Experiment C09: The Ideal Gas
(Pressure Sensor - Absolute, Temperature Sensor)
Concept: gas laws
Time: 15 m
SW Interface: 300, 500 & 700
Macintosh® file: C09 Ideal Gas
Windows® file: C09_IDEA.SWS
Adapted by Tom Russo from MicroChemistry, distributed by Theta Technologies, 203 Bluegrass Ave., Suite 179H, South Gate, KY 41071, (606) 441-4768.
EQUIPMENT NEEDED
• Science Workshop™ Interface
• pressure sensor - absolute
• temperature sensor
• beaker, 1000 mL (2)
• constant volume device* (see diagram)
• eyedropper stem (glass part)
• heat source (for hot water bath)
• rubber stopper, solid (2)
• rubber stopper, two hole
• apron and safety goggles
Chemicals and Consumables
• crushed ice
• glycerin
• water
(*The constant volume device consists of a copper or galvanized iron pipe "T" , 1/2" diameter, with solid rubber stoppers in two ends and a two-hole rubber stopper in the "T".)
PURPOSE
This laboratory activity shows the theoretical limit of low temperature. The theoretical lowest temperature which can exist is called Absolute Zero.
THEORY
All matter is made up of tiny particles called molecules. Matter can exist in four states: solid, liquid, gas and plasma. The last state, plasma, while the most common in the Universe (the insides of all stars), is uncommon on Earth. The first three states of matter are the only ones commonly found on this planet. The only difference among all these states is the movement of molecules.
The kinetic energy of all molecules, at any specific temperature, is constant. Kinetic energy wants to move molecules apart while intermolecular forces want to hold them together. There are three states of matter because the forces which bind some molecules together at a particular temperature are greater than the kinetic energy of the molecules.
The Ideal Gas is one in which there are NO intermolecular forces. In fact, the Ideal Gas has no mass and occupies no volume! While this idealized state is fictional, gases behave at room temperature and pressure as if their molecules were ideal. It is only at high pressures or low temperatures that the kinetic energy of molecules is overcome by intermolecular forces and the molecules can "grab onto" one another.
In the Ideal State, the product of the Pressure on the gas and its Volume is equal to a constant at a constant temperature.
P * V = k
The value of the product of the volume and pressure would remain constant. For example, imagine that the gas pressure in a balloon is 1 atmosphere and has a volume of 12 liters. The value of k is 12 liter - atmospheres.
If the balloon were to rise to a point in the atmosphere where the pressure is 0.5 atmospheres, the balloon would expand to 24 liters to hold the value of k at 12 liter - atmospheres.
At the same time, the volume of a gas is directly proportional to the temperature. If a gas is heated, the volume of the gas increases. If it is cooled, the volume of the gas decreases, thus:
V = T * k2
or
What happens at lower temperatures if the pressure/volume relationship is equal to a constant, k ? For real gases the molecules become closer, the intermolecular forces overcome kinetic energy and the gas turns into a liquid. At still lower temperatures and higher pressures, the liquid is forced into a rigid structure we call a solid. For an Ideal Gas, the gas would continue to show a constant pressure/volume relationship. So as the temperature is decreased, the volume of the gas would decrease and the pressure would also decrease to maintain a constant Pressure * Volume relationship.
At absolute zero all molecular motion stops and all matter is solid. In this experiment the value of the volume is a constant. This is insured by the use of a rigid container which will not change in volume as the temperature is changed. At a constant volume then,
P is proportional to T
or
P = T * k3
SAFETY PROCEDURES
Follow all safety directives given by your teacher.
PROCEDURE
For this activity, the pressure sensor measures the vapor pressure of a gas (air) and the temperature sensor measures the temperature of the gas as the gas is cooled. The Science Workshop program records and displays the data. A plot of pressure and temperature shows the relationship betweeen them. The extrapolation of the best fit line of the plot of pressure and temperature shows the temperature of Absolute Zero.
• Start to boil water in a beaker. Check the water bath occasionally as you set up the rest of the equipment.
PART I: Computer Setup
1. Connect the Science Workshop interface to the computer, turn on the interface, and turn on the computer.
2. Connect the DIN plug of the temperature sensor to Analog Channel A on the interface. Connect the DIN plug of the pressure sensor to Analog Channel B on the interface.
3. Open the Science Workshop file titled as shown;
Macintosh: C09 Ideal Gas
Windows: C09_IDEA.SWS
• The document has a Graph display of the gas Pressure in kiloPascals (kPa) and the Temperature in degrees Celsius (C).
• Note: For quick reference, see the Experiment Notes window. To bring a display to the top, click on its window or select the name of the display from the list at the end of the Display menu. Change the Experiment Setup window by clicking on the "Zoom" box or the Restore button in the upper right hand corner of that window.
4. The "Sampling Options…" for this experiment are: Periodic Samples = Slow at 1 measurement per second.
5. The vertical axis of the Graph (Pressure) is scaled from -10 kPa to 150 kPa. The horizontal axis of the Graph (Temperature) is scaled from -300 C to 100 C.
PART II: Sensor Calibration and Equipment Setup
• You do not need to calibrate the temperature sensor. The temperature sensor produces a voltage that is proportional to temperature (10 mV = 1.0 Celsius). The default calibration is 110.000 C = 1.100 V and -10.000 C = -0.100 V.
• You do not need to calibrate the pressure sensor. The pressure sensor produces a voltage that is proportional to pressure (1V = 100 kPa). The default calibration is 101 kPa equals approximately one volt.
1. Put the barb end of a quick release connector into one end of a piece of plastic tubing that comes with the Pressure Sensor.
2. Put a drop of glycerin in the bottom of one of the holes of the two-hole rubber stopper. Fit the tip end of the eyedropper stem upward through the hole so that the tip of the eyedropper extends above the top side of the rubber stopper.
3. CAREFULLY put the tip of the eyedropper into the end of the piece of plastic tubing that will connect to the Pressure Sensor.
4. Put a drop of glycerin into the other hole of the two-hole rubber stopper. Slide the temperature sensor through the hole. Temporarily place the two hole stopper with the temperature sensor and eyedropper into the top of the iron pipe "T".
5. Make sure that the end of the temperature sensor does not hit the inside of the iron pipe. The end of the sensor should be about at the midline of the horizontal section of the iron pipe.
6. Remove the two hole stopper from the iron pipe.
7. Align the quick-release connector on one end of the plastic tubing with the connector on the PRESSURE PORT of the Pressure Sensor. Push the connector onto the port, and then turn the connector clockwise until it clicks (about one-eighth turn).
• You will not need to put the two-hole stopper with sensors into the "T" apparatus until after the iron pipe has been cooled in an ice water bath.
8. Put crushed ice into a beaker. Place the open iron pipe "T" apparatus into the ice bath. Do not allow water to enter the "T". Allow the pipe to cool to the temperature of the ice.
PART III: Data Recording
1. You are ready to begin the experiment when the iron pipe has been cooled. Remove the "T" from the ice bath. CAREFULLY but quickly force the rubber stopper with sensors attached into the iron pipe "T" apparatus.
2. Click the "REC" button to begin recording data.
3. Place the "T" apparatus in the hot water bath. Turn off the heat source for the water bath.
4. Continue recording data until the pressure reaches a maximum (about 2 or 3 minutes).
5. Click the "STOP" button to end data recording. Remove the apparatus from the water bath.
ANALYZING THE DATA
1. Click the Graph window to make it active. Find the part of the curve that relates the increase in pressure to the increase in temperature. (Ignore the vertical heating part of the curve).
2. Use the mouse to click-and-draw a rectangle around the part of the curve that relates pressure to temperature.
3. Click the "Statistics" button.
• NOTE: The Statistics area will probably cover the curve. To rescale the Graph so the data is in the visible part of the Graph, click on the horizontal axis and type in "-300" as the minimum and "100" as the maximum.
3. Click the "Statistics" menu button in the Statistics area. Select "Curve Fit, Linear Fit" from the menu.
4. Click the "Smart Cursor" button in the lower left corner of the Graph. Move the cursor into the Graph area. The cursor changes to a crosshair.
• Move the cursor to the point where the Linear Fit line crosses the X-axis of the Graph.
• The X-coordinate of the intercept point is the approximate experimental value of Absolute Zero, the temperature at which no pressure is exerted by an ideal gas because its volume is zero.
DATA & CALCULATIONS
1. In the Graph, use the Statistics area to find the point where the linear fit line crosses the Y-axis of the Graph, the "a1" parameter under Linear Fit, or Y-intercept. Enter the value of the Y-coordinate of the intercept into the Data Table.
2. Find the highest temperature (maximum for "x") and the highest pressure (maximum for "y"). Enter these values into the Data Table.
3. Find the lowest temperature (minimum "x") and the lowest pressure (minimum "y"). Enter these values into the Data Table.
DATA TABLE
|
Datum |
Measurement |
Value |
|
1 |
Highest temperature |
C |
|
2 |
Highest pressure |
kPa |
|
3 |
Lowest temperature |
C |
|
4 |
Lowest pressure |
kPa |
|
5 |
Y-coordinate of intercept |
kPa |
CALCULATIONS
1. Use the formula below to find the slope of the data:
(Calculation 1)
2. Use the general formula of a straight line to find the value for Absolute Zero ("x" in the formula below):
Since Y = 0 at the Y-intercept,
(Calculation 2)
Alternate Calculation
• Use the value of the "a2" parameter from the Statistics area of the Graph as the slope:
QUESTIONS
1. How does your first calculated value for Absolute Zero compare to the accepted value?
2. Compare your value from the Alternate Calculation for Absolute Zero to the accepted value.
3. What are possible sources of error or limitations in this experiment? For each one, try to decide what effect it might have on the experimental results.