Measurement of Pressure

The pressureForce per unit area; in gases arising from the force exerted by collisions of gas molecules with the wall of the container. of the atmosphereA unit of pressure equal to 101.325 kPa or 760 mmHg; abbreviated atm. Also, the mixture of gases surrounding the earth. is exerted in all directions, not just downward, at any given altitude. This can easily be demonstrated with a water glassA solid material that does not have the long-range order of a crystal lattice; an amorphous solid. A glass melts over a range of temperatures instead of having the definite melting temperature characteristic of crystalline solids. and a flat sheet of cardboard or plastic. Fill the glass to the brim with water and carefully slide the cardboard across the top so that no air is trapped within the glass. While holding the cardboard, turn the glass upside down. Now you can remove your fingers from the cardboard, and atmospheric pressure will hold both cardboard and water up. (Eventually, of course, some air will leak in, there will be an increase in pressure above the cardboard, and the water will spill from the glass. If you try this, be sure a sink is handy.)

Figure 1 A mercury barometer. (a) A tube filled with Hg(l) is stoppered with a cork and inverted in a beaker of mercury. (b) When the cork is removed, mercury flows out of the tube until atmospheric pressure (at point A) just balances pressure due to the column of mercury (at point B). The region C above the mercury in the tube is an almost perfect vacuum with zero pressure. Therefore the pressure of the mercury column, of height h, equals atmospheric pressure.

The maximum height of liquidA state of matter in which the atomic-scale particles remain close together but are able to change their positions so that the matter takes the shape of its container which can be supported by atmospheric pressure provides a measure of that pressure It turns out that a column of water about 10 m (more than 30 ft) high can be held up by earth's atmosphere. This would be an inconvenient height to measure in the laboratory, and so a much denser liquid, mercury, is used instead. The mercury barometer, a device for measuring atmospheric pressure, is shown in Fig. 1.

EXAMPLE 1 A barometer is constructed as shown in Fig. 1. The cross-sectional area of the tube is 1.000 cm², and the height of the mercury column is 760.0 mm. Calculate the atmospheric pressure.

SolutionA mixture of one or more substances dissolved in a solvent to give a homogeneous mixture. First calculate the volume of mercury above point B. Use the densityThe ratio of the mass of a sample of a material to its volume. of mercury to obtain the massA measure of the force required to impart unit acceleration to an object; mass is proportional to chemical amount, which represents the quantity of matter in an object., and from this, calculate force and pressure as in Example 1 from "Pressure."

    V = 1.000 cm² × 760.0 mm = 1000 cm × 760.0 mm × 1 cm × (10 mm)^–1 = 76.00 cm³

m_Hg = 76.00 cm³ × 13.595 g cm^–3 = 1033.2 g = 1.0332 kg

    F = ma = 1.0332 kg × 9.807 m s^-2 = 10.133 kg m s^-2 = 10.133 N

The preceding example shows that a mercury column 760.0 mm high and 1.000 cm² in area produces a pressure of 101.33 kPa (1 atm). It can also be shown that only the height of the mercury column affects its pressure. For a larger cross section there is a greater mass of mercury and therefore a greater force, but this is exerted over a greater area, leaving force per unitA particular measure of a physical quantity that is used to express the magnitude of the physical quantity; for example, the meter is the unit of the physical quantity, length. area unchanged. For this reason it is convenient to measure pressures of gases in terms of the height of a mercury column that can be supported. That is, we might report the atmospheric pressure in Example 1 as 760 mmHg instead of 101.3 kPa or 1.000 atm. It is useful to remember that

760 mmHg = 1.000 atm = 101.3 kPa

The pressure of a gas in a container is often measured relative to atmospheric pressure using a manometerA device for measuring the pressure of a gas in relation to the pressure of the atmosphere.. This is a U-shaped tube containing mercury and connecting the container to the air (Fig. 2).

EXAMPLE 2 A mercury manometer is used to measure the pressure of a gas in a flask. As shown in Fig. 2b, the level of mercury is higher in the arm connected to the flask, but the difference in levels is 43 mm. Barometric pressure is 737 mmHg. Calculate the pressure in the container (a) in millimeters of mercury; (b) in kilopascals; and (c) in atmospheres.

Solution

a) P_gas + P_Hg = P_A      P_gas = P_A – P_Hg
                                  P_gas = 737 mmHg – 43 mmHg = 694 mmHg

b)

c)

Note that essentially the same procedure suffices to convert from millimeters of mercury to either kilopascals or atmospheres. Laboratory measurements are usually made in millimeters of mercury, but further calculations almost invariably are more convenient if kilopascals or atmospheres are used.

Figure 2 Use of a mercury manometer. (a) Measuring a pressure greater than atmospheric; (b) measuring a pressure less than atmospheric. P_A = atmospheric pressure, P_Hg = pressure of mercury column; P_gas = pressure of confined gas.

Although the pascal is the accepted SI unit of pressure, it is not yet in general use in the United States. Therefore, one must also be familiar with the atmosphere. The atmosphere is also convenient because 1.000 atm is nearly the same as the atmospheric pressure each of us experiences every day of our lives. This gives a concrete reference with which other pressures can be compared. For these reasons we will usually employ the atmosphere as the unit of pressure for the remainder of this chapter. Nevertheless, there are a number of cases where using the pascal gives a significant insight into gas behavior. In such cases we shall use the newer inter- nationally recognized unit