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. |

**"The molar volume of an element is the volume occupied by 1 mole (6 $\times$ 10**

^{23}atoms) of the element."It is very dependent on atomic radius and structure (packing). Suppose the relative atomic mass of the element is A

_{r}and its density is $\rho$ g cm^{-3}.- 6 $\times$ 10
^{23}atoms of the element have a mass of A_{r}g. - Therefore 6 $\times$ 10
^{23}atoms of the element have a volume of $\frac{A_{r}}{\rho}$ cm^{3}.

**"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

Where

- V
_{m}is the molar volume - MW
_{t}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.

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.

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

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

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

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

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.

**Quantity symbol**: $V_{m}$

**SI unit is cubic meter per mole (m**

^{3}/mol).**Definition:**Volume of a substance divided by its amount of substance. The units of molar volume is m

^{3}/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.

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.

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

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.

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

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 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 $\times$ 10

Molar volume of some gases are listed below.

^{23}particles of gas.Molar volume of some gases are listed below.

Gas | Molecular Formula | GMW (in g) | No.of Moles | Molar Volume dm^{3} or l | No.of moles in 1 mole |
---|---|---|---|---|---|

Hydrogen | H_{2} | 2 | 1 | 22.4 | 6.023 $\times$ 10^{23} |

Oxygen | O_{2} | 32 | 1 | 22.4 | 6.023 $\times$ 10^{23} |

Nitrogen | N_{2} | 28 | 1 | 22.4 | 6.023 $\times$ 10^{23} |

Chlorine | Cl_{2} | 71 | 1 | 22.4 | 6.023 $\times$ 10^{23} |

Carbon dioxide | CO_{2} | 44 | 1 | 22.4 | 6.023 $\times$ 10^{23} |

Nitrogen dioxide | NO_{2} | 46 | 1 | 22.4 | 6.023 $\times$ 10^{23} |

Ammonia | NH_{3} | 17 | 1 | 22.4 | 6.023 $\times$ 10^{23} |

Methane | CH_{4} | 16 | 1 | 22.4 | 6.023 $\times$ 10^{23} |

Sulfur dioxide | SO_{2} | 64 | 1 | 22.4 | 6.023 $\times$ 10^{23} |

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

Molar volume for certain gases are listed below. Thus molar volume of water at 1atm and 298K is

**0.018 L mol**no matter how little or how much water is present.^{-1}S.No |
Gases |
Molar volume (m^{3}/mol) |

1 | Molar volume of hydrogen (or) Molar volume of hydrogen gas (or) Molar volume of H _{2} |
22.4 |

2 |
Molar volume of oxygen |
22.4 |

3 |
Molar volume of air | 22.414 |

4 |
Molar volume of CO_{2} (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 |

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.

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.

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.

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 (CO

_{2}) = 44

Amount of CO

_{2 }= $\frac{mass}{molar\ mass}$

= $\frac{4.4g}{44\ gmol^{-1}}$ = 0.1 mol

1 mol CO

_{2}at rtp has a volume of 24 liters

0.1 mol CO

_{2}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}m

^{3}

Molar volume = 22.4 $\times$ 10

^{-3}m

^{3}

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

= 7.102 $\times$ 10

^{4}

Thus the required molar volume to atomic volume is 7.102 $\times$ 10

^{4}