The volumes of gases involved in reactions can be calculated using Avogadro’s Law:
Avogadro’s Law – equal volumes of all gases at the same temperature and pressure contain the same number of molecules.
This means that if we have two containers, both the exact same volume, and fill one with oxygen and one with hydrogen the number of oxygen molecules will be exactly the same as the number of hydrogen molecules. This applies for any gases as long as the temperature and pressure are the same.
Molar Volume
Molar volume – the volume occupied by one mole of a gas.
From Avogadro’s law we know the volume occupied by one mole of a gas must be the same for all gases if the temperature and pressure are the same. This is because one mole of all gases contains the same number of molecules (6.02 x 1023).
For all gases at RTP one mole of a gas occupies a volume of 24dm3 (24,000cm3).
IMPORTANT: Room temperature and pressure (RTP) conditions are conditions with a temperature of 298K (25°C) and a pressure of 1atm (101kPa).
As this is the volume occupied by one mole of gas the molar volume, at RPT, for all gases is 24dm3 mol-1.
The amount of a gas (n), in mol, can be calculated using the equation below:
Where V is the volume in dm3. This unit is very important and you should always pay attention to the units given in a question incase you need to convert them.
For example, if we know a gas occupies a volume of 6 dm3 at RTP we can substitute this into the equation:
to get that n = 0.25 mol. This is the amount of any gas at RTP in a volume of 6 dm3.
Although one mole of all gases occupy the same volume, the mass of one mole of each of the gases varies. Therefore, the same volume of one gas could be much heavier than the same volume of another.
For example, 1 mol (24dm3) of oxygen has a mass of 32g whereas 1 mol (24dm3) of H2 has a mass of only 2g. To find out how to calculate the masses click here.
Worked Examples
Example 1
Calculate the volume, in dm3, of 0.67 mol of a gas at RTP.
Example 2
Calculate the amount, in mol, of any gas in 303,000cm3 at RTP.
Example 3
Calculate the volume of 22g of carbon dioxide (CO2) at RTP. The relative atomic masses of carbon and oxygen are given below:
Carbon: 12.0u
Oxygen: 16.0u
You might find this post on atomic masses and this post on moles helpful for answering this question.
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