# Experiment 11 The Gas Laws

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1 11-1 Experiment 11 The Gas Laws Introduction: In this experiment you will (1) determine whether Boyle s Law applies to a mixture of gases (air) and (2) calculate the gas constant, R, by determining the volume of a known amount of gas (H 2 ) at a measured temperature and pressure. Determination of Whether Boyle s Law Applies to Air Boyle s Law states that for a fixed amount of gas at constant temperature, the pressure of the gas will vary inversely with the volume so that P 1/V or PV = a constant (if n and T are constant). To determine whether this relationship holds for a mixture of gases, the pressure of a fixed amount of air (which is a mixture of gases) will be measured as the volume of the air is varied while keeping the temperature of the air constant. Determination of the Gas Constant, R The ideal gas law arises from several different gas laws. Boyle s law describes the inverse relationship between pressure and volume, P 1/V, for a sample of gas at constant temperature. Charles law describes the direct relationship between volume and temperature, V T, for a sample of gas at a constant pressure. The Gay-Lussac law describes the direct relationship between pressure and temperature, P T, for a sample of gas at constant volume. Together these lead to what s referred to as the combined gas law, used to relate the properties of a given sample of gas at two different sets of conditions, labeled 1 and 2. PV 1 T 1 1 = P2 V T 2 2 (1) Note that all three of the gas laws are satisfied by this equation. For example, if temperature is constant, T 1 = T 2 so that T 1 and T 2 can be eliminated from the equation, leaving P 1 V 1 = P 2 V 2, which is Boyle s Law. Another relationship between gas properties is Avogadro s Principle. It states that for the case in which the pressure and temperature of a gas are held constant, the volume of the gas is proportional to the number of moles, or V n, or V/n = a constant. Adding this relationship to the combined gas law gives the following: PV n T PV = = 1 1 n2t2 Constant (2) The constant in the above equation is the ideal gas law constant, or simply, the gas constant, R, calculated for a near ideal gas, such as H 2. Replacing Constant with R in equation (2) gives the Ideal Gas Law:

2 11-2 PV = nrt (3) Equation (3) describes the relationship between the properties P, V, n and T for any sample of gas behaving as an ideal gas. No matter what changes are made to any of the properties, the relationship still is true as long as the conditions are near ideal. But the equation is only useful if the value of R is known. In this experiment you will calculate a value for R by generating a known number of moles of H 2, under conditions in which it behaves like an ideal gas, by the reaction: Mg(s) + 2HCl(aq) MgCl 2 (aq) + H 2 (g) Based on the reaction stoichiometry, if the HCl(aq) is in excess, the moles of H 2 produced must be equal to the moles of Mg reacted, which can be calculated from the mass of Mg used and its formula mass. If the volume, pressure and temperature of the known number of moles of H 2 produced are measured, then equation (3) can be used to calculate R. The H 2 will be generated in the Erlenmeyer shown in Figure 1 below by adding the HCl solution in the syringe to the Erlenmeyer containing the Mg ribbon. Figure 1. Apparatus for Determination of R. Initially the pressure will be that of the air in the Erlenmeyer, designated P(air). Once the HCl is added, the reaction generating H 2 gas will occur, thus increasing the pressure. The total pressure measured in the Erlenmeyer after the reaction has been completed, P(total), will be the sum of (1) the pressure of the H 2 produced by the reaction, P(H 2 ); (2) the measured pressure of air initially in the Erlenmeyer flask, P(air), and (3) the vapor pressure

3 11-3 of water, P(H 2 O), present in the Erlenmeyer due to the presence of the water in the HCl solution added to the Erlenmeyer. Thus the pressure of the dry H 2 gas present in the Erlenmeyer will be obtained as P(H 2 ) = P(total) P(H 2 O) P(air) (4) P(H 2 O) can be obtained from the table at the end of Part B since the temperature of the gases (including the temperature of the collected H 2 ) in the Erlenmeyer will be the same as that measured for the water bath. With the pressure, temperature and number of moles of H 2 having been obtained, it is only necessary to measure the volume of the H 2 gas collected. This is the volume of the Erlenmeyer plus the volume of the tube connecting the flask to the pressure detector. Pre-Laboratory Notebook: Provide a title, purpose, brief summary of the procedures, and table of reagents (HCl and Mg) in your notebook before coming to lab. Equipment: Vernier computer interface Vernier temperature and pressure sensors (and accessories) TI -84 calculator Logger Pro 3.3 software (on computer in Room 242), for graphing results Water reservoir in plastic tub 125 ml Erlenmeyer flask 50 ml and 100 ml Beakers 100 ml graduated cylinder In Lab Experimental Procedure (Note: Work in pairs) Part A: Determination of Whether Boyle s Law Applies to Air 1. Set up the LabPro system according to the first section of the Vernier tutorial, and connect the gas pressure sensor into channel 1 of the LabPro and the temperature probe into channel With the 20-mL syringe disconnected from the gas pressure sensor, move the piston of the syringe until the front edge of the inside black ring is positioned at the 10.0 ml mark, then attach (by twisting on) the syringe to the white port of the gas pressure sensor as shown in Figure 2. Do not over tighten. 3. Turn on the calculator, press APPS and scroll down to select the DATAMATE program. After pressing CLEAR to reset the program, pressure and temperature readings should appear. If the calculator displays a gas pressure set to units other than MMHG in CH 1, change the units to MMHG (same as torr). To do this, press 1:SETUP to get a display of channels. With the cursor at CH1 press ENTER and then select 2: Gas Pressure (MMHG). Select 1: OK two times to return to the main screen.

8 11-8

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