In this study guide we will discuss gases and gas pressure. Air is a solution of gases — mainly nitrogen, oxygen, and argon. It is a homogeneous solution of gas particles. Without air to breath, life would not exist here on earth. Dry air at sea level has the following composition of gases:
O2 20.95% volume with a percent mass of 23.14%
Ar 0.93% volume with a percent mass of 1.29%
CO2 0.040% volume with a percent mass of 0.060%
Ne 1.82 x 10-3% with a percent mass of 1.27 x 10-3%
He 5.24 x 10-4% with a percent mass of 7.24 x 10-5%
CH4 1.7 x 10-4% with a percent mass of 9.4 x 10-5%
Kr 1.14 x 10-4% with a percent mass of 3.3 x 10-4%
Matter can exist in one of three states—a solid, liquid, or a gas. Whether a substance is a solid, liquid, or a gas depends on the kinetic energy (the amount of heat) and the intermolecular forces (attractions) within the system. Recall, particles in a solid are highly ordered and have minimal kinetic energy and very strong intermolecular forces. In the liquid state, the particles are less ordered, moving randomly about one another, and possess high kinetic energy and strong intermolecular forces. In the gas state, the kinetic energy of the particles is very strong, the intermolecular forces or attractions are very weak, and the particles are very far apart and move randomly about.
A solid has invariable shape and volume, a liquid has invariable volume and variable shape, whereas a gas has both variable volume and shape. A gas will take on the shape and volume of its container. Liquids and solids are known as condensed phases because the particles are so much closer together than the particles of a gas.
In this study guide we will focus on the gaseous state. Gas behavior at the molecular level is easily understood. The properties of gases can be described in terms of how the gas particles, molecules or atoms, of a gas behave.
The volume of a gas significantly changes with pressure while solid and liquid volumes are not greatly affected by pressure. The volume of a gas changes significantly with temperature. Gases expand when they are heated and they contract when they are cooled. The volume change is 50 to 100 times greater for gases than for solids and liquids. Gases flow freely, have relatively low densities, and are compressible. Gases form a solution in any proportions. In other words gasses are miscible with one another.
Kinetic Molecular Theory and Properties of Gases
Gases have different properties from those of liquids and solids. They have low densities and can be compressed to smaller volumes allowing them to be stored in tanks. A scuba diver uses a tank that provides air for him to breathe while under water. Hospitals have oxygen tanks for their patients that require oxygen. Unlike a liquid or solid, a gas will take on the shape and volume of its container. Gases, like air, are homogeneous mixtures. The behavior and properties of gases can be explained by the kinetic-molecular theory which is based on several postulates (assumptions):
2. The space between the gas particles is very large compared to the size of the particles.
3. The average kinetic energy of the gas particles increases with an increase in temperature (K).
4. Collisions of gas particles, either with other gas particles or the wall of the container, are elastic (the total kinetic energy is constant).
Because gases move randomly, different gases mix together. One example is the air that we breathe. Air is a homogeneous mixture that consists of the gases oxygen, nitrogen, some argon, carbon dioxide, and water vapor. The volume of a gas can be compressed because of the very small gas particle size relative to the large unoccupied volume. As temperature increases, gas particles move faster resulting in an increase of average kinetic energy. A neon atom moves at an average speed of approximately 450 meters/s. Collisions of gas particles against the wall of a container is the pressure of the gas. Gas pressure increases with an increase in collisions and with more forceful collisions. A tire stays inflated due to the collisions of gas particles against the wall of the inner tube. Gases that obey the assumptions of the kinetic-molecular theory are called ideal gases. We will in this and other study guides see that many gases exhibit ideal behavior at moderate pressures and high temperatures.
Many of us have experienced “ear popping” when a plane descends. This popping is a result of a change in air pressure against the eardrum. Pressure is defined as the force, F, per unit area, A, that pushes against a surface. Gas particles move randomly through a volume that is mainly empty space. The collisions of these randomly moving particles with the wall of the container exert a force per unit area that is the pressure of the gas.
where P is the pressure, F is the force in the Newton (N), A is the area in m2, m is the mass in kg, and a is the acceleration due to gravity which is equal to 9.81\(\frac{m}{s^2}\). One N is equal to 1\(\frac{kg⋅m}{s^2}\).
The SI unit for pressure is the Pascal, Pa.
There are many other pressure units that can be used. In the lab we use atm (atmosphere), torr, and mmHg. You are probably familiar with psi (lb/in2). See the table below for the pressure units and their equivalences to 1 atm. For example, 760 mm Hg is equal to 1 atm and 1.01325 x 105 Pa is equal to 1 atm.
The gases in our atmosphere all exert an atmospheric pressure here on earth due to the gravitational pull on the air. The molecules and atoms that make up the air collide with all of the matter here on earth. Atmospheric pressure varies with location and altitude and also with weather conditions. At sea level the atmospheric pressure is about 14.7 pounds per square inch (psi) and about 12.4 psi, at one mile high, in Denver, Colorado. The common unit for measuring atmospheric pressure is the millimeter of mercury, mm Hg. At sea level the atmospheric pressure is equivalent to 760. mm Hg.
Atmospheric pressure is measured using a mercury barometer (see figure below). A barometer consists of a long glass tube called a column, about 1 meter long, filled with mercury and closed at one end. The tube is inverted into a container containing more mercury. When inverted, some of the mercury will flow into the dish resulting in the formation of a vacuum above the mercury in the tube. The mercury stops flowing from the tube when the downward pressure of the mercury in the tube is equal to the atmospheric pressure that pushes down on the mercury in the container. The height of the mercury in the tube is the atmospheric pressure. At sea level, the height of the mercury column is 760. mm. We say the pressure is 760. mm Hg.
The pressure of a gas can be measured with a manometer. If we had a closed end manometer with the stopcock of the flask closed, the mercury levels would be equal because both arms of the U-tube are evacuated. Once the stopcock is opened, the gas in the flask would push the Hg level down the left arm. The difference in the levels, Δh, would equal the gas pressure. The figure below shows two open end manometers. In the first figure, the pressure of the gas, Pgas is greater than atmospheric pressure, Patm, because the gas has pushed the mercury up in the left had side of the U-tube. In the second figure, Pgas is less than atmospheric pressure.
If Pgas is greater than Patm, add Δh to Patm.
If Pgas is less than Patm, subtract Δh to Patm.
In a later study guide, we will see that pressure is proportional to density. The constant, g, is the acceleration due to gravity and h is the height of the column.
We can calculate the height of a column based on the density and pressure of a liquid. For example, if water were used in a column, the column would be many times larger than that used for mercury.
We set the pressures equal to one another. The value of g will cancel out. The density of mercury is 13.6 g/mL and the density of water is 1.00 g/mL. The height of the mercury is 0.760 m. We solve for the height of the water column.
The water column would be much more than ten times longer than the mercury column. Any liquid can be used in a barometer, but one should be chosen as to keep the column as short as possible.
Worksheet: Gases and Gas Pressure
Exercises
Exercise 1. How many kPa is 1.22 atm?
Exercise 2. The pressure for a tire is 32.0 psi. What is this pressure in atm and in mm Hg?
Exercise 3. Vacuum pump oil has a density of 0.88 g/mL. Mercury has a density of 13.6 g/mL. What is the height of a barometer column based on vacuum pump oil if the atmospheric pressure is 745 torr?
Exercise 4.
Use the figure of the open end manometer below to determine the pressure of the gas in the flask if the atmospheric pressure is 763.4 mm Hg. Determine the pressure in mm Hg, torr, and atm.
Check Answers/Solutions to Exercises
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