9.2 Characteristics of Gases
1 What’s special about gases?
Fig. 9.3 Difference Between Gas & Liquid
First, we know that a gas has no definite volume or shape; a gas will fill whatever volume is available to it. Contrast this to the behavior of a liquid, which always has a distinct upper surface when its volume is less than that of the space it occupies.
The other outstanding characteristic of gases is their low densities, compared with those of liquids and solids. One mole of liquid water at 298 K and 1 atm pressure occupies a volume of 18.8 cm3, whereas the same quantity of water vapor at the same temperature and pressure has a volume of 30200 cm3, more than 1000 times greater.
The most remarkable property of gases, however, is that to a very good approximation, they all behave the same way in response to changes in temperature and pressure, expanding or contracting by predictable amounts. This is very different from the behavior of liquids or solids, in which the properties of each particular substance must be determined individually.
We will see later that each of these three macroscopic characteristics of gases follows directly from the microscopic view— that is, from the atomic nature of matter.
The pressure of a gas
Figure 9.4 Gas Particles in a container
For some deeper insight into the meaning of pressure, see John Denker’s page A Fluid Has Pressure Everywhere
The molecules of a gas, being in continuous motion, frequently strike the inner walls of their container. As they do so, they immediately bounce off without loss of kinetic energy, but the reversal of direction (acceleration) imparts a force to the container walls. This force, divided by the total surface area on which it acts, is the pressure of the gas.
The pressure of a gas is observed by measuring the pressure that must be applied externally in order to keep the gas from expanding or contracting. To visualize this, imagine some gas trapped in a cylinder having one end enclosed by a freely moving piston. In order to keep the gas in the container, a certain amount of weight (more precisely, a force, f ) must be placed on the piston so as to exactly balance the force exerted by the gas on the bottom of the piston, and tending to push it up. The pressure of the gas is simply the quotient f/A, where A is the cross-section area of the piston.
Pressure units
The unit of pressure in the SI system is the pascal (Pa), defined as a force of one newton per square metre (1 Nm–2 = 1 kg m–1 s–2.)
At the Earth’s surface, the force of gravity acting on a 1 kg mass is 9.81 N. Thus if, in the illustration above, the weight is 1 kg and the surface area of the piston is 1 M2, the pressure of the gas would be 9.81 Pa. A 1-gram weight acting on a piston of 1 cm2 cross-section would exert a pressure of 98.1 pA. (If you wonder why the pressure is higher in the second example, consider the number of cm2 contained in 1 m2.)
In chemistry, it is more common to express pressures in units of atmospheres or torr: 1 atm = 101325 Pa = 760 torr.
Need to convert pressure units? Use this on-line converter.
The older unit millimetre of mercury (mm Hg) is almost the same as the torr; it is defined as one mm of level difference in a mercury barometer at 0°C. In meteorology, the pressure unit most commonly used is the bar:
1 bar = 105 N m–2 = 750.06 torr = 0.987 atm.
In engineering work the pound per square inch is still widely used; standard atmospheric pressure is 14.7 psi. For the definition of the standard atmosphere, see here.
The pressures of gases encountered in nature span an exceptionally wide range, only part of which is ordinarily encountered in chemistry. Note that in the chart below, the pressure scales are logarithmic; thus 0 on the atm scale means 100 = 1 atm.
Figure 9.5 Atmospheric Pressure
Atmospheric pressure and the barometer
Figure 9.6 Atmospheric Pressure at sea level
The column of air above us exerts a force on each 1-cm2 of surface equivalent to a weight of about 1034 g. The higher into the air you go, the smaller the mass of air above you, and the lower the pressure (right).
The surface pressure of 1034 g cm–2 is obtained by solving Newton’s law f = ma for m, using the acceleration of gravity for a:
Figure 9.7 Determination of Gas Pressure
Table of atmospheric pressure by elevation – go here for elevation of your US city
So, if this huge column of air are constantly pressing down on your body, why do you not feel it?
Answer: because every other part of your body (including within your lungs and insides) also experiences the same pressure, so there is no net force (other than gravity) acting on you.
Figure: 9.8
Gas pressure
The pressure of a gas is the force exerted when gas particles strike the surface of the walls of the container. The pressure a gas exerts on a surface, such as the walls of a container, results from the continual bombardment on the walls of the container by the rapidly moving gas molecules. We use an instrument called barometer to measure atmospheric pressure. One type of barometer consists of a long glass tube that is completely filled with mercury and then inverted into a pool of mercury in a dish. Because there is no air at the top of the mercury column inside the tube no gas pressure is exerted on the mercury column. The atmosphere, however, exerts its pressure on the mercury in the open dish. The difference in the heights of the two mercury levels is a measure of the atmospheric pressure. Pressure is measured by barometer and units are:
Atmosphere(atm), millimeter of Hg( mm Hg) , torr.
1atm= 760 torr=760 mm of Hg= 14.7 psi= 101,325 Pa
Other units of pressure are pascal, bar etc. All the units can be interconverted.
Figure 9.20 Determination of Atmospheric Pressure
Ref: commons.wikimedia.org/
Example: On a dry day, atmospheric pressure is 734 torr. What is the pressure in atmospheric unit?
Ans: 734 torr * 1 atm = 0.966 atm
760 torr
The manometer
This Davidson College page has a very good treatment of pressure measurement with a manometer, with simulations. And this manufacturer’s site surveys the many kinds of devices used to measure the pressure of gases in practical applications.
The temperature of a gas
If two bodies are at different temperatures, heat will flow from the warmer to the cooler one until their temperatures are the same. This is the principle on which thermometry is based; the temperature of an object is measured indirectly by placing a calibrated device known as a thermometer in contact with it. When thermal equilibrium is obtained, the temperature of the thermometer is the same as the temperature of the object.
Temperature scales
A thermometer makes use of some temperature-dependent quantity, such as the density of a liquid, to allow the temperature to be found indirectly through some easily measured quantity such as the length of a mercury column. The resulting scale of temperature is entirely arbitrary; it is defined by locating its zero point, and the size of the degree unit.
At one point in the 18th century, 35 different temperature scales were in use!
Figure: 9.18 Temperature Scale
The Celsius temperature scale locates the zero point at the freezing temperature of water; the Celsius degree is defined as 1/100 of the difference between the freezing and boiling temperatures of water at 1 atm pressure.
The older Fahrenheit scale placed the zero point at the coldest temperature it was possible to obtain at the time (by mixing salt and ice.) The 100° point was set with body temperature (later found to be 98.6°F.) On this scale, water freezes at 32°F and boils at 212°F. The Fahrenheit scale is a finer one than the Celsius scale; there are 180 Fahrenheit degrees in the same temperature interval that contains 100 Celsius degrees, so 1F° = 5/9 C°. Since the zero points are also different by 32F°, conversion between temperatures expressed on the two scales requires the addition or subtraction of this offset, as well as multiplication by the ratio of the degree size.
If you take the effort to understand the above paragraph, you will never need to waste your time with formulas for converting between Fahrenheit and Celsius!
…and if you live in any country other the U.S. or Belize, you can forget about Fahrenheit altogether.
Notice also that temperature is expressed by placing the degree symbol in front of the scale abbreviation (37°C), whereas a temperature interval is written with the degree sign following the symbol (2 C°).
Absolute temperature
In 1802 the French mathematician and physicist Joseph Gay-Lussac discovered that for each Celsius degree that the temperature of a gas is lowered, the volume of the gas will diminish by 1/273 of its volume at 0°C. The obvious implication of this is that if the temperature could be reduced to –273°C, the volume of the gas would contract to zero. Of course, all real gases condense to liquids before this happens, but at sufficiently low pressures their volumes are linear functions of the temperature
(Charles’ Law), and extrapolation of a plot of volume as a function of temperature predicts zero volume at -273°C. This temperature, known as absolute zero, corresponds to the total absence of thermal energy.
The temperature scale on which the zero point is –273.15°C was suggested by Lord Kelvin, and is usually known as the Kelvin scale. Since the size of the Kelvin and Celsius degrees are the same, conversion between the two scales is a simple matter of adding or subtracting 273.15; thus room temperature, 20°, is about 293 K.
A rather fine point to note: the degree symbol is not used with the “K”, which should always be separated from the preceding number by a space. See here for an explanation.
Because the Kelvin scale is based on an absolute, rather than on an arbitrary zero of temperature, it plays a special significance in scientific calculations; most fundamental physical relations involving temperature are expressed mathematically in terms of absolute temperature. In engineering work, an absolute scale based on the Fahrenheit degree is sometimes used; this is known as the Rankine scale.
About Temperature is a far-ranging but very readable site by Beverly Lynds.
How ultra low temperatures are achieved and measured
4 The volume occupied by a gas
The volume of a gas is simply the space in which the molecules of the gas are free to move. If we have a mixture of gases, such as air, the various gases will coexist within the same volume. In these respects, gases are very different from liquids and solids, the two condensed states of matter.
The volume of a gas can be measured by trapping it above mercury in a calibrated tube known as a gas burette. The SI unit of volume is the cubic metre, but in chemistry we more commonly use the litre and the millilitre (ml). The cubic centimetre (cc) is also frequently used; it is very close to 1 milliliter (mL).
igure: 9.19 manometer Diagram
It’s important to bear in mind, however, that the volume of a gas varies with both the temperature and the pressure, so reporting the volume alone is not very useful. A common practice is to measure the volume of the gas under the ambient temperature and atmospheric pressure, and then to correct the observed volume to what it would be at standard atmospheric pressure and some fixed temperature, usually 0° C or 25°C.
What you should be able to do
Make sure you thoroughly understand the following essential ideas which have been presented above. It is especially important that you know the precise meanings of all the green-highlighted terms in the context of this topic.
State the three major properties of gases that distinguish them from condensed phases of matter.
Define pressure, and explain why a gas exerts pressure on the walls of a container.
Explain the operation of a simple barometer, and why its invention revolutionized our understanding of gases.
Explain why a barometer that uses water as the barometric fluid is usually less practical than one which employs mercury.
How are the Celsius and Fahrenheit temperature scales defined? How do the magnitudes of the “degree” on each scale related?
Why must the temperature and pressure be specified when reporting the volume of a gas?
Question:
- A scuba diver begins diving at 3000 psi. Convert this pressure into 1) atm 2) mm of Hg.