature to cause this pressure? d. Do they strike the insides of the outlet tubing with the same force per unit area (pressure) as they do the inner walls of the flask? e. What is the pressure of the air on the surface of the water in the 400 ml beaker? f. Why should bubbles not come out of the outlet tubing before the gas is heated? 5. If 7.41 L of gas at 20.8 C was heated to 125.5 C, what would the volume be, assuming that pressure remained constant? 6
GAS LAWS REPORT SHEET Sec: Name: Partner s Name(s): Boyle s Law the relationship between pressure and volume of a gas. Atmospheric Pressure in mm Hg (read off the barometer) mm Hg Weight of the atmosphere in kg kg (given by the instructor) Trial Mass added (kg) Volume (ml) Pressure * (total mass supported in kg) P V (Show pre-rounded and rounded values. Remember units) 1 2 3 4 5 6 7 8 9 10 11 * Do not round pressure values; rather underline non-significant figures. Why is pressure in the title of the 4 th column in quotes? 7
Charles Law the relationship between temperature and volume of a gas. V w, Volume of water drawn into flask when cooled in ml V 1, Total volume of flask in ml V 2 (experimental) in ml Temperature of air in flask when cooled, in C T 2, Temperature of air in flask when cooled in K Temperature of air in flask when heated, in C T 1, Temperature of air in flask when heated in K Calculated (theoretical) value of V 2 in ml Show calculation: % Error of experimental V 2 Show calculation 8
Post-Lab Questions Boyle s Law 1. Do your P V values demonstrate support of Boyle's Law? Explain briefly why you feel that they do or do not support Boyle's Law. 2. Calculate the volume expected in Trial 3, assuming Boyle's Law (P 1 V 1 =P 2 V 2 ) is valid for this gas. For V 1 and P 1, use your volume and pressure (total mass supported by the gas) for Trial 1, and for P 2 use the pressure (total mass supported by the gas) for Trial 3. Show your calculation below: Experimental V Calculated V 3. Calculate the % error in your experiment V value, using the calculated V value as the "true value". Show the calculation: 9
Charles Law 1. At the beginning of the experiment (before heating), how does the pressure inside the flask compare to the pressure outside the flask? During the experiment, does the pressure outside the flask, ie the pressure of the room, vary significantly? 2. When the air in the flask is heated by the boiling water, what happens to the speed of the molecules in the flask? 3. Based on your answer to questions 1 and 2, during the heating step how does the pressure inside the flask compare to the pressure outside the flask? 4. What is the result of this pressure differential? (i.e., what did you observe experimentally?) 5. How does the pressure inside compare to the pressure outside the flask when the bubbling stops? 6. When the flask cools down, what happens to the motion of the molecules in the flask and to the pressure they exert? 7. While the air in the flask is cooling, how does the pressure inside the flask compare to the pressure outside the flask and what is the result (i.e., what did you observe experimentally)? 8. Based on your percent error calculations, did your data from the experiment with air obey Charles Law? Explain how you reached this conclusion. 9. What types of intermolecular forces exist between the various molecules in a sample of air? in a sample of water vapor? 10. Would you expect air and water vapor both to behave as ideal gases? Explain in depth, referring to the kinetic molecular theory. Use a separate sheet, if needed. 10