### Gas Laws

The gas laws are a set of laws that describe the relationship between thermodynamic temperature (T), pressure (P) and volume (V) of gases. It is a loose collection of rules developed between the late Renaissance and early 19th century.

Three earlier gas laws – Boyle’s law (1662), Charles’s law (1787-1802), and Gay-Lussac’s law (1809) – were combined to form the combined gas law: $\frac {P_1V_1} {T_1} = \frac {P_2V_2} {T_2}$

which with the addition of Avogadro’s law later gave way to the ideal gas law: $\qquad\qquad P V = n R T$

where

(The above units are the SI ones. The law works equally well with any consistent set of units, provided that the temperature scale is such that it is zero at absolute zero.)

Other important gas laws include Dalton’s law of partial pressures. The kinetic theory of gasesGraham’s law of effusionand root mean square velocity all explain how individual molecules in a gas act and their relation to pressure, volume, and temperature.

A gas that obeys these gas laws exactly is known as an ideal gas (or perfect gas). An ideal gas does not exist; however, some gases follow the laws more closely than others given standard conditions.

Italy 1811

(1776-1856)

## Boyles Law

England 1662

Robert Boyle (1627-91)

## Charles's Law

1787 France

Jacques Charles (1746-1823)

## Lussac's Law

1809 France

Joseph Louis
Gay-Lussac
(1778-1850)

Equal volumes of all gases at the same temperature and pressure contain the same number of molecules.

Avogadro’s law is one of the gas laws. The law is named after Amedeo Avogadro, who in 1811 hypothesized that equal volumes of gases, at the same temperature and pressure, contain the same number of particles, or molecules. Thus, the number of molecules in a specific volume of gas is independent of the size or mass of the gas molecules

The minor aspect of the law can be stated mathematically as:

.

-where:

• V is the volume of the gas.
• n is the number of moles in the gas.
• a is a constant.

However, this above equation is just a trivial one, which is valid for all homogeneous substances, including homogeneous liquids and solids. This relation is easy to deduce, its validity was assumed before Avogadro’s work.

The most important consequence of Avogadro’s law is the following: The ideal gas constant has the same value for all gases. This means that the constant const of

has the same value for all gases, independent of the size or mass of the gas molecules. This statement is nontrivial, and it embodies Avogadro’s ingenious insight in the nature of ideal gases. It took decades to prove Avogadro’s law based on the kinetic theory of gases.

One mole of an ideal gas occupies 22.4 liters (dm3) at STP. This is often referred to as the molar volume of an ideal gas. Real gases may deviate from this value.

The number of molecules in one mole is called Avogadro’s number: approximately 6.022×1023 particles per mole.

Avogadro’s law, together with the combined gas law, forms the ideal gas law.

### Boyles Law

The volume of a given mass of gas at a constant temperature is inversely proportional to its pressure.

If the pressure of a gas is doubled, then its volume halved. In the equation form pV = constant, or

p1V1 = p2V2   where the subscripts 1 and 2 refer to the values of the pressure and volume at any two readings during the experiment.

### Charles’s Law

The volume of a given mass of gas at a constant pressure is directly proportional to its absolute temperature.

If the temperature of a gas is doubled, then the volume is doubled. In the equation form, V/T = constant, or V1 /T1 = V2 /T2  where V is the volume of the gas at a temperature T1 (in kelvin) and the V2 new volume at a new temperature T2.

### Lussac’s Law

Volumes of gases which combine or which are produced in chemical reactions are always in the ratio of small whole numbers.
Gay-Lussac’s law states that the ratio between the combining volumes of gases and the product, if gasous, can be expressed in small whole numbers, which Gay-Lussac discovered in 1809. In 1811Avogadro used Gay-Lussac’s data to form Avogadro’s hypothesiswhich later gave way to modern gas stoichiometry.

The other law, discovered in 1802, states that the pressure of a fixed amount of gas at fixed volume is directly proportional to its temperature in kelvins. It is expressed mathematically as: $\frac{P}{T}=k$

-Where:

This law holds true because temperature is a measure of the average kinetic energy of a substance; as the kinetic energy of a gas increases, its particles collide with the container walls more rapidly, thereby exerting increased pressure.

For comparing the same substance under two different sets of conditions, the law can be written as: $\frac{P_1}{T_1}=\frac{P_2}{T_2} \qquad \mathrm{or} \qquad {P_1}{T_2}={P_2}{T_1}$

Charles’s Law was also known as the Law of Charles and Gay-Lussac, because Charles used some of Gay-Lussac’s data to formulate his law. However, in recent years the term has fallen out of favor since Gay-Lussac has the second but related law presented here attributed to him. This related form of Gay-Lussac’s Law, Charles’s Law, and Boyle’s law form the combined gas law. The three gas laws in combination with Avogadro’s Law can be generalized by the ideal gas law.