## Example

gas laws

### Calculation of pressure using the

Calculate the pressure at 25°C within an aerosol container of internal volume 250 cm3 containing 160 cm3 of concentrate above which has been introduced 0.04 mol of nitrogen gas. Assume ideal behaviour.

2.2 Ideal and nonideal gases

Ideal gases obey the combined gas law

where P is the pressure in Pa, V is the volume in m3, n is the number of moles of gas, T is the temperature in kelvins and R is the gas constant (8.314 J mol1 K1).

Equation (2.1) can be derived from the kinetic theory of gases assuming the gas molecules to behave as perfectly elastic spheres having negligible volume with no intermolecular attraction or repulsion.

In some types of aerosol (compressed gas aerosols) an inert gas under pressure is used to

For a given number of moles of gas the quantity PV/RT should, according to equation (2.1), be independent of changes in P, V or T providing such changes do not involve a change of state. A convenient means of expressing departure from ideality is by a plot of PV/RT as a function of pressure for 1 mole of each gas (Fig. 2.1). It is important to note the magnitude of the pressures involved in Fig. 2.1. The narrow shaded area represents the pressure normally met in pharmaceutical systems and it is clear from this that the ideal gas laws are sufficient for most purposes.

Where it is clear that equation (2.1) is inadequate in describing the behaviour of a particular gaseous system, however, a better approximation to real behaviour may be achieved using the van der Waals equation:

where a and b are constants for a particular gas. At the moment of impact of a molecule with the container wall, the molecule is subjected to an imbalance of forces which tend to

Figure 2.1 Departure of gases from ideal behaviour.

pull it back into the bulk of the gas and so lessen the force of impact. Since pressure is a consequence of collisions of molecules with the walls, there is a resultant reduction of pressure, which may be corrected by addition of the a/V2 term. Around each molecule of a gas is a particular volume from which other molecules are excluded for purely physical reasons. The bulk molar volume, V, of the gas is consequently an overestimation of the true molar

Table 2.1 Van der Waals constants for some gases

 Gas Van der Waals constant (N m4 mol-2) (m3 mol-1 " 105) Hydrogen
0 0