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Toggle**Gas laws** describe the general behavior of gases. When conditions are normal, all gases exhibit similar behavior. However, even minor changes in physical conditions such as pressure, temperature, or volume cause a deviation. Thus, gas laws define relationships among the temperature, pressure, and volume of a gas. The gas laws are:

**Boyle’s law****Charle’s law****Gay-Lussac’s law****Avogadro’s law****Combined gas law**

## Boyle’s Law

Boyle’s law, given by Robert Boyle in 1662, describes the pressure-volume relationship of gases at a constant temperature. Boyle’s law states that “**At a constant temperature, the volume of a given mass of a gas is inversely proportional to its pressure**“.

**V ∝ 1/P** (At a constant temperature for a given mass of gas)

**V = k × 1/P**, where V is the volume, P is the pressure and k is the proportionality constant

**PV = k** = a constant

Thus, Boyle’s law can be also stated as “**the product of the pressure and volume of the given mass of gas is constant at a constant temperature**“.

If P_{1}, V_{1} are the initial pressure and volume of a given sample of gas at temperature T K and P_{2}, V_{2} the changed pressure and volume at the same temperature, then

**P _{1} V_{1} = P_{2} V_{2}**

Thus, the volume of a gas corresponding to any changed pressure can be calculated at a constant temperature using the above Boyle’s law equation.

## Charle’s Law

Charle’s law, given by Jacques Charles in 1787, describes the relationship between volume and temperature of gases at a constant pressure. Charle’s law states that “**At constant pressure, the volume of the given mass of a gas is directly proportional to the absolute temperature of the gas**“. This law can be expressed mathematically as:

**V ∝ T** (At a constant pressure for a given mass of gas)

**V = k × T**, where V is the volume, T is the pressure, and k is the proportionality constant

Thus, the volume of a gas corresponding to any changed temperature can be calculated at a constant pressure using the above Charle’s law equation.

## Gay-Lussac’s law

Gay-Lussac’s law, given by Joseph Gay Lussac in 1802, describes a general relation between

the temperature and pressure of a gas at constant volume. Gay-Lussac’s law states that “**At constant volume, the pressure of a given mass of gas is directly proportional to the absolute temperature of** **the gas**“.

**P ∝ T** (At a constant volume for a given mass of gas)

**P =** **k × T**, where P is the pressure, T is temperature, and k is the proportionality constant

Thus, the pressure of a gas corresponding to any changed temperature can be calculated at a constant volume using the above Gay-Lussac’s law equation.

## Avogadro’s Law

Avogadro’s law, given by Amadeo Avogadro in 1811, describes the relationship between volume and the number of molecules of gas at constant temperature and pressure. Avogadro’s law states that “**Under similar conditions of temperature and pressure, equal volumes of all gases contain an equal number of molecules**“.

**V ∝ n**^{,} (At constant temperature and pressure)

Number of moles, n = Number of molecules / 6.023 **×** 10^{23}

or, n = **n**^{,} / N

or, n ∝ n^{,}

**V ∝ n** i.e. volumes of gases at constant temperature and pressure are directly proportional to their number of moles.

**V = k × n**, where V is the volume of gas, n is the number of moles, and k is the proportionality constant

## Combined gas law

Combined gas, the combination of Boyle’s law and Charles’ law describes the effect of changes in pressure and temperature on the volume of a gas. The combined law states that “**For a given mass of gas, the volume is directly proportional to the absolute temperature while inversely proportional to the pressure.**

From Boyle’s law, **V ∝ 1/P**

From Charle’s law, **V ∝ T**

On combining both,

**V ∝ T/P**

**V = k × T/P**

This equation is the required combined gas law equation.

## Gas laws Video

## References

- Arun Bahl, B. S. Bahl & G. D. Tuli,
*Essentials of Physical Chemistry*, S. Chand and Company Ltd., New Delhi, 2012. - Castka, Joseph F.; Metcalfe, H. Clark; Davis, Raymond E.; Williams, John E. (2002).
*Modern Chemistry*. Holt, Rinehart, and Winston. - J. N. Gurtu and A. Gurtu,
*Advanced Physical Chemistry Experiments*, (6th Edition).