 Chemistry only- higher tier

### Gases, moles and volumes

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

gas molecular formula Ar or Ar mass of 1 mole/g volume gas will occupy at RTP/dm3
hydrogen H2 2 2 24
helium He 4 -4 24
oxygen O2 32 32 24
methane CH4 16 16 24
carbon dioxide CO2 44 44 24
butane C4H10 58 58 24

### Molar volume Remember gases are mostly empty space with large gaps between the particles. 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 it 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 293K 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 will occupy the same volume as 32g of oxygen or 44g of carbon dioxide or 58g of butane or 4g 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.

### Example

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

##### CaCO3(s) → CaO(g) + CO2(s)
How much carbon dioxide is released by the thermal decomposition of 50g of calcium carbonate and what volume will this carbon dioxide occupy at RTP?

Ar of Ca =40, Ar of C=12, Ar of O=16, Mr of CaCO = 40+ 12 + (16x3) =100

Step 1- You need a balanced symbolic equation. Luckily the equation above is balanced, you can see that 1 mole of calcium carbonate produces 1 mole of carbon dioxide gas.
Step 2- calculate the number of moles of calcium carbonate present:
Use the formula:
##### Number of moles = mass/ Mr
Number of moles calcium carbonate present = 50g/100 = 0.5 moles present.
Since 1 mole of CaCO3 will produce 1 mole of carbon dioxide(44g).
Then 0.5 moles of CaCO3 will produce 0.5 mole of carbon dioxide (22g).
0.5 moles of CO2 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 24dm3. 