Calculating gas volumes using moles

In a nutshell

The molar volume $$(V_m)$$ of a gas can be used to determine either the amount of gas in moles or the volume a gas occupies when at least one of the variables is given.

Equations

$$volume\ of\ gas\ = molar\ volume\ \times\ amount$$

​

$$amount\ =\frac{volume\ of\ gas}{molar\ volume}$$​​​

Variable units

Gas volumes 

Avogadro's law states that equal volumes of gas at the same temperature and pressure have the same number of molecules. Therefore, one mole of gas at a given temperature and pressure occupies the same volume regardless of the gas composition.

The volume occupied by a gas depends on the:

• Amount of gas present in moles
• Temperature
• Pressure

Molar gas volume 

The molar volume ($$V_m$$) is the volume one mole of gas occupies at room temperature and pressure. 

$$V_m\ =\ 24 \, dm^3/mol\ or\ 24 \, 000 \, cm^3/mol$$​ 

Converting between $$\pmb{cm^3}$$​ and $$\pmb{dm^3}$$​​

To convert between $$cm^3$$​ and $$dm^3$$, multiply or divide by a thousand. 

$$volume\ (cm^3)\ =\ \frac{volume\ (dm^3)}{1000}$$​​

​$$volume\ (cm^3)\ =\ volume\ (dm^3)\ \times\ 1000$$​​

Calculating gas volume

To calculate the volume of gas the amount of gas in moles must be known.

​$$volume\ of\ gas\ =\ molar\ volume\ \times\ amount$$​​

Procedure

Example

Calculate the gas volume of $$2.5\ mol$$ $$CO_2$$ in $$dm^3$$​. 

First write the equation that will be used:

​$$\ volume\ of\ gas\ = \ molar\ volume\ \times\ amount$$​​

Work out the value for the molar volume depending on the units required ($$dm^3$$):

$$Molar\ volume\ =\ 24\ dm^3/mol$$​​

Use this value along with the number of moles ($$2.5 \ mol$$) to calculate the volume of gas:

$$Volume \ of \ gas\ =\ 24 \ dm^3/mol \times\ 2.5 \, mol = 60 \, dm^3$$​​

At room temperature and pressure, $$2.5 \, moles$$ takes up $$\underline{60 \, dm^3}$$ of gas volume. 

Calculating amount of gas

To calculate the amount of moles in a gas, the volume of the gas has to be known. From this the volume of gas can be divided by the molar volume to determine the amount of gas in $$(mol)$$.​

​$$amount\ = \frac{volume\ of\ gas}{molar\ volume}$$

​

Example

Nitrogen is stored in a $$100 \, dm^3$$ tank at room temperature and pressure. How many moles of nitrogen are present in the tank?

First write the equation that will be used:

$$amount\ = \frac{volume\ of\ gas}{molar\ volume}$$​​

Work out the total volume:

$$Total\ volume\ =\ 100 \, dm^3$$​​

Based on the units of the volume of gas ($$dm^3$$), work out the value for the molar volume:

$$Molar\ volume\ =\ 24 \, dm^3/mol$$

Use the molar volume and total volume of gas to calculate the number of moles:

​​

$$\frac{100 \, dm^3}{24 \ dm^3/mol}\ =\ 4.167 \,mol$$

$$\underline{4.167 \, moles}$$​ fit in a $$100\ dm^3$$ tank at room temperature and pressure.