Technology and the Forgotten Gas Law

Page 1 - Technology and the Forgotten Gas Law
Technology and the Forgotten Gas Law
Pressure versus Temperature
Introduction
Avogadro, Boyle, Charles- these scientists and their gas laws are well known. Together th eir
work defined the relationsh ips among the four measurabl e gas properties, pressure, volume ,
temp erature, and the number of moles of gas. Among the contri butions of these scien tists,
th e experime nts by Amontons describin g the effect of temperat ur e on the press ure of a gas
have largely been forgotten. Let's see how modern technology can help us rediscover the forgotte n gas law an d the relat ionship between pressure and tem perature.
Concepts
• Boyle's law
• Arnontons's law
• Absolute zero
• Kinetic-molecula r theory
Background
The systematic study of gases began almost 350 years ago with Robert Boyle and his experiments on th e relationship between the pressure and volume of air. Based on measure ments of
how the pressure of air changed as it was compressed and expanded, Boyle derived the mathematical relatio nship that today bears his name . Accordin g to Boyle's law, th e pressure of a gas
is inversely proportional to its volum e if the temperature is held cons tant. In studying the
behavior of gases, Robert Boyle was also aware of the effect of heat on gases, nam ely, that
gases tended to expand when heated. Since no temperature scale existed at the time, Boyle
lacked a mathemati cal means of relating th e "hotness" of a gas to its volume or pressure.
In 1702, the French physicist Guillaume Amontons invented th e air thermometer to measure
temperature changes based on an increase in the volume of a gas as it was heated. This is
essentially th e principl e behind Charles's law. Amontons also measure d the pressure of a
fixed volume of air as it was heated from room temperature to the temperatu re of boiling
wat er. The relat ionsh ip between the temperature and pressure of a gas is known as
Amontons's law-the pressure of a gas is proportional to its temperature if th e volume and
the amount of th e gas are held constant.
Experiment Overview
The purpose of this technology -based experiment is to carry out a modern version of
Amonto ns's original experiments relating th e pressure and tempe rature of a gas. The experiment will be carried out by trapping a fixed volume of air inside a flask at about 80 °C. The
flask will be sealed, equipped with a pressure sensor, and gradually cooled in a series of steps
in a water bath . The temperature of the bath will be measured using a temperatu re sensor.
As th e temp erature decreases, th e pressure of th e air sampl e trapped inside the flask will also
change. The mathemat ical relat ionshi p between tempe rature and pressure will be derived by
plotti ng th e data on a gra ph.
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Pre-Lab Questions
1. One of the reasons Amontons's law is often ignored is that it can be derived by combining
Boyle's law and Charles's law. Combine the equations for Boyle's law (P x V = constant)
and Charles's law (VIT = constant) to obtain the mathematical relationship for
Amontons's law. Note: The Charles'slaw equation is only valid if the temperature is
expressed in kelvins on the absolute temperature scale.
2. The gas lawsexplain how gases behave, but do not explain why, According to the kineticmolecular theory (l{.\ IT), the temperature of a gas is a measure of the average kinetic
energy of the gas part icles-how fast they are moving. Collisions of the fast-moving gas
particles with the container give rise to the pressure, definedas the force of these collisions divided by the area. Use the IUoIT to predict how the pressure of a gas will change
when the gas is heated in a fixed-volume container.
3. The "Egg in the Bottle" is a favorite demonstration of many chemistry teachers. In this
demonstration, a piece of burning paper is placed inside a bottle and a peeled, hard-boiled
egg is placed over the bottle's mouth as soon as the fire burns out. As the bottle cools, the
egg is forced into tile bollle. Use Amontons's law to explain how this demonstration works.
Materials
Beakers, 400-mL and I-L, I each
Beral-type pipet, jumbo
Clamp, 1
Computer interface system (LabPro)
Computer or calculator for data analysis
Data collection software (Logger f-ro)
Erlenmeyer fl ask, Pyrex", 125-mL
Hot plate
Pressure sensor and attached tubingPressure relief valve (stopcock)"
Rubber stopper, two-hole, with adaptersSupport (ring) stand
Temperature sensor
Water
Thermometer (optional)
Tray (optional)
Ice
Gloves, heat -resistant
"The pressure sensor is attached via a plastic connector to a short length of tubing that has
a second plastic connector at the other end. The sensor also comes equipped with a relief
valve and stopper. See Figure 1.
Safety Precautions
The Erlenmeyer flask will develop a slight vacuum as the hot air inside the flask cools. Use
only Purex" flasks with heavy-duty rims and carefully check the flask before use for chips or
cracks. Makesure that the flask is securely held in the water bath and that it is not touching the sides or bottom of the beaker. Work carefully to aooid hitting or bumping the flask.
Wear heat-resistant glot'es and use caution when working with the hot water bath to avoid
scaldingor bums. Wear chemicalsplash goggles at all times when working with chemicals,
glassware or heat in the laboratory.
Flinn Che m'Io pic" Labs - The Gas Laws
Page 3 - Technology and the Forgotten Gas Law
Procedure
Preparation
1. Fill a l-L beaker about %-full with water and heat th e water on a hot plate at a mediumhigh sett ing to obtain a water-bath temperature of about 80 °C. Note: Turn down the setting on the hot plate as needed to avoid overheating the water.
2. If necessary, assemble the pressure sensor as follows. Attach the pressure sensor to a connector at one end of a piece of plastic tubing. Attach t he connector at the other end of th e
tubing to one of the adapte rs in th e two-hole rubber stopper. Attach th e pressure relief
valve to the second adapter in the two-hole rubber stopp er.
3. Open th e data collect ion software and connect the interface system to the compute r or
calculator. Plug th e temperatur e sensor (Channel l) and th e pressur e sensor (Channel 2)
into the interface.
4. Set up the interface system for remote data collection.
• Select Setup and Data Collection from the main screen, th en choose Selected Events
from the Mode menu.
• Select Set Up LabPro from the Remote menu. Follow th e on-screen instructions.
• Save th e experiment file so that it can be used later to retrieve the data from the interface.
• Disconnect the inte rface from the computer.
Part A. Collecting the Data
5. Place the interface system with its attached sensors and rubb er-stopper assembly on the
lab bench where th e hot water bath has been prepared.
6. Open the pressure relief valve on th e rub ber stopper assembly and place th e stopper
securely into a dry, l25-mL Erlenm eyer flask.
7. Immerse th e flask in th e hot water bath at 80 °C and clamp the rubber-stopper assem bly
to a ring stand . The flask should be submerged to th e height of the rubbe r sto pper. Do
not allow th e flask to touch th e bottom or sides of th e beaker (see Figure 1). Note: Make
sure the pressure relief valve (stopcock) on the rubbe r stopper assembly is open during
this ti me.
Pressure
Relief -,
Valve "'-
Temperature
Senso r
/ Pressure
/ _ Sensor
Figure 1.
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8. With the pressure relief valve open, allow th e air inside the flask to adjust to the temperature of th e wat er bath . Place th e temperature sensor in the water bath and clamp it if
needed.
9. After 3- 5 minutes, close the pressure relief valve and press the Start/Stop button on the
int erface. A light on the int erface should blink as th e interface takes th e first temperature
and pressure readin g.
10. Tum off th e hot plate and unplu g it. Wearin g heat-resistant gloves. carefully remove th e
hot water bath from the hot plate and place it on a tray (optional) to collect any spillover
water. Lower th e flask and temperature sensor back into th e hot water bath.
11. Add a few ice cubes to the hot water to lower the bath tempe rature. Monitor the temperature of th e water bath with a thermometer. Remove excess water as needed using th e
jumbo. Beral-type pipet.
12. When the temperature of th e bath is about 65 °C, press the Start/Stop button on the
int erface to take a second pressure-temperature reading .
13. Continue adding ice (and removing excess water as needed) to lower the temperature
more quickly. Take a series of pressure and temperature readings (at least five) between
65 °C and 5 °C. Wait about a minute at each desired temperature before pressing th e
Start/Stop button.
14. When all of the data has been collected, open the pressure relief valve on the flask and
unplug th e sensors from th e int erface.
IS. Remove the rubber stopper assembly from the flask and dismantle the apparatus as needed.
Part B. Analyzing the Data
16. Open th e saved experiment fil e on the computer and reconne ct the interface system to
the computer.
17. Select Retriere Data from th e Remote menu . The data will automatically be graphed and
displayed in a table. Click on the x-axis in th e graph to select temperature as the x-axis
(independent) variable. Click on th e y-axis to select pressure as the y-axis (dependen t)
variable.
18. Click on the lowest and highest values on each axis to rescale th e graph. Set the x-axis
scale from - 300 °C to 100 °C, th e y-axis scale from 0 kPa to 120 kPa.
19. Select Linear Fit-Best Curve Fit from the Analyze menu to draw th e best-fit stra ight line
th rough th e data
Flinn Chem'Iopic" Labs - The Gas Laws
Page 5 - Technology and the Forgotten Gas Law
Name:
_
Class/Lab Period:
_
Technology and the Forgotten Gas Law
Data Table'
Temperature (0C)
Pressure (kPa)
Temperature (K)t
*Computer-generated data tables and graphs may be substituted for the data table and PostLab Questions #1 and 5.
"See Post-Lab Question #5.
Post-Lab Questions
1. Plot or obtain a graph of pressure on the y-axis versus temperature on the x-axis. Note:
See the Procedure section for the recommended scale for each axis.
2. Looking at the data, is the pressure of a gas proportional to its temperature over the temperature range studied? Use a computer or calculator to generate the best-fit straight line
through the data points.
3. Extend the straight line backwards to estimate the x-intercept, the point at which the line
crosses the x-axis. The x-intercept corresponds to absolute zero-the minimum temperature that would be needed to reduce the pressure of a gas to zero. What is the estimated
value of absolute zero? How close is your value of absolute zero to the accepted value?
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4. Anoth er way to see how well th e data fits Amonto ns's law is to plot pressure versus temperatu re in kelvins on th e abso lute temperature scale.
(a) Conver t each temperatu re reading to kelvins using th e equati on
T(K)
=
WC) + 273.
(b) Plot or obtain a graph of pressure in kl'a on th e y-axis versus temperature in kelvins
on the x-axis,
(c) Start ing at the origin, draw a best-fit straight line throu gh th e data. The point (0,0)
sat isfies the condition th at at absolute zero th e pressure of th e gas should be zero.
How well does th is lin e fit th e data?
5. Amontons 's law is explained on th e basis of the kinetic-molecu lar theory for ideal gases.
Wou ld you expect to see grea ter deviations from ideal gas behavior at high or low temperature s? At h igh or low pr essu res? Explain.
6. The safety warnings on aerosol cans illustrate a real-world application of Amontons's law.
Most aeros ol cans will have a warni ng sim ilar to th e following:
"Do not place in hot water or near radiators. stoves or other sources of heat.
Do not puncture or incinerate container or store at temperatures over 120 "E"
Use the results of this experiment to pred ict what will happen to the gas in an aerosol
conta iner at elevated temperatur es and to explain why th e warning label is neede d.
Flinn Chem'Iopic" Labs - The Gas Laws