Experiment 11: The Ideal Gas Law

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1 Experiment 11: The Ideal Gas Law The behavior of an ideal gas is described by its equation of state, PV = nrt. You will look at two special cases of this. Part 1: Determination of Absolute Zero. You will determine the Celsius temperature of absolute zero by seeing how cold a gas would have to be for its pressure to be zero. (If V and n are kept constant, then PV = nrt reduces to P = (constant)t, sometimes called Gay-Lussac's Law. Notice from this that if the absolute temperature is zero then P = 0.) The procedure is to put a flask containing air in a beaker of water on a hot plate. The hot plate heats the water, the water heats the air in the flask. As the air heats up, its temperature and pressure are monitored by probes connected to a computer. Since P = (constant)t is a linear equation, you can draw a line through the points on a P versus T graph. Extending the line to where it reaches the horizontal axis shows you the temperature where the pressure would be zero. PROCEDURE: 1. Put a cork with a hole in it tightly in a 125 ml flask. (Don t let water in the flask or n, the number of moles, will change as it evaporates.) Put the flask in a 1000 ml beaker on a hot plate. Put a clamp on a ring stand, and put the other end just above the cork, as shown. The clamp is just to keep the flask from floating, and need not hold the flask tightly. (In the no picture, too much of the flask is out of the water.) Don t add the ice water yet; it works best to do that last (step 4). 2. Attach the hose coming from the cork to the pressure sensor and connect the pressure sensor to channel A of the interface. Connect the temperature sensor to channel B, and hang the temperature sensor from a clamp on another ring stand. Its bottom should be about 4 cm above the bottom of the beaker, since the bottom water heats up faster than average. 3. Get the computer ready: a. Connect the interface to the computer with the USB cable. Turn both the computer and the interface on. (The button at the upper left of the interface should turn blue.) Open PASCO Capstone on the computer. b. Click Hardware Setup at the upper left. Click the yellow circle by Channel A on the picture. Click Pressure Sensor, Low. Click channel B s yellow circle. Click Temperature sensor. (Just Temperature Sensor, not one with a longer name.) Click Hardware Setup again to hide that window.

2 c. The sampling rate is at the bottom center. It probably says 20 Hz now. Click the down arrow until it says 10 s. (10 s not 10 Hz.) d. The sensor reads gauge pressure, not absolute. Have the computer add atmospheric pressure to the readings to obtain the total pressure in the flask: i. The instructor will read the barometer in the chemistry lab and convert the reading into kilopascals. (cm of Hg times equals kpa.) ii. Click Calculator on the left. Click New at the top. Calc 1 = should appear in the window. Move the cursor to the right of the =, then click the colored triangle about two inches below this. Click Pressure (kpa). Type a plus sign followed by atmospheric pressure. Press enter. Put kpa for the unit and press Enter again. Click Calculator to hide it. e. Near the center of the screen, click Graph & Digits. Click <Select measurement> by the graph s vertical axis and select Calc 1 (kpa) under Equations/ Constants. Click Time (s) by the horizontal axis and select Temperature ( C). By dragging the numbers near the axes, change scales so that the vertical axis goes from about 0 to about 110 kpa and the horizontal scale goes from about -300 to + 60 C or so. In the digital displays at the top, select Pressure (kpa) for one measurement and Temperature ( C) for the other. 4. Fill the beaker to the bottom of the cork with water near 0 C. Check that none of the wires or hoses touches the hot plate. Turn the hot plate all the way up. Click Record near the lower left. Check the two digital displays: Neither should read zero! If either does, it probably means you don t have the sensor wire shoved far enough into the interface box. This is a good way to record twenty minutes of nothing, and end up doing the whole thing over. Push harder. Now, wait 15 or 20 minutes for it to reach 9.5 kpa. (You might see only the first data point on the graph for a while.) Work on part two in the meantime. At 9.5 kpa, click Stop. (The sensor can't read more than 10 kpa) Turn off the hot plate. 5. Get the graph back and do a best fit line: On the toolbar at the top, click the triangle in. Select Linear: mx + b and a line will appear. The dots should lie along a somewhat wiggly diagonal line. If they curve or level off at the ends, exclude the questionable points by clicking. Drag the sides of the box which appears so it contains just the points you want. Adjust the scale so that the x intercept and the data are both visible. You do not need to attach a hard copy of the graph to your report if the instructor looks at it on the computer screen. Do not delete the file until you are completely done and the instructor has approved your paper. Result: As discussed earlier, absolute zero temperature is where the absolute pressure is zero. Zoom in on this point so you can see it better and read absolute zero from the graph. In your conclusion, compare it to the accepted value. Assume its uncertainty is about + 20 C. (The uncertainty of the graph may be smaller, but does not include factors such as the temperature not being uniform throughout the beaker.) Shut down the computer and put it in the cart, plugged in.

3 PART II: BOYLE'S LAW You will experimentally verify Boyle s law. If the temperature and the amount of gas are kept constant, PV = nrt reduces to PV = constant, which is known as Boyle's Law. Some air is in a transparent cylinder with a piston at one end. Different pressures are created by having different weights on top of or hung from the piston. For each trial, you observe the volume from the piston s position, and calculate the pressure from the weight on the piston and its area. After converting to absolute pressure, you calculate PV for each trial, and compare these values to each other. If you always get the same thing (within uncertainty) then PV is in fact a constant as Boyle said. 1. Start with the bottom of the piston at the 80 mark. If you see the piston sinking under just its own weight, a hose clamp at the bottom is not tight. 2. Place some mass on top of the piston. Using 0,.5, 1.0 and 1.5 kg for your first four trials works pretty well. 3. As soon as you release the mass, notice the position the piston goes to; don t delay. It may continue to slowly sink; do not use a later reading. (The apparatus leaks. Better seals would cause more drag on the piston, so you would just trade one problem for another.) From the scale written on the cylinder, record where the bottom of the piston was under "volume". This is in some non-si unit; don t worry about what to call it. If you are suspicious of your result for any reason, replace any air that leaked out, then double check. 4. Open a valve at the bottom. Pull the piston back up to its original position to replace the air that leaked out. Close the valve again. 5. Put a different mass on and repeat for a total of four trials. Don't use more than 1.5 kg; the higher the pressure, the faster the air leaks. 6. Now expand the air instead of compressing it: Hold the cylinder upside-down in your hand, with the original volume at 80 as before. Use the platform, which is now on the bottom, as a hanger for the large slotted weights. Hold it over the counter in case the weights fall off; a kilogram landing on your foot will hurt. 7. Release both clamps at the bottom when you're done, so the hoses don't become permanently flattened. Calculations: 1. Record the diameter of the piston, which is written on the apparatus, and compute its area in square meters. 2. Find the force (weight) which the mass exerts.

4 3. From the force and the area which this force is distributed over, find the gauge pressure: positive if above atmospheric, negative if below atmospheric. For this to come out in N/m 2, the area must be in m 2 not mm 2. If you calculated it in mm 2, note that there are (1000 mm) 2 = mm 2 in a square meter, not Find the absolute pressure, P, from this. 5. Multiply P times V. (PV is not in SI units because of the non-standard unit used for the volume. In this case, converting would be more trouble than it's worth.) As your conclusion, state whether PV is in fact remaining constant within uncertainty. Take the uncertainty in each PV value to be about 5%, much of which is due to air leakage.

5 Experiment 11: The Gas Law Part 1: Atmospheric pressure: Name of person with your group's graph: Your value for absolute zero: Part 2: Piston diameter = Compute area of piston:

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