## Gases

A gas is a state of matter in which substances retain no independent shape nor volume and are compressible. Four variables are significant when it comes to gases: pressure (P), volume (V), temperature (T), and amount of gas (n).

# Measuring Gas Pressures

Pressure is defined as force exerted per unit area. Several tools can be used to measure pressure. A barometer is an instrument used to measure atmospheric pressure. It looks like this. The column contains a liquid, usually mercury:

A Barometer: The height of the liquid column is the pressure reading.

A manometer is another instrument for measuring the pressure of gases. In an open end manometer, the difference in height of the manometer liquid subtracted (if the side open to the atmosphere is lower) or added (if the  side open to the atmosphere is higher) from atmospheric pressure is the gas pressure. In a closed end (sealed from the atmosphere) manometer, the difference in height of the manometer liquid is the gas pressure. A manometer generically looks like this:

A generic manometer.

# Units of Pressure

Mercury is usually used in barometers and manometers due to its high density (13.5961 g/mL). One millimeter rise in mercury corresponds to a pressure unit of one torr or one mL Hg. Atmospheric pressure is typically 760torr, so one atm (atmospheric pressure unit) is 760 torr. The Pascal (Pa) is the official SI unit of pressure (101325Pa is 1 atm). Pounds per square inch (psi) is a unit of pressure based on the English System: approximately 14.7 psi is one atm.

# Kinetic Molecular Theory

Kinetic Molecular Theory defines ideal gases. The theory postulates the following about ideal gases:

• The gas consists of volumeless particles, all with non-zero mass (so-called point masses).
• The number of molecules is large such that statistical treatment can be applied.
• These molecules are in constant, random motion. The rapidly moving particles constantly collide elastically with the walls of the container and each other. The speed of the molecules corresponds to the temperature.
• The interactions among particles are negligible. They exert no forces on one another except during collisions.
• The total volume of the individual gas molecules added up is negligible compared to the volume of the container.

A gas tends to behave more ideally under low pressures and high temperatures.

The ideal gas law states that

PV=nRT

where: pressure (P), volume (V), temperature (T), and amount of gas (n).

R is the “ideal gas constant.” Its value depends upon which units are used:

Values of R
Units
8.314 472(15) J K−1 mol−1
1.985 8775(34) cal K−1 mol−1
8.314 472(15) × 107 erg K−1 mol−1
8.314 472(15) L kPa K−1 mol−1
8.314 472(15) m3 Pa K−1 mol−1
8.314 472(15) cm3 MPa K−1 mol−1
8.314 472 × 10−5 m3 bar K−1 mol−1
8.205 746 × 10−5 m3 atm K−1 mol−1
82.05 746 cm3 atm K−1 mol−1
8.314 472 × 10−2 L  bar K−1 mol−1
0.082 057 46(14) L atm K−1 mol−1
62.363 67(11) L mmHg K−1 mol−1
62.363 67(11) L Torr K−1 mol−1
6.132 440(10) ft lbf K−1 g-mol−1
1545.349(3) ft lbf °R−1 lb-mol−1
10.731 59(2) ft3 psi °R−1 lb-mol−1
0.730 2413(12) ft3 atm °R−1 lb-mol−1
998.9701(17) ft3 mmHg K−1 lb-mol−1
1.986 Btu lb-mol−1 °R−1

# Boyle’s Law

Boyle’s law describes that absolute pressure  and and the volume of a gas are inversely proportional if the temperature and amount of gas is kept constant within a closed system:

Boyle's Law

# Charle’s Law

Charle’s Law states that volume is directly proportional to absolute temperature given constant amount of gas and pressure:

Charle's Law

# Gay-Lussac’s Law

Gay-Lussac’s Law states that absolute pressure is directly proportional to absolute temperature given constant amount of gas and volume:

Gay-Lussac's Law

Avogadro’s Law states that the amount of gas is directly proportional to the gas volume given constant temperature and pressure:

All four of the previous laws are self-evident in the ideal gas law.

# Dalton’s Law of Partial Pressures

Dalton’s Law of Partial Pressures states that the total pressure exerted by a gaseous mixture is equal to the sum of the partial pressures of each individual component in a gas mixture:

where p is the partial pressure of an individual gas component in the gas mixture.

# Graham’s Law of Diffusion and Effusion

Graham’s Law states that the rate of effusion or diffusion of a gas is inversely proportional to the square root of the molar mass of its particles. Diffusion is the process by which gas particles spread in space, for instance in a room or bottle. Effusion is the process in which individual gas molecules flow through a very tiny hole without collisions between molecules.

Graham's Law