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.
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 1.333 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.
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.
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/m2, the area must be
in m2 not mm2. If you calculated it in mm2, note that there are (1000 mm)2 = 1 000 000 mm2 in a
square meter, not 1000.
4. 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.
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: