6.2.4

# Ideal Gases 2

Test yourself

## Work Done on an Ideal Gas

You can find out the work done on an object by multiplying the average force by the displacement of the object moved in the direction of the force.

### Substitute pressure

• Since P = F/A, where A is the cross-sectional area of the piston, you can substitute this into the expression for work done.
• W = force × distance travelled (where the distance travelled = the distance the force pushes in the piston).
• Work done on the gas = P × A × Δx assuming the pressure in the piston is constant.

### Derive equation

• A × Δx = the change in volume of the gas, ΔV.
• The work done by an expanding gas which experiences a change in volume ΔV, is given by W = p × ΔV.
• This is more likely to be shown on any formula sheet as W = p ΔV.

## Molecular Mass

As chemicals and atoms are so small, it is often more useful to use other measures of mass rather than kilograms.

• Avogadro’s number, NA, is the number of particles in 1 mole of any given substance.
• E.g. 1 mole of helium atoms is a collection of 6.02 ×1023 atoms, because Avagodro’s number is defined to be 6.02 ×1023.

### Relative molecular mass

• You can calculate the relative molecular mass (RMM) of a molecule by adding the relative atomic masses (RAM) of all of the atoms in that molecule.
• E.g. The hydrogen atom has a RAM of 1 and the oxygen atom has a RAM of 16. So, the RMM of water (H2O) is given by (2 × 1) + 16 = 18.

### Molecular mass

• You can find the molecular mass by multiplying the RMM of a molecule by the atomic mass unit, u.
• 1 u = 1.66 × 10-27 kg

### Molar mass

• You can find the molar mass of a given molecule really easily.
• If the RMM of a molecule is X, then the mass of a mole of that molecule is X grams.
• Water has an RMM of 18, so 1 mole of water has a mass of 18g.
• This is most useful in gas law calculations because measuring the mass of a gas can be experimentally tricky.