To calculate the volume of gases in a mixture, you can use the ideal gas law in conjunction with the mole fraction of each gas present.

The ideal gas law states that the volume of a gas is directly proportional to the number of moles of that gas and the temperature, while being inversely proportional to the pressure. This relationship is mathematically expressed as:

where:

• $P$ represents the pressure,
• $V$ denotes the volume,
• $n$ is the number of moles,
• $R$ is the ideal gas constant, and
• $T$ is the absolute temperature.

To determine the volume of a specific gas in a mixture, you first need to calculate the mole fraction of that gas. The mole fraction is defined as the ratio of the number of moles of a particular gas to the total number of moles of all gases in the mixture. For instance, if a mixture contains $2$ moles of gas A and $3$ moles of gas B, the mole fraction of gas A can be calculated as follows:

Once you have the mole fraction, you can apply the ideal gas law to find the volume of the specific gas. If you know the total volume of the gas mixture, you can multiply this total volume by the mole fraction to determine the volume of the individual gas. For example, if the total volume of the mixture is $10$ liters, the volume of gas A would be calculated as:

It is important to note that this method assumes ideal gas behavior. While this assumption is typically valid under many conditions, real gases can deviate from ideal behavior, particularly at high pressures or low temperatures.