Notes on The Gas Laws

Boyle’s Law:     Pressure is inversely proportional to the volume   P x V = constant

                          P₁V₁=P₂V₂ 

You need to know the graphs, pressure against volume and pressure against (1/V)

Charle’s Law:    Volume is proportional to the temperature. V/T = constant

                            V₁/T₁ = V₂/T₂

                                      You need to know the graph of Volume against temperature (⁰C) and how it can be    

                             extrapolated to give a value of absolute zero. Should be -273 ^oC (0K)

The Ideal Gas Law and the gas constant:

The volume of a gas depends on:

·         The temperature

·         The number of moles

·         The pressure

The volume of the gas particles themselves is insignificant compared to the space between them. Therefore, it doesn’t matter which gas you are referring to, one mole of gas at a fixed temperature and pressure will occupy the same volume. One mole of any gas at 1atm and 273K will occupy 22.4 dm³ (litres).

So the gas constant for one mole of a gas under standard conditions (STP, 1atm, 273K) can be easily worked out. However, its value depends on if you use atmosphere (atm) for pressure or pascals (Pa) or KPa.

For 1atm, 273 K. Note: if you are using atm use dm³  as your volume units

PV/T = constant        = 1 x 22.4/273   = 0.082 atm dm³ k^-1 mol^-1

1 atm = 101317 Pa  Note: 1Pa = 1 N/m². Remember pressure is force/area. So you have to use m³ for the units of volume if you are using pascals and dm³   if you are using kPa.

PV/T = constant     = (101325 x 0.0224)/273  = 8.314 Pa m³ k^-1 mol^-1   

Note: 1 N/m = J  so it can be written as: 8.314 J K^-1 mol^-1

So for n moles PV/T = nR    where R is the gas constant.

So PV = nRT

Unit conversions:

1atm = 101325Pa = 101.325kPa = 760 mm Hg