Pressure, volume and temperature in balance. Explore the gas laws and the words that describe moving molecules.
These terms were extracted from Chemistry by OpenStax, eCampusOntario (© 2016 Rice University; adapted by BCcampus) which is licensed under a Creative Commons Attribution 4.0 International License.
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unit of pressure; 1 atm = 101,325 Pa
We are surrounded by an ocean of gas—the atmosphere—and many of the properties of gases are familiar to us from our daily activities.
(bar or b) unit of pressure; 1 bar = 100,000 Pa
Calculate the pressure in bar of 2520 moles of hydrogen gas stored at 27 °C in the 180-L storage tank of a modern hydrogen-powered car.
device used to measure atmospheric pressure
We can measure atmospheric pressure, the force exerted by the atmosphere on the earth’s surface, with a barometer (Figure 3).
pressure exerted by a fluid due to gravity
The pressure exerted by a fluid due to gravity is known as hydrostatic pressure, p:
device used to measure the pressure of a gas trapped in a container
A manometer is a device similar to a barometer that can be used to measure the pressure of a gas trapped in a container.
SI unit of pressure; 1 Pa = 1 N/m²
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.
unit of pressure common in the US
The sample of gas in Figure 5 has a volume of 15.0 mL at a pressure of 13.0 psi.
force exerted per unit area
In this chapter, we will examine the relationships between gas temperature, pressure, amount, and volume.
unit of pressure;
A typical barometric pressure in Kansas City is 740 torr.
temperature at which the volume of a gas would be zero according to Charles’s law.
Note that temperatures must be on the kelvin scale for any gas law calculations (0 on the kelvin scale and the lowest possible temperature is called absolute zero).
(also, Gay-Lussac’s law) pressure of a given number of moles of gas is directly proportional to its kelvin temperature when the volume is held constant
Because of this, the P–T relationship for gases is known as either Amontons’s law or Gay-Lussac’s law.
volume of a gas at constant temperature and pressure is proportional to the number of gas molecules
According to Avogadro’s law, equal volumes of gaseous N₂, H₂, and NH₃, at the same temperature and pressure, contain the same number of molecules.
volume of a given number of moles of gas held at constant temperature is inversely proportional to the pressure under which it is measured
It is summarized in the statement now known as Boyle’s law: The volume of a given amount of gas held at constant temperature is inversely proportional to the pressure under which it is measured.
volume of a given number of moles of gas is directly proportional to its kelvin temperature when the pressure is held constant
Charles’s law states that the volume of a given amount of gas is directly proportional to its temperature on the kelvin scale when the pressure is held constant.
hypothetical gas whose physical properties are perfectly described by the gas laws
Eventually, these individual laws were combined into a single equation—the ideal gas law—that relates gas quantities for gases and is quite accurate for low pressures and moderate temperatures.
constant derived from the ideal gas equation R = 0.08206 L atm mol⁻¹ K⁻¹ or 8.314 L kPa mol⁻¹ K⁻¹
where P is the pressure of a gas, V is its volume, n is the number of moles of the gas, T is its temperature on the kelvin scale, and R is a constant called the ideal gas constant or the universal gas constant.
relation between the pressure, volume, amount, and temperature of a gas under conditions derived by combination of the simple gas laws
Eventually, these individual laws were combined into a single equation—the ideal gas law—that relates gas quantities for gases and is quite accurate for low pressures and moderate temperatures.
273.15 K (0 °C) and 1 atm (101.325 kPa)
Chemists sometimes make comparisons against a standard temperature and pressure (STP) for reporting properties of gases: 273.15 K and 1 atm (101.325 kPa).
volume of 1 mole of gas at STP, approximately 22.4 L for gases behaving ideally
At STP, an ideal gas has a volume of about 22.4 L—this is referred to as the standard molar volume (Figure 10).
total pressure of a mixture of ideal gases is equal to the sum of the partial pressures of the component gases.
This observation is summarized by Dalton’s law of partial pressures: The total pressure of a mixture of ideal gases is equal to the sum of the partial pressures of the component gases:
concentration unit defined as the ratio of the molar amount of a mixture component to the total number of moles of all mixture components
where PA, XA, and nA are the partial pressure, mole fraction, and number of moles of gas A, respectively, and nTotal is the number of moles of all components in the mixture.
pressure exerted by an individual gas in a mixture
The pressure exerted by each individual gas in a mixture is called its partial pressure.
pressure exerted by water vapor in equilibrium with liquid water in a closed container at a specific temperature
The vapor pressure of water, which is the pressure exerted by water vapor in equilibrium with liquid water in a closed container, depends on the temperature (Figure 4).
movement of an atom or molecule from a region of relatively high concentration to one of relatively low concentration (discussed in this chapter with regard to gaseous species, but applicable to species in any phase)
In a closed environment, diffusion will ultimately result in equal concentrations of gas throughout, as depicted in Figure 1.
transfer of gaseous atoms or molecules from a container to a vacuum through very small openings
A process involving movement of gaseous species similar to diffusion is effusion, the escape of gas molecules through a tiny hole such as a pinhole in a balloon into a vacuum (Figure 2).
rates of diffusion and effusion of gases are inversely proportional to the square roots of their molecular masses
In 1832, Thomas Graham studied the rates of effusion of different gases and formulated Graham’s law of effusion.
average distance a molecule travels between collisions
The mean free path is the average distance a molecule travels between collisions.
amount of gas diffusing through a given area over a given time
We are often interested in the rate of diffusion, the amount of gas passing through some area per unit time:
theory based on simple principles and assumptions that effectively explains ideal gas behavior
An ideal gas is a hypothetical construct that may be used along with kinetic molecular theory to effectively explain the gas laws as will be described in a later module of this chapter.
measure of average velocity for a group of particles calculated as the square root of the average squared velocity
In the KMT, the root mean square velocity of a particle, urms, is defined as the square root of the average of the squares of the velocities with n = the number of particles:
ratio of the experimentally measured molar volume for a gas to its molar volume as computed from the ideal gas equation
This ratio is called the compressibility factor (Z) with:
modified version of the ideal gas equation containing additional terms to account for non-ideal gas behavior
The van der Waals equation improves upon the ideal gas law by adding two terms: one to account for the volume of the gas molecules and another for the attractive forces between them.