MathConnections
CH 3 CHCH 2 CH3CH2CH2CH2
5.7 Gas Sensors
The U.S. Environmental Protection Agency lists more than 180 substances as toxic air pollutants and specifi es acceptable levels that can be less than 1 ppm in some cases.
To track the effects of pollutants at such trace levels, fi rst we must be able to mea- sure their concentrations reliably. One way to describe the concentration of a gas, of course, is to report its pressure or partial pressure. Although a mercury barometer quite similar to one that might have been used hundreds of years ago will allow us to monitor the weather, it will not be of much help here. Instead we will need to rely on a number of more modern instruments that offer fundamental advantages over a barometer. A variety of devices now can allow us to measure exceedingly small pres- sures or changes in pressure. Some can also allow us to measure selectively the partial pressure of a particular component in a gas mixture. In this section, we will look at a couple of representative examples and try to show how their clever designs exploit the basic properties of gases to make incredibly sensitive measurements.
Capacitance Manometer
One sensor frequently used to measure pressure in the laboratory is the capacitance manometer. This type of pressure gauge, shown schematically in Figure 5.9, directly exploits the fact that pressure is force per unit area.
A capacitor is an electronic component, as you may know from a physics class.
One way to create a capacitor is to position two parallel metal plates with a space between them. In such an arrangement the distance between the plates determines the capacitance. A capacitance manometer is based on a capacitor in which one of these plates is actually a thin metal diaphragm and the other is fi xed and rigid. The space The term manometer refers to any
pressure-measuring device.
The term manometer refers to any pressure-measuring device.
Figure 5.9 ❚ Schematic diagram of a capacitance manometer. The tube on the left is connected to the gas sample whose pressure is to be measured. As the gas molecules strike the diaphragm, the force of the collisions determines the space between the diaphragm and the fi xed electrode assemblies.
Baffle
Gas sample
Diaphragm
Electrode assembly
To electronics
between the plates is kept under vacuum. We connect the sensor so that the other side of the diaphragm is exposed to the gas whose pressure we want to measure. The pres- sure of the gas produces a force on the diaphragm, causing it to bend toward the second (fi xed) plate of the capacitor. This, in turn, changes the capacitance of the device. If we construct an electric circuit in which the capacitor is one component, we can measure a voltage in that circuit that will be related to the pressure applied to the diaphragm.
To make the sensor easy to use, that circuit can be designed so that we can measure a single voltage whose value is directly proportional to the pressure. Monitoring the voltage allows us to see any changes in pressure.
Capacitance manometers are most often used to measure pressures in the range of 0.001–1000 torr. This range includes moderate levels of vacuum frequently encoun- tered in the laboratory. One advantage of this type of gauge is that it has virtually no moving parts; as long as the diaphragm is not damaged, the gauge should work reliably for very long periods of time.
Thermocouple Gauge
Both the barometer and the capacitance manometer respond fairly directly to the force exerted by gas molecules. But not all pressure sensors work that way. A useful pressure-measuring device can be based on any gas property that varies predictably with pressure.
Pressures between 0.01 and about 1.0 torr, for example, are frequently measured using a thermocouple vacuum gauge (Figure 5.10). A thin fi lament is heated by pass- ing a fi xed electric current through it, and the temperature of the fi lament is then measured using a device called a thermocouple. So how does this measurement tell us anything about pressure? The fi lament is in contact with the gas whose pressure we want to determine. As the molecules in that gas collide with the hot fi lament, they will tend to carry away some energy, reducing the fi lament temperature. The higher the pressure, the more molecules will collide with the fi lament, and the lower its tempera- ture will be. The thermocouple produces a voltage that is related to the fi lament tem- perature and therefore to the gas pressure. A readout device connected to the gauge translates the voltage output into pressure units.
Ionization Gauge
Capacitance manometers can be effective to pressures as low as about 0.001 torr. That is a very low pressure, just over a millionth of an atmosphere. But in certain types of experiments, such as studies of extremely clean metal surfaces, laboratory vacu- ums as low as 10−11 torr are necessary. At such low pressures, it is no longer feasible
Pressures on the order of 10 –14 torr are found in outer space.
Pressures on the order of 10 –14 torr are found in outer space.
Thermocouple junction
Millivoltmeter Milliammeter
Power Filament
Figure 5.10 ❚ Schematic diagram of a thermocouple gauge. An electric current heats the fi lament, and a thermocouple monitors the fi lament’s temperature. Gas molecules collide with the fi lament and cool it. So the higher the pressure, the lower the fi lament temperature will be. A readout circuit usually converts the
measured fi lament temperature into pressure units for display.
to measure the force produced by molecular collisions, so other types of gauges are needed. The most common of these is the ionization gauge, shown in Figure 5.11.
A fi xed electric current fl ows through the fi lament of the ionization gauge, heat- ing it until it glows red. At these high temperatures, the metal atoms in the fi lament emit electrons. Some of these electrons then collide with gas molecules, and the re- sulting impact can knock an electron off the molecule, producing a positive ion. Sup- pose some or all of the gas present is N2. Electrons from the fi lament would then produce N2+ ions, through a process that we could write as
e−+ N2: N2++ 2 e−
The resulting positive ions are then collected by a wire. Measuring the current fl owing into this wire will measure how many ions were collected. The number of ions formed will be proportional to the number of gas molecules in the region of the gauge: more gas will allow more ions to be formed. Finally, we simply have to real- ize that the number of gas molecules present is proportional to the pressure. So the current, which is fairly easy to measure, will be proportional to pressure. In practice, the same electronics that read the current will also be calibrated so that they can dis- play the reading directly as pressure.
Cylindrical electron collection grid
Hot filament electron emitter
Fine wire ion collector
Current amplifier
Gauge display Gas
Gas ion +
Figure 5.11 ❚ Schematic diagram of an ionization gauge. Electrons emitted from the hot fi lament collide with gas molecules and knock an electron free. The resulting cations are collected at the center of the gauge, and the current they produce is a measure of the gas pressure.
The photo shows (from left to right) a thermocouple gauge, a capacitance manometer, and an ionization gauge. The electronics needed to operate the gauges are not shown.
Lawrence S. Brown
Mass Spectrometer
Both the capacitance manometer and the ionization gauge measure the total pres- sure of a gas. But if we want to measure the level of a pollutant in air, for example, we will really want to know its partial pressure. One way to measure partial pressures is with a mass spectrometer, which we saw earlier in Figure 2.4 (page 35). As in the ionization gauge, gas molecules are converted to positive ions by electron bombard- ment. But before the ions are collected, they are sent through a magnetic fi eld that serves as a mass fi lter and sorts the stream of ions by mass. In this arrangement, the current that is measured consists only of ions with a chosen mass. This lets us moni- tor the partial pressure of a gas by looking at the ions of the corresponding mass.
Control electronics allow these instruments to scan continuously over a range of masses and thus can tell us the partial pressure of a number of components in the same gas mixture.
FO C U S O N P RO B L E M S O LV I N G
Question A balloon is to be used to fl oat instruments for observation into the up- per atmosphere. At sea level, this balloon occupies a volume of 95 L at a temperature of 20°C. If helium gas is used to fi ll the balloon, how would you determine the maxi- mum height that this balloon and its instruments will attain?
Strategy This is the type of question that the engineers who design apparatus such as this must answer. The law of nature here is that objects that are less dense fl oat on those that are denser. The balloon will fl oat upward until it reaches a height where its density is equal to that of the atmosphere. With this understanding, we can begin to defi ne the variables we need to understand in this problem and note the relation- ships between those variables that would allow us to estimate an answer to such a problem.
Solution First identify what is known about the variables in the problem. In this case we have a gas that will be at low pressures, so we can assume it will behave as an ideal gas. We note that we will release this balloon from sea level where the pressure can be estimated as 1 atm. Therefore, we can establish the initial pressure, volume, and temperature. We also know the molar mass of helium.
The key relationship is provided by the ideal gas law, which allows us to calculate density. To see this, think about n/V as the number of moles per unit volume. This is equal to the mass density divided by the molar mass. Replacing n/V with that relation- ship gives us a gas law in terms of density:
P = rRT
— MM , or r = — MM?P RT
Looking at this set of equations, the importance of temperature and pressure is apparent.
Because the key condition is the point at which the density of the helium in the balloon is equal to that of the atmosphere we must look up or determine the density of the atmosphere as a function of altitude. The source of this information might also provide the temperature and pressure of the atmosphere as a function of altitude.
Knowing T and P provides the density of helium at various altitudes via the equa- tion above. Having looked up the density of the atmosphere as a function of altitude, we must simply fi nd the altitude at which this calculation equals the looked up value to estimate the maximum height that can be achieved by the balloon. We must rec- ognize, however, that the mass of the instruments must be considered if we wish an accurate answer to this type of problem.
S U M M A RY
The study of gases was extremely important in the development of a molecular description of matter, and still offers us the most direct glimpse into the connections between molecular behavior and macroscopically observable properties. In our everyday ex- perience, no gas is more important than air. For those who live in urban areas, the reality of pollution plays a critical role in that experience.
To understand gases, we need to think in terms of four key variables: pressure, temperature, volume, and quantity. Pressure can be measured over wide ranges by various devices, ranging from traditional barometers to modern mass spectrometers. To understand the origin of gas pressure, we must realize that the molecules in the gas exert a force when they collide with objects.
Although any individual molecular collision imparts only a tiny force, the vast number of such collisions in a macroscopic sample of gas is enough to sum to a measurable value.
For most applications, the ideal gas law, PV = nRT, provides the machinery necessary for quantitative understanding of gases.
This equation includes the universal gas constant, R, in addition to the four variables we just noted. There are a number of ways
in which this equation can be used, but it is always important to watch the units used carefully. The equation itself is only valid if temperature is expressed on an absolute scale, usually the Kelvin scale. Although pressure and volume can be expressed in any convenient units, we must express R in units that are compatible with the other variables. The ideal gas law can be used to deter- mine changes in a variable for a single gas—essentially recreating historic gas laws such as Boyle’s law or Charles’s law. It also al- lows us to extend our methodology for stoichiometry problems to include reactions involving gases. By applying the ideal gas law to each component of mixtures of gases, we can understand the concept of partial pressure and calculate the contribution of each gas in the mixture.
The postulates of the kinetic–molecular theory provide a molecular scale explanation of what it means for a gas to be ideal. A careful examination of those postulates also points us to the conditions where gases are most likely to deviate from ideal behavior: high pressures and low temperatures. Under these con- ditions, empirical equations, such as the van der Waals equation, can account for observed deviations from ideal behavior.
K E Y T E R M S
absolute temperature (5.6) atmosphere, atm (5.2) average speed (5.6) Avogadro’s law (5.3) barometer (5.2) Boyle’s law (5.3) Charles’s law (5.3) criteria pollutant (5.1)
Dalton’s law of partial pressures (5.4) distribution function (5.6)
ionization gauge (5.7)
kinetic–molecular theory (5.6) manometer (5.7)
Maxwell-Boltzmann distribution (5.6) mean free path (5.6)
mole fraction (5.4) most probable speed (5.6) nonattainment area (5.1) part per million (5.1) partial pressure (5.4) pascal, Pa (5.2)
photochemical reaction (5.1)
pressure (5.2) primary standard (5.1) root-mean-square speed (5.6) secondary standard (5.1) standard temperature and pressure (STP) (5.5) thermocouple gauge (5.7) torr (5.2)
universal gas constant, R (5.1) van der Waals equation (5.6)
volatile organic chemical (VOC) (5.1)
P RO B L E M S A N D E X E RC I S E S
■ denotes problems assignable in OWL.
INSIGHT INTO Air Pollution
5.1 List two types of chemical compounds that must be pres- ent in the air for photochemical smog to form. What are the most common sources of these compounds?
5.2 When ozone levels in urban areas reach unhealthy levels, residents are typically urged to avoid refueling their cars during daylight hours. Explain how this might help to reduce smog formation.
5.3 In the production of urban air pollution shown in Figure 5.1, why does the concentration of NO decrease during day- light hours?
5.4 VOCs are not criteria pollutants. Why are they monitored to understand urban air pollution?
5.5 Asphalt is composed of a mixture of organic chemi- cals. Does an asphalt parking lot contribute directly to the formation of photochemical smog? Explain your answer.
5.6 Do a web search to identify which (if any) of the EPA’s cri- teria pollutants are prevalent in your city or state.
5.7 One observable property of gases is the variability of den- sity based on conditions. Use this observation to explain why hot air balloons rise.
Pressure
5.8 If you are pounding a nail and miss it, the hammer may dent the wood, but it does not penetrate it. Use the con- cept of pressure to explain this observation.
5.9 How do gases exert atmospheric pressure?
5.10 Why do mountain climbers need to wear breathing ap- paratus at the tops of high mountains such as Denali in Alaska?
5.11 If you had a liquid whose density was half that of mercury, how tall would you need to build a barometer to measure atmospheric pressure in a location where the record pres- sure recorded was 750 mm Hg?
5.12 Water has a density that is 13.6 times less than that of mer- cury. How high would a column of water need to be to measure a pressure of 1 atm?
5.13 Water has a density that is 13.6 times less than that of mer- cury. If an undersea vessel descends to 1.5 km, how much pressure does the water exert in atm?
5.14 Does the vacuum above the mercury in the column of a barometer affect the reading it gives? Why or why not?
5.15 ■ Gas pressures can be expressed in units of mm Hg, atm, torr, and kPa. Convert these pressure values. (a) 720. mm Hg to atm, (b) 1.25 atm to mm Hg, (c) 542 mm Hg to torr, (d) 740. mm Hg to kPa, (e) 700. kPa to atm
5.16 If the atmospheric pressure is 97.4 kPa, how much is it in mm Hg? In atm?
5.17 Why do your ears “pop” on occasion when you swim deep underwater?
The Gas Law
5.18 When helium escapes from a balloon, the balloon’s volume decreases. Based on your intuition about stretch- ing rubber, explain how this observation is consistent with the gas law.
5.19 ■ A sample of CO2 gas has a pressure of 56.5 mm Hg in a 125-mL fl ask. The sample is transferred to a new fl ask, where it has a pressure of 62.3 mm Hg at the same tem- perature. What is the volume of the new fl ask?
5.20 A gas has an initial volume of 39 mL at an unknown pres- sure. If the same sample occupies 514 mL at 720 torr, what was the initial pressure?
5.21 When you buy a MylarTM balloon in the winter months in colder places, the shopkeeper will often tell you not to worry about it losing its shape when you take it home (outside) because it will return to shape once inside. What behavior of gases is responsible for this advice?
5.22 Why should temperature always be converted to kelvins when working with gases in problem solving?
5.23 What evidence gave rise to the establishment of the abso- lute temperature scale?
5.24 ■ Calculate the missing variable in each set.
V1 = 2.0 L, T1 = 15°C, V2 = ?, T2 = 34°C V1 = ?, T1 = 149°C, V2 = 310 mL, T2 = 54°C V1 = 150 L, T1 = 180 K, V2 = 57 L, T2 = ?
5.25 Why is it dangerous to store compressed gas cylinders in places that could become very hot?
5.26 A balloon fi lled to its maximum capacity on a chilly night at a carnival pops without being touched when it is brought inside. Explain this event.
5.27 A gas bubble forms inside a vat containing a hot liquid.
If the bubble is originally at 68°C and a pressure of 1.6 atm with a volume of 5.8 mL, what will its volume be if the pressure drops to 1.2 atm and the temperature drops to 31°C?
5.28 ■ A bicycle tire is infl ated to a pressure of 3.74 atm at 15°C.
If the tire is heated to 35°C, what is the pressure in the tire? Assume the tire volume doesn’t change.
5.29 ■ A balloon fi lled with helium has a volume of 1.28 × 103 L at sea level where the pressure is 0.998 atm and the tem- perature is 31°C. The balloon is taken to the top of a mountain where the pressure is 0.753 atm and the tem- perature is –25°C. What is the volume of the balloon at the top of the mountain?
5.30 How many moles of an ideal gas are there if the volume of the gas is 158 L at 14°C and a pressure of 89 kPa?
5.31 ■ A newly discovered gas has a density of 2.39 g/L at 23.0°C and 715 mm Hg. What is the molar mass of the gas?
5.32 Calculate the mass of each gas at STP. (a) 1.4 L of SO2, (b) 3.5 × 105 L of CO2
5.33 What are the densities of the following gases at STP?
(a) CF2Cl2, (b) CO2, (c) HCl
5.34 A cylinder containing 15.0 L of helium gas at a pressure of 165 atm is to be used to fi ll party balloons. Each balloon must be fi lled to a volume of 2.0 L at a pressure of 1.1 atm.
What is the maximum number of balloons that can be infl ated? Assume that the gas in the cylinder is at the same temperature as the infl ated balloons. (HINT: The “empty”
cylinder will still contain helium at 1.1 atm.)
5.35 ■ A cylinder is fi lled with toxic COS gas to a pressure of 800.0 torr at 24°C. According to the manufacturer’s speci- fi cations, the cylinder may rupture if the pressure exceeds 35 psi (pounds per square inch; 1 atm = 14.7 psi). What is the maximum temperature to which the cylinder could be heated without exceeding this pressure rating?
5.36 ■ Cylinders of compressed gases are often labeled to show how many “SCF” or “standard cubic feet” of gas they con- tain. 1 SCF of gas occupies a volume of 1 ft3 at a standard temperature and pressure of 0°C and 1 atm. A particular cylinder weighs 122 lbs when empty and 155 lbs when filled with krypton gas at 26°C. How many SCF of Kr does this cylinder contain?
Partial Pressure
5.37 Defi ne the term partial pressure.
5.38 Defi ne the term mole fraction.
5.39 How does the mole fraction relate to the partial pressure?
5.40 ■ What is the total pressure exerted by a mixture of 1.50 g H2 and 5.00 g N2 in a 5.00-L vessel at 25°C?
5.41 What is the total pressure (in atm) of a 15.0-L container at 28.0°C that contains 3.5 g N2, 4.5 g O2, and 13.0 g Cl2? 5.42 For a gas sample whose total pressure is 740 torr, what are
the partial pressures if the moles of gas present are 1.3 mol N2, 0.33 mol O2, and 0.061 mol Ar?