Chemistry only- higher tier

### Gases, moles and volumes

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

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

### 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 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 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. It 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.

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

### Example 1

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

##### CaCO3(s) → CaO(s) + CO2(g)
How much carbon dioxide gas 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 mole present.
Since 1 mole of CaCO3 will produce 1 mole of carbon dioxide(44g).
Then 0.5 moles of CaCO3 will produce 0.5 moles 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 the molar volume, that is 24dm3. This of course assumes that the temperature and pressure are at room temperature/pressure.

### Example 2

The Haber process for making ammonia gas can be shown by the equation below:

##### N2(g) + 3H2(g) ⇌ 2NH3(g)

Here 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 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.