# 5.5.1 Boyle’s Law (Pressure – Volume Relationship)

On the basis of his experiments, Robert Boyle reached to the conclusion that at constant temperature, the pressure of a fixed amount (i.e., number of moles n) of gas varies inversely with its volume.

This is known as Boyle’s law. Mathematically, it can be written as where k1 is the proportionality constant. The value of constant k1 depends upon the amount of the gas, temperature of the gas and the units in which p and V are expressed.

On rearranging equation (5.2) we obtain  pV = k1

It means that at constant temperature, product of pressure and volume of a fixed amount of gas is constant.

If a fixed amount of gas at constant temperature T occupying volume V1 at pressure p1 undergoes expansion, so that volume becomes V2 and pressure becomes p2, then according to Boyle’s law :

P1 V1  = p2 V2 = constant

Figure 5.5 shows two conventional ways of graphically presenting Boyle’s law. Fig. 5.5 (a) is the graph of equation (5.3) at different temperatures. The value of k1 for each curve is different because for a given mass of gas, it varies only with temperature.

Each curve corresponds to a different constant temperature and is known as an isotherm (constant temperature plot). Higher curves correspond to higher temperature.

It should be noted that volume of the gas doubles if pressure is halved. Table 5.1 gives effect of pressure on volume of 0.09 mol of CO2 at 300 K.  Fig 5.5 (b) represents the graph between p and 1/v . It is a straight line passing through origin. However, at high pressures, gases deviate from Boyle’s law and under such conditions a straight line is not obtained in the graph.

Experiments of Boyle, in a quantitative manner prove that gases are highly compressible because when a given mass of a gas is compressed, the same number of molecules occupy a smaller space.

This means that gases become denser at high pressure. A relationship can be obtained between density and pressure of a gas by using Boyle’s law:

By definition, density ‘d’ is related to the mass ‘m’ and the volume ‘V’ by the relation d = m/V.

If we put value of V in this equation from Boyle’s law equation, we obtain the relationship.

This shows that at a constant temperature, pressure is directly proportional to the density of a fixed mass of the gas.