12.1: Gases and Pressure

Learning Objectives

• To describe the gas phase.

The gas phase is unique among the three states of matter in that there are some simple models we can use to predict the physical behavior of all gases—independent of their identities. We cannot do this for the solid and liquid states. 

How is it that we can model all gases independent of their chemical identity? The answer is in a group of statements called the kinetic theory of gases:

• Gases are composed of tiny particles that are separated by large distances.
• Gas particles are constantly moving, experiencing collisions with other gas particles and the walls of their container.
• The velocity of gas particles is related to the temperature of a gas.
• Gas particles do not experience any force of attraction or repulsion with each other.

Did you notice that none of these statements relates to the identity of the gas? This means that all gases should behave similarly. A gas that follows these statements perfectly is called an ideal gas. Most gases show slight deviations from these statements and are called real gases. However, the existence of real gases does not diminish the importance of the kinetic theory of gases.

One of the statements of the kinetic theory mentions collisions. As gas particles are constantly moving, they are also constantly colliding with each other and with the walls of their container. There are forces involved as gas particles bounce off the container walls (Figure \(\PageIndex{1}\)). The force generated by gas particles divided by the area of the container walls yields pressure. Pressure is a property we can measure for a gas, but we typically do not consider pressure for solids or liquids.

Figure \(\PageIndex{1}\): Gas Pressure. Pressure is what results when gas particles rebound off the walls of their container.

Common pressure units used in science include pascals (Pa), bars (bar), atmospheres (atm), and millimeters of mercury (mm Hg). One pascal is not a very large amount of pressure. A more useful unit of pressure is the bar, which is 100,000 Pa (1 bar = 100,000 Pa). The units of pressure that we will use most often in this course are the atmosphere (atm), which was originally defined as the average pressure of Earth’s atmosphere at sea level; and mm Hg (millimeters of mercury), which is the pressure generated by a column of mercury 1 mm high. The unit millimeters of mercury is also called a torr, named after the Italian scientist Evangelista Torricelli, who invented the barometer in the mid-1600s. There are exactly 760 mm Hg (or torr) in 1 atm. A bar equals 1.01325 atm. The ability to convert from one pressure unit to another is a useful skill because different instruments measure in different units.

Example \(\PageIndex{1}\): Converting Pressures

How many atmospheres are in 1,547 mm Hg?

Solution

Because there are 760 mm Hg in 1 atm, we can use this conversion factor to do the mathematical conversion:

\(\mathrm{1,547\: mm\:Hg\times \dfrac{1\: atm}{760\: mm\:Hg}=2.04\: atm}\)

Note how the mm Hg units cancel algebraically.

Exercise \(\PageIndex{1}\): Converting Pressures

How many millimeters of mercury are in 9.65 atm?

Answer

\(\mathrm{9.65\: atm\times \dfrac{760\: mm\:Hg}{1\: atm}=7,334 \: mm\:Hg}\).

The kinetic theory also states that there is no interaction between individual gas particles. Although we know that there are, in fact, intermolecular interactions in real gases, the kinetic theory assumes that gas particles are so far apart that the individual particles don’t “feel” each other. Thus, we can treat gas particles as tiny bits of matter whose identity isn’t important to certain physical properties.

Concept Review Exercise

1. What is pressure, and what units do we use to express it?

Answer

1. Pressure is the force per unit area; common units include pascals, torr, millimeters of mercury, or atmospheres.

Key Takeaway

• The gas phase has certain general properties characteristic of that phase.

Exercises

1. What is the kinetic theory of gases?

2. According to the kinetic theory of gases, the individual gas particles are (always, frequently, never) moving.

3. Why does a gas exert pressure?

4. Why does the kinetic theory of gases allow us to presume that all gases will show similar behavior?

5. Arrange the following pressure quantities in order from smallest to largest: 1 mm Hg, 1 Pa, and 1 atm.

6. Which unit of pressure is larger—the torr or the atmosphere?

7. How many mm Hg are there in 1.56 atm?

8. Blood pressures are expressed in millimeters of mercury. What would be the blood pressure in atmospheres if a patient’s systolic blood pressure is 120 mm Hg and the diastolic blood pressure is 82 mm Hg? (In medicine, such a blood pressure would be reported as “120/82,” spoken as “one hundred twenty over eighty-two.”)

9. In weather forecasting, barometric pressure is expressed in inches of mercury (in. Hg), where there are exactly 25.4 mmHg in every 1 in. Hg. What is the barometric pressure in millimeters of mercury if the barometric pressure is reported as 30.21 in. Hg?

Answers

1. Gases are composed of tiny particles that are separated by large distances. Gas particles are constantly moving, experiencing collisions with other gas particles and the walls of their container. The velocity of gas particles is related to the temperature of a gas. Gas particles do not experience any force of attraction or repulsion with each other.

2. always

3. A gas exerts pressure as its particles rebound off the walls of its container.

4. Because the molecules are far apart and don't have attractive forces (intermolecular forces) between them

5. 1 Pa, 1 mm Hg, and 1 atm

6. atm

7. 1,190 mm Hg

8. 0.158 atm; 0.108 atm

9. 767.3 mm Hg