Molar Volume

Molar volume and molar volume of a gas is an extension of Avogadro law, which state that,"At any given temperature and pressure equal volume of any gases would contain equal number of moles or molecules".

According to Avogadro, the volumes of the two gases at fixed temperature (T) and pressure (P), the number of moles is found to be equal. Molar gas volume plays an important role in determining degree of salvation, etc.

One mole of any gas at a given temperature and pressure has same fixed volume and is better known as its Molar gas volume.
In order to to compare the molar volume of gases, chemists use a fixed reference of temperature and pressure. This is called as "Standard temperature and pressure (abbreviated as S.T.P)".

The standard temperature used is 273 Kelvin or 0^o C and the standard pressure is 1 atmospheres (760 mm Hg). At STP we find experimentally that one mole of any gas occupies a volume of 22.4 liters. The equation can be written as

1 mole of a gas at STP = 22.4 liters of a gas

According to the ideal gas law, and the three simple gas laws

1. Boyle's Law : V ∞ 1/P (T, n constant)
2. Charle's Law : V ∞ T (n, P constant)
3. Avogadro's Law : V ∞ n ( P, T constant)

These three laws can be combined into a single more general law

V ∞ n T / P

This is called as Universal Gas Law. It is also called Ideal Gas Law as it applies to all gases which exhibit ideal behavior. i.e, obey the gas laws perfectly. The ideal gas law may be stated as

"The volume of a given amount of gas is directly proportional to the number of moles of gas, directly proportional to the temperature and inversely proportional to the pressure."

Introducing the proportionality constant R in the expression (1), we can write

V = R n T/P

P V = n R T

Molar volume is considered to be the volume occupied by one mole of any gas at a given pressure and temperature.
This is denoted by V_m.
The Molar volume unit is found to be litre per mole or milliliter per mole.
The Molar volume determination of any substance is invariably depending on temperature and pressure.
As per the Avogadro law, "at constant temperature and pressure equal volumes of any gas would contain equal number of molecules." This leads to the assumption that equal number of molecules of any gas, should occupy the same volume, provided there is constant temperature and pressure.

Example of oxygen

Mass of 1 liter of oxygen at STP = 1.59 g

Mass of 1 mole of oxygen = 32 g

Volume : Mass

1 liter : 1. 59 g

x : 32 g

'x' = (32 / 1.59) litres = 20.126 litres

The table given below provides the relationship existing between Gram Molecular Weight (GMW), moles, the molar volume and the number of particles of gases at standard temperature pressure.

Gas	Molecular Formula	GMW (in g)	No.of Moles	Molar Volume dm3 or l	No.of moles in 1 mole
Hydrogen	H2	2	1	22.4	6.023x 1023
Oxygen	O2	32	1	22.4	6.023x 1023
Nitrogen	N2	28	1	22.4	6.023x 1023
Chlorine	Cl2	71	1	22.4	6.023x 1023
Carbon dioxide	CO2	44	1	22.4	6.023x 1023
Nitrogen dioxide	NO2	46	1	22.4	6.023x 1023
Ammonia	NH3	17	1	22.4	6.023x 1023
Methane	CH4	16	1	22.4	6.023x 1023
Sulphur dioxide	SO2	64	1	22.4	6.023x 1023

Standard molar volume of a gas is the volume occupied by 1 mole of any gas at 273 K and 1 atmospheric pressure (STP). It is equal to 22.4 liters of 22,400 ml. It is the same for all gases.

S.T.P. = Standard Temperature and Pressure

Standard Temperature = 0^oC or 273 K

Standard Pressure = 1 atm or 760 mm of mercury

When a liquid is present in a mixture, the volume of one component depends upon the molecules that are surrounding that particular liquid. Partial molar volume is the volume contributed by any particular component in the mixture. So, if A and B are present in a mixture, the partial molar volume will be given both with respect to A and with respect to B.

Thus, Partial molar volume of A would be: Change in volume of the mixture, per mole of A added to it. This can be best represented with the help of one solvent, say water, added to another solvent, like Benzene or ether.
Partial molar volume of B would be: Change in the volume of the mixture per mole of B added to it. We know that volume occupied by one mole of a gas is its molar volume. This applies to a liquid and a solid too. So, Molar volume of water, a liquid is the volume occupied by one mole of water, in any form. So, 1 mole of water occupies 18 grams. Since density of water is almost equal to 1, we take the grams of water as volume of water. So, Molar volume, or the volume occupied by one mole of water would be 18 milliliters.

Now, what would be the partial volume of water in a mixture?
To give an example for partial molar volume, let us take two solvents

• Water
• Ethanol

When we add one mole of water to 100 liters of water already present in a vessel, the volume of the liquid will increase by 18 ml. So, this shows that water has a partial molar volume of 18ml/mol in that mixture.

When we add the same one mole of water to 1000ml of Ethanol, instead of 18 ml increase, the volume of the mixture was raised only by 14 ml. So, the partial molar volume depends upon the degree of solvation or the number of moles of surrounding water particles per one mole of water particle. Below are the solved examples on calculating molar volume -