Molar volume

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The molar volume of a substance, symbolized V_m, is the volume of one mole of the substance. The unit of the International System of Units is the cubic meter per mole:

m3 · mol^-1

A mol of any substance contains ${displaystyle 6,022140cdot 10^{23}}$ particles. In the case of molecular gaseous substances a mol contains NA molecules. Hence, taking into account the law of Avogadro, that a mol of any gaseous substance will always occupy the same volume (measured in the same conditions of pressure and temperature).

Experimentally and through the ideal gas law, it has been possible to verify that the volume occupied by one mole of any ideal gas under standard conditions (pressure of 10⁵ pascals (1 bar), Temperature 273.15 K, 0 °C) is 22.7 liters. If 1 Atm (101325 Pa) is used as pressure instead of 1 bar, this value changes to 22.4 L (22.3983 L to be more specific). This value is known as normal molar volume of a gas .

This value of the molar volume corresponds to the so-called ideal gases or perfect gases; ordinary gases are not perfect and their molar volume deviates slightly from this value. Thus the molar volumes of some gases are:

Carbon monoxide (CO) = 22.4 L
Sulphur dioxide (SO)₂= 21.9 L
Carbon dioxide (CO)₂) = 22.3 L

In the case of substances in a solid or liquid state, the molar volume is much smaller and differently for each substance. For example:

For liquid nitrogen (–210 °C) the molar volume is 34.6 cm3.
For liquid water (4 °C) the molar volume is 18,0 cm3.

Example

What volume occupy 30 grams of nitrogen gas, N₂, at zero degrees Celsius and a pressure atmosphere? (Nitrogen atomic mass: 14,0067).

Making the rule of three:

{displaystyle {begin{array}{rcl}2cdot 14{,}0067;{text{g N}}&longrightarrow &1;{text{mol}}=22{,}4;{text{L}}\30;{text{g N}}&longrightarrow &x;{text{L}}end{array}}}

Clearing $x$ :2

{displaystyle x={frac {22{,}4;{text{L}}cdot 30;{text{g N}}}{2cdot 14{,}0067;{text{g N}}}}}

Once the operations are done, the result is:

{displaystyle x=23,99;{text{L}}}

which is the volume occupied by 30 grams of nitrogen at zero degrees Celsius and one atmosphere pressure.

What is the mass of 50 liters of oxygen gas, or₂at zero degrees Celsius and a pressure atmosphere? (Oxygen atomic mass: 15,9994).

By rule of three we have to:

{displaystyle {begin{array}{rcl}1;{text{mol}}=22{,}4;{text{L}}&longrightarrow &2cdot 15{,}9994;{text{g O}}\50;{text{L}}&longrightarrow &x;{text{g O}}end{array}}}

solving for x:

{displaystyle x={frac {2cdot 15{,}9994;{text{g O}}cdot 50;{text{L}}}{22{,}4;{text{L}}}}}

Once the operations are done, the result is:

{displaystyle x=71{,}43;{text{g O}}}

which is the mass in grams of 50 liters of oxygen under normal conditions: zero degrees Celsius and one atmosphere pressure.

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