Volume of Gas

The molar volume of a gas

A mol of a substance is defined as \(6,022\cdot 10^{23}\) units of that substance (such as atoms, molecules, or ions). This big number is known as Avogadro's number. For example, 1 mol of carbon molecules will have \(6,022\cdot 10^{23}\) molecules of carbon.

The volume occupied by one mole of ANY gas at room temperature and atmospheric pressure is equal to \(24\,\,\mathrm{ cm}^3\). This volume is called the molar volume of gases as it represents the volume of 1 mol for any gas. In general, we can say that the molar volume of a gas is \(24\,\,\mathrm{ dm}^3/\mathrm{\text{mol}}\). Using this, we can calculate the volume of any gas as follows:

\[\text{volume}=\text{mol}\times\text{molar volume.}\]

Where mol means how many moles we have of the gas, and the molar volume is constant and equal to \(24\,\,\mathrm{ dm}^3/\mathrm{\text{mol}}\) .

Fig. 2: One mole of any gas will have the same volume at room temperature and atmospheric Pressure.

As you can see from the image above, one mole of any gas will have a volume of \(24\,\,\mathrm{dm}^3\). These volumes of gas will have different masses between different gases, though, as the molecular weight differs from gas to gas.

The above equation holds true only at room temperature and atmospheric pressure. But what if the pressure and temperature change as well? The volume of a gas is affected by changes in pressure and temperature. Let us look into their relationship.

Now let's study the effect of a change in pressure on the volume of a gas.

Relationship between pressure and volume of a gas

Fig. 3: As the volume of the gas decreases the pressure increases. This is because the frequency and the impact of the collisions between the gas molecules and the walls of the container increase.

Now consider a fixed amount of gas kept at a constant temperature. Decreasing the volume of the gas will cause the gas molecules to move closer to one another. This will increase the collisions between the molecules and the walls of the container. This causes an increase in the pressure of the gas. Let's look at the mathematical equation for this relation, called Boyle’s Law.

Formula describing the volume of a gas

Boyle's law gives the relation between the pressure and the volume of a gas at a constant temperature.

This relation can also be mathematically depicted as follows:

\[pV=\text{constant},\]

Where \(p\) is the pressure in pascals and \(V\) is the volume in \(\mathrm{m}^3\). In words, Boyle's law reads

\[\text{pressure}\times \text{volume}=\text{constant}.\]

The equation above is true only if the temperature and amount of gas are constant. It can also be used while comparing the same gas under different conditions, 1 and 2:

\[p_1v_1=p_2V_2,\]

or in words:

\[\text{initial pressure}\times \text{initial volume}=\text{final pressure}\times \text{final volume}.\]

To summarize, for a fixed amount of gas (in mol) at a constant temperature, the product of pressure and volume is constant.

Examples of calculations with the volume of a gas

This brings us to the end of the article. Let's look at what we've learned so far.