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When dealing with gases it is easier to consider the volume they occupy rather than their mass. Gases have a rather useful property in that one mole of any gas occupies the same volume at the same temperature and pressure. Clearly the gas will decrease in volume if the pressure is increased (that is, the gas is squashed into a smaller volume), or will increase in volume if the temperature increases (when it will expand). Molar volume is the volume occupied by one mole of any gas at a particular temperature and pressure. The most useful temperature and pressure to consider is room temperature (25°C) and one atmosphere pressure, that is the usual laboratory conditions. This is sometimes known as RTP. |
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At room temperature and pressure 1 mole of any gas occupies 24 dm3 |
Use common sense to calculate the volume of quantities of gas other than one mole. Clearly two moles of gas would occupy 48 dm3, that is 2 × 24. So, in general, multiply the number of moles by 24 to get the volume of gas in dm3 at room temperature and pressure.
Example
What is the volume of 4 g of methane gas (CH4) at room temperature and pressure?
CH4 = 16 so we have 4/16 = 0.25 moles of methane
0.25 moles of any gas at RTP occupies 0.25 × 24 = 6 dm3
Exercise
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1. What is the volume of 34 g of ammonia gas (NH3) at room temperature and pressure? |
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2. What is the volume of 1.00 g of butane gas (C4H10 used in cigarette lighters) at room temperature and pressure? Give your answer to three significant figures. |
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We can also work in the reverse direction - given a volume of gas we can calculate the number of moles. This appears in some practical assessments as a method of measuring molar mass.
If you are asked to plan an experiment to measure a gas volume it is important that you chose an appropriate quantity of material to start with. We would usually measure a gas volume with a 100 cm3 gas syringe. This means that we must make sure that the planned volume of gas is around 60 -80 cm3. Too much gas will go over the 100 cm3 maximum and too little introduces a large percentage measurement error. At room temperature and pressure one mole occupies 24000 cm3, so 60 cm3 is 60/24000 = 0.0025 mol. We should therefore aim to make around 0.0025 mol of gas to give a reasonable volume in the gas syringe.
Example
In an experiment to measure the purity of a sample of sodium hydrogencarbonate it is proposed to measure the volume of carbon dioxide gas formed on thermal decomposition. The equation for this decomposition is:
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2NaHCO3(s) ⇒ Na2CO3(s) + H2O(l) + CO2(g) |
Suggest a suitable mass of sodium hydrogencarbonate if the gas is to be collected in a 100 cm3 gas syringe.
We saw above that to make 60 cm3 of gas we need 0.0025 moles.
According to the equation we need twice as many moles of NaHCO3 as CO2.
So we need 0.0050 moles of NaHCO3.
NaHCO3 = 84
\ mass of NaHCO3 required = 84 × 0.0050 = 0.42 g
Now try the following:
In all the above exercises we have assumed that the volume measurements have been made at room temperature and pressure. For extra accuracy we should measure the temperature and pressure (pressure is measured using a barometer). The measured volume can then be corrected (using the ideal gas equation) to allow for any error.
The following is some useful extension work, it is not required for your exam.
Molar gas volume is a very useful concept. If we need to work out the volume of a gas at other temperatures and pressures, we need to use the ideal gas equation. Real gases may not follow these rules precisely, but the volumes we work out are usually accurate enough for "A" level Chemistry.
