8.5 Gases and Pressure

David W. Ball; Jessie A. Key

Learning Objectives

Define the property of pressure
Define and convert among the units of pressure measurements
Describe the operation of common tools for measuring gas pressure
Calculate pressure from manometer data

The earth’s atmosphere exerts a pressure, as does any other gas. Although we do not normally notice atmospheric pressure, we are sensitive to pressure changes—for example, when your ears “pop” during take-off and landing while flying, or when you dive underwater. Gas pressure is caused by the force exerted by gas molecules colliding with the surfaces of objects (Figure 8.21). Although the force of each collision is very small, any surface of appreciable area experiences a large number of collisions in a short time, which can result in a high pressure. In fact, normal air pressure is strong enough to crush a metal container when not balanced by equal pressure from inside the container.

The left side of this figure includes a graphic of the earth with an inverted rectangular prism extending from a point on it. Near the top of the image, the label, “square inch column of air molecules” is connected to the prism with a line segment. This label is also connected with a line segment to a downward pointing arrow at the right side of the figure. Beneath the arrow is a red circle labeled, “atmospheric pressure.” A narrow rectangle with a dashed line border extends from the bottom of the arrow vertically through the circle. Directly beneath this rectangle at the lower edge of the circle is a hand with a thumb appearing to be resting on a tabletop. The thumb is connected with a line segment to the label, “14.7 lbs of pressure on 1 square inch.” The red circle is sitting on top of the thumb.

Atmospheric pressure is caused by the weight of the column of air molecules in the atmosphere above an object. At sea level, this pressure is roughly the same as that exerted by a full-grown African elephant standing on a doormat, or a typical bowling ball resting on your thumbnail. These may seem like huge amounts, and they are, but life on earth has evolved under such atmospheric pressure. If you actually perch a bowling ball on your thumbnail, the pressure experienced is twice the usual pressure, and the sensation is unpleasant.

In general, pressure is defined as the force exerted on a given area: $P = \frac{F}{A}$ . Note that pressure is directly proportional to force and inversely proportional to area. Thus, pressure can be increased either by increasing the amount of force or by decreasing the area over which it is applied; pressure can be decreased by decreasing the force or increasing the area.

Let’s apply this concept to determine which would be more likely to fall through thin ice in Figure 8.22—the elephant or the figure skater? A large African elephant can weigh 7 tons, supported on four feet, each with a diameter of about 1.5 ft (footprint area of 250 in²), so the pressure exerted by each foot is about 14 lb/in²:

$\text{pressure per elephant foot} = 14,000 \frac{\text{lb}}{\text{elephant}} \times \frac{1 \;\text{elephant}}{4 \;\text{feet}} \times \frac{1 \;\text{foot}}{250 \;\text{in}^2} = 14 \;\text{lb/in}^2$

The figure skater weighs about 120 lbs, supported on two skate blades, each with an area of about 2 in², so the pressure exerted by each blade is about 30 lb/in²:

$\text{pressure per skate blade} = 120 \frac{\text{lb}}{\text{skater}} \times \frac{1 \;\text{skater}}{2 \;\text{blades}} \times \frac{1 \;\text{blade}}{2 \;\text{in}^2} = 30 \;\text{lb/in}^2$

Even though the elephant is more than one hundred-times heavier than the skater, it exerts less than one-half of the pressure and would therefore be less likely to fall though thin ice. On the other hand, if the skater removes her skates and stands with bare feet (or regular footwear) on the ice, the larger area over which her weight is applied greatly reduces the pressure exerted:

$\text{pressure per human foot} = 120 \frac{\text{lb}}{\text{skater}} \times \frac{1 \;\text{skater}}{2 \;\text{feet}} \times \frac{1 \;\text{foot}}{30 \;\text{in}^2} = 2 \;\text{lb/in}^2$

This figure includes two photographs. Figure a is a photo of a large gray elephant on grassy, beige terrain. Figure b is a photo of a figure skater with her right skate on the ice, upper torso lowered, arms extended upward behind her chest, and left leg extended upward behind her. — 8.22 Although (a) an elephant’s weight is large, creating a very large force on the ground, (b) the figure skater exerts a much higher pressure on the ice due to the small surface area of her skates. (credit a: modification of work by Guido da Rozze; credit b: modification of work by Ryosuke Yagi)

The SI unit of pressure is the pascal (Pa), with 1 Pa = 1 N/m², where N is the newton, a unit of force defined as 1 kg m/s². One pascal is a small pressure; in many cases, it is more convenient to use units of kilopascal (1 kPa = 1000 Pa) or bar (1 bar = 100,000 Pa). In the United States, pressure is often measured in pounds of force on an area of one square inch—pounds per square inch (psi)—for example, in car tires. Pressure can also be measured using the unit atmosphere (atm), which originally represented the average sea level air pressure at the approximate latitude of Paris (45°). Table 8.4 provides some information on these and a few other common units for pressure measurements

Unit Name and Abbreviation	Definition or Relation to Other Unit
pascal (Pa)	1 Pa = 1 N/m² recommended IUPAC unit
kilopascal (kPa)	1 kPa = 1000 Pa
pounds per square inch (psi)	air pressure at sea level is ~14.7 psi
atmosphere (atm)	1 atm = 101,325 Pa air pressure at sea level is ~1 atm
bar (bar, or b)	1 bar = 100,000 Pa (exactly) commonly used in meteorology
millibar (mbar, or mb)	1000 mbar = 1 bar
inches of mercury (in. Hg)	1 in. Hg = 3386 Pa used by aviation industry, also some weather reports
torr	$1 \;\text{torr} = \frac{1}{760} \;\text{atm}$ named after Evangelista Torricelli, inventor of the barometer
millimeters of mercury (mm Hg)	1 mm Hg ~1 torr
Table 8.4 Pressure Units

Example 8.6

Conversion of Pressure Units
The United States National Weather Service reports pressure in both inches of Hg and millibars. Convert a pressure of 29.2 in. Hg into:

(a) torr

(b) atm

(c) kPa

(d) mbar

Solution
This is a unit conversion problem. The relationships between the various pressure units are given in Table 8.4.

(a) $29.2 \;\rule[0.5ex]{2.2em}{0.1ex}\hspace{-2.2em}\text{in Hg} \times \frac{25.4 \;\rule[0.25ex]{1.2em}{0.1ex}\hspace{-1.2em}\text{mm}}{1 \;\rule[0.25ex]{0.6em}{0.1ex}\hspace{-0.6em}\text{in}} \times \frac{1 \;\text{torr}}{1 \;\rule[0.25ex]{2em}{0.1ex}\hspace{-2em}\text{mm Hg}} = 742 \;\text{torr}$

(b) $742 \;\rule[0.5ex]{1.8em}{0.1ex}\hspace{-1.8em}\text{torr} \times \frac{1 \;\text{atm}}{760 \;\rule[0.25ex]{1.2em}{0.1ex}\hspace{-1.2em}\text{torr}} = 0.976 \;\text{atm}$

(c) $742 \;\rule[0.5ex]{1.8em}{0.1ex}\hspace{-1.8em}\text{torr} \times \frac{101.325 \;\text{kPa}}{760 \;\rule[0.25ex]{1.0em}{0.1ex}\hspace{-1.0em}\text{torr}} = 98.9 \;\text{kPa}$

(d) $98.9 \;\rule[0.5ex]{1.9em}{0.1ex}\hspace{-1.9em}\text{kPa} \times \frac{1000 \;\rule[0.25ex]{0.9em}{0.1ex}\hspace{-0.9em}\text{Pa}}{1 \;\rule[0.25ex]{1.1em}{0.1ex}\hspace{-1.1em}\text{kPa}} \times \frac{1 \;\rule[0.25ex]{0.9em}{0.1ex}\hspace{-0.9em}\text{bar}}{100,000 \;\rule[0.25ex]{1.0em}{0.1ex}\hspace{-1.0em}\text{Pa}} \times \frac{1000 \;\text{mbar}}{1 \;\rule[0.25ex]{1.0em}{0.1ex}\hspace{-1.0em}\text{bar}} = 989 \;\text{mbar}$

Check Your Learning
A typical barometric pressure in Kansas City is 740 torr. What is this pressure in atmospheres, in millimeters of mercury, in kilopascals, and in bar?

Answer:

0.974 atm; 740 mm Hg; 98.7 kPa; 0.987 bar

We can measure atmospheric pressure, the force exerted by the atmosphere on the earth’s surface, with a barometer (Figure 8.23). A barometer is a glass tube that is closed at one end, filled with a nonvolatile liquid such as mercury, and then inverted and immersed in a container of that liquid. The atmosphere exerts pressure on the liquid outside the tube, the column of liquid exerts pressure inside the tube, and the pressure at the liquid surface is the same inside and outside the tube. The height of the liquid in the tube is therefore proportional to the pressure exerted by the atmosphere.

This figure shows two barometers. The barometer to the left contains a shallow reservoir, or open container, of mercury. A narrow tube extends upward from the reservoir above the reservoir. This tube is sealed at the top. To the right, a second similar setup is shown with a reservoir filled with water. Line segments connect the label “vacuum” to the tops of the two narrow tubes. The tube on the left shows the mercury in the reservoir extending in a column upward in the narrow tube. Similarly, the tube on the right shows the water in the reservoir extending upward into the related narrow tube. Double-headed arrows extend from the surface of each liquid in the reservoir to the top of the liquid in each tube. A narrow column or bar extends from the surface of the reservoir to the same height. This bar is labeled “atmospheric pressure.” The level of the water in its tube is significantly higher than the level of mercury in its tube.

If the liquid is water, normal atmospheric pressure will support a column of water over 10 meters high, which is rather inconvenient for making (and reading) a barometer. Because mercury (Hg) is about 13.6-times denser than water, a mercury barometer only needs to be $\frac{1}{13.6}$ as tall as a water barometer—a more suitable size. Standard atmospheric pressure of 1 atm at sea level (101,325 Pa) corresponds to a column of mercury that is about 760 mm (29.92 in.) high. The torr was originally intended to be a unit equal to one millimeter of mercury, but it no longer corresponds exactly. The pressure exerted by a fluid due to gravity is known as hydrostatic pressure, p:

$p = h\rho g$

where h is the height of the fluid, ρ is the density of the fluid, and g is acceleration due to gravity.

Example 8.7

Calculation of Barometric Pressure
Show the calculation supporting the claim that atmospheric pressure near sea level corresponds to the pressure exerted by a column of mercury that is about 760 mm high. The density of mercury = 13.6 g/cm³.

Solution
The hydrostatic pressure is given by p = hρg, with h = 760 mm, ρ = 13.6 g/cm³, and g = 9.81 m/s². Plugging these values into the equation and doing the necessary unit conversions will give us the value we seek. (Note: We are expecting to find a pressure of ~101,325 Pa:)

$101,325 N/ \text{m}^2 = 101,325 \frac{\text{kg} \cdot \text{m/s}^2}{\text{m}^2} = 101,325 \frac{\text{kg}}{\text{m} \cdot \text{s}^2}$

$\begin{array}{l @{{}={}}l} p & (760 \;\text{mm} \times \frac{1 \;\text{m}}{1000 \;\text{mm}}) \times (\frac{13.6 \;\text{g}}{1 \;\text{cm}^3} \times \frac{1 \;\text{kg}}{1000 \;\text{g}} \times \frac{(100 \;\text{cm})^3}{(1 \;\text{m})^3}) \times (\frac{9.81 \;\text{m}}{1 \;\text{s}^2}) \\[1em] & (0.760 \;\text{m}) (13,600 \;\text{kg/m}^3) (9.81 \;\text{m/s}^2) = 1.01 \times 10^5 \;\text{kg/ms}^2 = 1.01 \times 10^5 \;N/ \text{m}^2 \\[1em] & 1.01 \times 10^5 \;\text{Pa} \end{array}$

Check Your Learning
Calculate the height of a column of water at 25 °C that corresponds to normal atmospheric pressure. The density of water at this temperature is 1.0 g/cm³.

Answer:

10.3 m

Measuring Blood Pressure

Blood pressure is measured using a device called a sphygmomanometer (Greek sphygmos = “pulse”). It consists of an inflatable cuff to restrict blood flow, a manometer to measure the pressure, and a method of determining when blood flow begins and when it becomes impeded (Figure 8.25). Since its invention in 1881, it has been an essential medical device. There are many types of sphygmomanometers: manual ones that require a stethoscope and are used by medical professionals; mercury ones, used when the most accuracy is required; less accurate mechanical ones; and digital ones that can be used with little training but that have limitations. When using a sphygmomanometer, the cuff is placed around the upper arm and inflated until blood flow is completely blocked, then slowly released. As the heart beats, blood forced through the arteries causes a rise in pressure. This rise in pressure at which blood flow begins is the systolic pressure—the peak pressure in the cardiac cycle. When the cuff’s pressure equals the arterial systolic pressure, blood flows past the cuff, creating audible sounds that can be heard using a stethoscope. This is followed by a decrease in pressure as the heart’s ventricles prepare for another beat. As cuff pressure continues to decrease, eventually sound is no longer heard; this is the diastolic pressure—the lowest pressure (resting phase) in the cardiac cycle. Blood pressure units from a sphygmomanometer are in terms of millimeters of mercury (mm Hg).

This figure includes two photographs. The first photo shows a young adult male placing a blood pressure cuff on the upper arm of a young adult female. The second image shows a typical sphygmomanometer, which includes a black blood pressure cuff, tubing, pump, and pressure gauge. — Figure 8.24. (a) A medical technician prepares to measure a patient’s blood pressure with a sphygmomanometer. (b) A typical sphygmomanometer uses a valved rubber bulb to inflate the cuff and a diaphragm gauge to measure pressure. (credit a: modification of work by Master Sgt. Jeffrey Allen)

Meteorology, Climatology, and Atmospheric Science

Throughout the ages, people have observed clouds, winds, and precipitation, trying to discern patterns and make predictions: when it is best to plant and harvest; whether it is safe to set out on a sea voyage; and much more. We now face complex weather and atmosphere-related challenges that will have a major impact on our civilization and the ecosystem. Several different scientific disciplines use chemical principles to help us better understand weather, the atmosphere, and climate. These are meteorology, climatology, and atmospheric science. Meteorology is the study of the atmosphere, atmospheric phenomena, and atmospheric effects on earth’s weather. Meteorologists seek to understand and predict the weather in the short term, which can save lives and benefit the economy. Weather forecasts (Figure 8.26) are the result of thousands of measurements of air pressure, temperature, and the like, which are compiled, modeled, and analyzed in weather centers worldwide.

A weather map of the United States is shown which points out areas of high and low pressure with the letters H in blue and L in red. Curved lines in grey, orange, blue, and red are shown. The orange lines are segmented. The red and blue lines have small red or blue semi-circles and triangles attached along their lengths. In dashed white lines, latitude and longitude are indicated. Underlined three and four digit numbers also appear across the map.

In terms of weather, low-pressure systems occur when the earth’s surface atmospheric pressure is lower than the surrounding environment: Moist air rises and condenses, producing clouds. Movement of moisture and air within various weather fronts instigates most weather events.

The atmosphere is the gaseous layer that surrounds a planet. Earth’s atmosphere, which is roughly 100–125 km thick, consists of roughly 78.1% nitrogen and 21.0% oxygen, and can be subdivided further into the regions shown in Figure 8.27: the exosphere (furthest from earth, > 700 km above sea level), the thermosphere (80–700 km), the mesosphere (50–80 km), the stratosphere (second lowest level of our atmosphere, 12–50 km above sea level), and the troposphere (up to 12 km above sea level, roughly 80% of the earth’s atmosphere by mass and the layer where most weather events originate). As you go higher in the troposphere, air density and temperature both decrease.

This diagram shows half of a two dimensional view of the earth in blue and green. A narrow white layer, labeled “troposphere 0 dash 12 k m” covers this hemisphere. This layer is also labeled “layer where most weather events originate.” Next, a thicker light blue layer labeled “Stratosphere 12 dash 50 k m” is shown. This is followed by a slightly thinner layer also in light blue labeled “Mesosphere 50 dash 80 k m.” Following this layer is a relatively thick light blue layer labeled “Thermosphere 80 dash 700 k m.” A blue layer appears that covers the rightmost two thirds of the diagram. This region gradually darkens from a lighter blue at the left to a dark blue at the right. This region of the diagram is labeled “exosphere greater than 700 k m.” — Figure 8.26 Earth’s atmosphere has five layers: the troposphere, the stratosphere, the mesosphere, the thermosphere, and the exosphere.

Climatology is the study of the climate, averaged weather conditions over long time periods, using atmospheric data. However, climatologists study patterns and effects that occur over decades, centuries, and millennia, rather than shorter time frames of hours, days, and weeks like meteorologists. Atmospheric science is an even broader field, combining meteorology, climatology, and other scientific disciplines that study the atmosphere.

Key Concepts and Summary

Gases exert pressure, which is force per unit area. The pressure of a gas may be expressed in the SI unit of pascal or kilopascal, as well as in many other units including torr, atmosphere, and bar. Atmospheric pressure is measured using a barometer; other gas pressures can be measured using one of several types of manometers.

Chemistry End of Chapter Exercises

Why are sharp knives more effective than dull knives (Hint: think about the definition of pressure)?
Why do some small bridges have weight limits that depend on how many wheels or axles the crossing vehicle has?
Why should you roll or belly-crawl rather than walk across a thinly-frozen pond?
A typical barometric pressure in Redding, California, is about 750 mm Hg. Calculate this pressure in atm and kPa.
A typical barometric pressure in Denver, Colorado, is 615 mm Hg. What is this pressure in atmospheres and kilopascals?
A typical barometric pressure in Kansas City is 740 torr. What is this pressure in atmospheres, in millimeters of mercury, and in kilopascals?
Canadian tire pressure gauges are marked in units of kilopascals. What reading on such a gauge corresponds to 32 psi?
During the Viking landings on Mars, the atmospheric pressure was determined to be on the average about 6.50 millibars (1 bar = 0.987 atm). What is that pressure in torr and kPa?
The pressure of the atmosphere on the surface of the planet Venus is about 88.8 atm. Compare that pressure in psi to the normal pressure on earth at sea level in psi.
A medical laboratory catalog describes the pressure in a cylinder of a gas as 14.82 MPa. What is the pressure of this gas in atmospheres and torr?
Consider this scenario and answer the following questions: On a mid-August day in the northeastern United States, the following information appeared in the local newspaper: atmospheric pressure at sea level 29.97 in., 1013.9 mbar.
(a) What was the pressure in kPa?

(b) The pressure near the seacoast in the northeastern United States is usually reported near 30.0 in. Hg. During a hurricane, the pressure may fall to near 28.0 in. Hg. Calculate the drop in pressure in torr.

Solutions

Answers to Chemistry End of Chapter Exercises

1. The cutting edge of a knife that has been sharpened has a smaller surface area than a dull knife. Since pressure is force per unit area, a sharp knife will exert a higher pressure with the same amount of force and cut through material more effectively.

3. Lying down distributes your weight over a larger surface area, exerting less pressure on the ice compared to standing up. If you exert less pressure, you are less likely to break through thin ice.

5. 0.809 atm; 82.0 kPa

7. 2.2 × 10² kPa

9. Earth: 14.7 lb in^–2; Venus: 13.1 × 10³ lb in⁻²

11. (a) 101.5 kPa; (b) 51 torr drop

Section 8.5 adapted from OpenStax: licensed under a Creative Commons Attribution 4.0 International License

Robinson, W. R., Flowers, P., Theopold, K., & Langley, R. (2019). Gas Pressure. In <i>Chemistry 2e</i>.
OpenStax. https://openstax.org/books/chemistry-2e/pages/9-1-gas-pressure
OpenStax is licensed under creative Commons Attribution License v4.0

License

Icon for the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License

Chem&121: Introduction to Chemistry Copyright © 2023 by Lake Washington Institute of Technology is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

Example 8.6

Answer:

Example 8.7

Answer:

Measuring Blood Pressure

Meteorology, Climatology, and Atmospheric Science

Key Concepts and Summary

Chemistry End of Chapter Exercises

Solutions

License

Share This Book