##### States & Matter: Gases & Liquid

A law in chemistry: equal volumes of all gases at the same temperature and pressure contain equal numbers of molecules—called also Avogadro's hypothesis.

The principle that equal volumes of all gases at the same temperature and pressure contain the same number of molecules. Thus, the molar volume of all ideal gases at 0° C and a pressure of 1 atm. is 22.4 liters.
Avogadro's law states that, "equal volumes of all gases, at the same temperature and pressure, have the same number of molecules".

For a given mass of an ideal gas, the volume and amount (moles) of the gas are directly proportional if the temperature and pressure are constant, which can be written as:
V / n = K
where:
V is the volume of the gas
n is the amount of substance of the gas (measured in moles).
k is a constant equal to RT/P, where R is the universal gas constant, T is the Kelvin
temperature, and P is the pressure. As temperature and pressure are constant, RT/P is also constant and represented as k. This is derived from the ideal gas law.

This law describes how, under the same condition of temperature and pressure, equal volumes of all gases contain the same number of molecules. For comparing the same substance under two different sets of conditions, the law can be usefully expressed as follows:
V1 / n1 = V2 / n2
The equation shows that, as the number of moles of gas increases, the volume of the gas also increases in proportion. Similarly, if the number of moles of gas is decreased, then the volume also decreases. Thus, the number of molecules or atoms in a specific volume of ideal gas is independent of their size or the molar mass of the gas.

#### Mathematical definition

Avogadro's law is stated mathematically as:

v / n = K

Where:

V is the volume of the gas(es).

n is the amount of substance of the gas.

k is a proportionality constant.

The most significant consequence of Avogadro's law is that the ideal gas constant has the same value for all gases. This means that:

P1.v1 / T1.n1 = p2.v2 = T2.n2 = constant

Where:

p is the pressure of the gas in the cell

T is the temperature in kelvin of the gas

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