Gases, moles and volumes

The table below gives the formula and the mass of 1 mole for a number of different gases.

Molar volume

Remember gases are mostly empty space with large gaps between the particle. The volume that a gas occupies depends on its temperature and pressure. If you heat a gas up it will expand and take up more space and if you cool it then its volume will decrease. Squashing a gas or putting it under pressure will also decrease its volume while reducing the pressure on a gas will cause it to expand. So when you talk about the volume a gas occupies you should really state the temperature and pressure as well.

In gcse chemistry we are mostly dealing with gases at room temperature and pressure (RTP), that is 20⁰C or 293Kelvin and 1 atmosphere pressure. According to Avogadro's theorem 1 mole of any gas will occupy the same volume at any given pressure and temperature. This means for example that 2g of hydrogen gas, that is 1 mole of hydrogen will occupy the same volume as 32g of oxygen (1 mole of oxygen) or 44g of carbon dioxide (1 mole of carbon dioxide) or 58g of butane 9 (1 mole of butane) or 4g of helium (1 mole of helium). At 20⁰C and 1 atmosphere pressure 1 mole of any gas will occupy 24dm³ or 24 litres. This is called the molar volume of a gas.

The table below is almost identical to the one above with the exception of the last column which shows the molar volume, that is the volume occupied by 1 mole of that particular gas. As you can see 1 mole of any gas occupies 24 litres or 25 dm³ at 20⁰C and 1 atmosphere pressure.

Calculations involving the volume of gases

Example 1

Calcium carbonate (CaCO₃) decomposes when heated according to the equation below:

Calcium carbonate_(s) → calcium oxide_(s) + carbon dioxide_(g)

CaCO3_(s) → CaO_(s) + CO_2(g)

Number of moles = mass of substance/M_r

So the number of moles calcium carbonate present = 50g/100 = 0.5 moles.
Now from the balanced symbolic equation above we already know that:
1 mole of CaCO₃will produce 1 mole of carbon dioxide (44g) gas.
So 0.5 moles of CaCO₃ will produce 0.5 moles of carbon dioxide (22g) gas.
So 0.5 moles of CO₂ gas will occupy 24dm³ x 0.5 = 12dm³

The formula to use to calculate the volume of a gas relies on knowing how many moles of gas you have, you simply multiply the number of moles by the molar volume, that is 24dm³. This of course assumes that the temperature and pressure are at room temperature and pressure.

Example 2

The Haber process is used to make ammonia gas (NH₃), this is shown in the equation below:

nitrogen_(g) + hydrogen_(g) ⇌ ammonia_(g)

N_2(g) + 3H_2(g) ⇌ 2NH_3(g)

This balanced symbolic equation shows that 1 mole of nitrogen gas reacts with 3 moles of hydrogen gas to produce 2 moles of ammonia gas.

What volume of ammonia gas will be produced if 500cm³ of nitrogen gas react with an excess of hydrogen gas at RTP?

This time instead of using reacting masses the question gives volumes of reactants. However we know that the temperature and pressure stay constant. We also know that:

• 1 mole of nitrogen produces 2 moles of ammonia.
or
• 24dm³ of nitrogen will produce 48dm³ of ammonia.
so
• 5oocm³ of nitrogen will produce 1000cm³ of ammonia.

Alternatively you can work out the number of moles of nitrogen gas present by simply dividing the reacting volume of the nitrogen gas; that is 500cm³ by 24 000 cm³, that is the reacting volume of nitrogen divided by the molar volume, which gives 0.02 moles of nitrogen gas reacting.
Now simply use the formula shown above to calculate the volume of ammonia produced:

Volume of gas = number of moles of gas X 24dm³

Practice questions

Check your understanding - practice questions on molar volumes