The molar gas volume in calculations, moles, gas volumes and Avogadro's Lawstudy examples carefully

9. The molar gas volume in calculations, moles, gas volumes and Avogadro's Law

• Avogadro's Law states that equal volumes of gases under the same conditions of temperature and pressure contain the same number of molecules.
  • So the volumes have equal moles of separate particles (molecules or individual atoms) in them.
  • Therefore one mole of any gas (formula mass in g), at the same temperature and pressure occupies the same volume .
  • This is 24dm³ (24 litres) or 24000 cm³, at room temperature of 25^oC/298K and normal pressure of 101.3 kPa/1 atmosphere (such conditions are often referred to as RTP).
  • The molar volume for s.t.p is 22.4 dm³ (22.4 litres) at 0^oC and 1atmosphere pressure.
  • Historically, s.t.p unfortunately stands for standard temperature and pressure, but these days 25^oC/298K is usually considered the standard temperature (RTP).
• Some handy relationships for substance Z below:

moles Z = mass of Z gas (g) / atomic or formula mass of gas Z (g/mol)

• mass of Z in g = moles of Z x atomic or formula mass of Z
• 
  
• atomic or formula mass of Z = mass of Z / moles of Z
• 1 mole = formula mass of Z  in g.

gas volume of Z = moles of Z x volume of 1 mole

• rearranging this equation gives ...
• moles of Z = gas volume of Z / volume of 1 mole

• moles = V(dm³) / 24   (at RTP)

The latter form of the equation can be used to calculate molecular mass from experimental data because

• moles = mass / molecular mass = gas volume / volume of 1 mole
• mass / molecular mass = gas volume / volume of 1 mole
• molecular mass = mass x volume of 1 mole/volume
• therefore at RTP: M_r = mass(g) x 24 / V(dm³)
• so, if you know the mass of a gas and its volume, you can work out moles of gas and then work out molecular mass.
• This has been done experimentally in the past, but these days, molecular mass is readily done very accurately in a mass spectrometer.

Note (i): In the following examples, assume you are dealing with room temperature and pressure i.e. 25^oC and 1 atmosphere pressure so the molar volume is 24dm³ or 24000cm³.

Note (ii):

• Apart from solving the problems using the mole concept (method (a) below, and reading any equations involved in a 'molar way' ...
• It is also possible to solve them without using the mole concept (method (b) below). You still use the molar volume itself, but you think of it as the volume occupied by the formula mass of the gas in g and never think about moles!

Methods of measuring how much gas is formed (volume can be compared with theoretical prediction!)

• (a) You can collect the gases in a calibrated gas syringe.
  

  • You must make sure too much gas isn't produced and too fast!
  • A gas syringe is more accurate than collecting the gas in an inverted measuring cylinder under water shown below, but its still only accurate to the nearest cm³.
  • You can collect any gas by this method.
• (b) The gas is collected in a measuring cylinder filled with water and inverted over a trough of water.Methods of measuring how much gas is formed

(volume can be compared with theoretical prediction!)

You can get a more accurate result by using an inverted burette instead of a measuring cylinder.
• However, this method is no good if the gas is soluble in water!
• Burettes are calibrated in 0.10 cm³ intervals. measuring cylinders to the nearest cm³ or worse!
• In both methods the reaction is carried out in conical flask fitted with a sealing rubber bung, but a tube enabling the gas evolved to be collected in some suitable container.
• (c) A third method is to measure the gas loss by carrying out the reaction in a flask set up on an accurate one-pan electronic balance.
• You need to put a cotton wool plug in the neck of the conical flask in case you lose any of the solution in a spray as the gas bubbles up - effervescence can produce an aerosol.
• This method can be used for any reaction that produces a gas, but the gas is released into the laboratory, ok if its harmless.
• It is potentially the most accurate method, BUT, the mass loss may be quite small especially hydrogen [M_r(H₂) = 2], better for the 'heavier' gas carbon dioxide [M_rCO₂) = 44]
• Molar