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Avogadro's principle states that equal volumes of different gases contain the same number of molecules. Doubling the number of molecules present doubles the volume (at constant pressure). Also according to the laws doubling the number of molecules present will double the pressure (at constant volume).

One mole of an ideal gas occupies the same volume under the same conditions of temperature and pressure. This assertion leads to the idea of the molar volume, the volume per mole of any gas under stated conditions. The numerical value of the molar volume depends on the temperature and pressure of a gas.

What is Molar Volume?

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"The molar volume of an element is the volume occupied by 1 mole (6 $\times$ 1023 atoms) of the element."

It is very dependent on atomic radius and structure (packing). Suppose the relative atomic mass of the element is Ar and its density is $\rho$ g cm-3.
  • 6 $\times$ 1023 atoms of the element have a mass of Ar g.
  • Therefore 6 $\times$ 1023 atoms of the element have a volume of $\frac{A_{r}}{\rho}$ cm3.

Molar Volume Definition

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The molar volume is defined as "the volume occupied by one mole of a material and is obtained by dividing the molecular weight of a material by its density."

$V_{m} = \frac{MW_{t}}{\rho}$

Where
  • Vm is the molar volume
  • MWt is the molecular weight of the substance
  • $\rho$ is the true density of the material

Since the density of a material is sensitive to both the volume occupied by the atoms and to their mass (atomic weight), molar volume is often used to compare the behavior of glasses. In many cases, seemingly anomalous behavior in density is readily explained by consideration of the molar volume.

Molar Volume Formula

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Knowing the density and molar mass of a substance we can readily compute its molar volume, that is the volume occupied by one mole of a substance.

$V_{m} = \frac{molar\ mass\ [g\ mol^{-1}]}{density\ [g\ cm^{-1}]}$

$V_{m} = \frac{MW_{t}}{\rho}$

$= molar\ volume\ (cm^{3} mol^{-1})$

The idea of molar volume allows us to calculate the amount in moles from the volume of a gas, and vice versa, provided we know the temperature and pressure of a gas.

Molar Volume Units

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Quantity symbol: $V_{m}$

SI unit is cubic meter per mole (m3/mol).

Definition: Volume of a substance divided by its amount of substance. The units of molar volume is m3/mol.

$V_{m} = \frac{V}{n}$

  • The word molar means "divided by amount of substance."
  • For a mixture this term is often called "mean molar volume."
  • The amagat should not be used to express molar volume or reciprocal molar volumes.

Molar Volume of a Gas

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The molar volume of gases is the number of liters occupied by 1 mole of the gas. Determining the molar volume of a gas is dividing the volume in liters by the number of moles gives the molar volume in liters per mole.

Molar volume of a gas at STP (standard temperature, pressure and atmosphere) is calculated below.

$\frac{V}{n} = \frac{RT}{P} = \frac{0.0821\ L\ atm\ mol^{-1}K^{-1} \times 273K}{1.00\ atm}$

$= 22.4\ L\ mol^{-1}$

The literature value of the molar volume of a gas is 22.4 L mol-1.

This indicates that 1 mole of an ideal gas at STP has a volume of 22.4 liters, a fact that is useful in stoichiometric calculations.

Molar Volume at STP

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Molar volume of a gas is defined as the volumes occupied by one mole of a gas. Thus the molar volume is also the volume occupied by 6.02 $\times$ 1023 particles of gas.

Molar volume of some gases are listed below.

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 6.023 $\times$ 1023
Oxygen O2 32 1 22.4 6.023 $\times$ 1023
Nitrogen N2 28 1 22.4 6.023 $\times$ 1023
Chlorine Cl2 71 1 22.4 6.023 $\times$ 1023
Carbon dioxide CO2 44 1 22.4 6.023 $\times$ 1023
Nitrogen dioxide NO2 46 1 22.4 6.023 $\times$ 1023
Ammonia NH3 17 1 22.4 6.023 $\times$ 1023
Methane CH4 16 1 22.4 6.023 $\times$ 1023
Sulfur dioxide SO2 64 1 22.4 6.023 $\times$ 1023

Molar Volume of Water

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The extensive properties of one component system at a constant temperature and pressure depend only on the amount of the system present. For example, the volume of water depends on the quantity of water present. If the volume is expressed as a molar quantity however it is an intensive property.

Thus molar volume of water at 1atm and 298K is 0.018 L mol-1 no matter how little or how much water is present.

Molar Volume Table

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Molar volume for certain gases are listed below.

S.No
Gases
Molar volume (m3/mol)
1 Molar volume of hydrogen (or)
Molar volume of hydrogen gas (or)
Molar volume of H2
22.4
2
Molar volume of oxygen
22.4
3
Molar volume of air 22.414
4
Molar volume of CO2 (or)
Molar volume of carbon dioxide
22.4
5
Molar volume of an ideal gas
22.4
6 Molar volume of ethanol 58.0
7
Molar volume of nitrogen 22.414

Partial Molar Volume

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The partial molar volume of a substance can be defined as the change in volume when one mole of the substance is added to a very large volume of the mixture. Mathematically it is expressed as

$\bar{V_{A}} = (\frac{\partial V}{\partial n_{A}})_{P, T, n_{B}}$

The partial molar volume of water at 298K is 0.018L and the partial molar volume of NaCl is 0.25L.

Standard Molar Volume

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For an ideal gas the standard molar volume is the volume that is occupied by one mole of substance (in gaseous form) at standard temperature temperature and pressure and is directly related to the universal gas constant R in the ideal gas law.

Apparent Molar Volume

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The apparent molar volume is a quantity that can be obtained from the experimental values of density of the solution. However the partial molar volumes cannot be determined directly from experimental data, although can be related to the corresponding apparent molar volumes.

Molar Volume Problems

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Finding molar volume is the volume occupied by one mole of any gas at a particular temperature and pressure. Example problems are given to calculate molar volume.

Solved Examples

Question 1: Calculate the volume occupied by 4.4g of carbon dioxide at room temperature and pressure.
Solution:
 
Relative formula mass (CO2) = 44

Amount of CO2 = $\frac{mass}{molar\ mass}$
= $\frac{4.4g}{44\ gmol^{-1}}$ = 0.1 mol

1 mol CO2 at rtp has a volume of 24 liters
0.1 mol CO2 at rtp has a volume of 2.4 liters.
 

Question 2: One mole of an ideal gas at NTP occupies 22.4 liters, which is called molar volume. What is the ratio of molar volume to atomic volume of hydrogen?
Solution:
 
Atomic volume = ($\frac{4}{3} \pi r^{3}$)N
Where N is Avogadro's number = 3.154 $\times$ 10-7 m3
Molar volume = 22.4 $\times$ 10-3 m3

$\frac{Molar\ volume}{Atomic\ volume} = \frac{22.4 \times 10^{-3}}{3.154 \times 10^{-7}}$
= 7.102 $\times$ 104

Thus the required molar volume to atomic volume is 7.102 $\times$ 104