Gas structure - A. Greg (Greg L at English Wikipedia), Public domain, via Wikimedia Commons

Gases are one of the four classical states of matter. In a gas, the particles are so loosely associated that they will drift apart to fill any space in which they are contained. If the volume of that container is reduced, then the spaces between the gas molecules will be decreased and the density of the gas increases. As a result, the number of collisions between the gas molecules increases and as does the number of collisions with the wall of the container. This is pressure. Such a description implies that the gas molecules are in constant motion (kinetic theory of matter) and from this, it easy to envisage that as the speeds the gas particles increase, so too does pressure. The speed at which the gas molecules move is a reflection of temperature and so there is a relationship between volume, temperature and pressure. In fact, for any (ideal) gas PV/T is a constant.

Temperature is measured in Kelvin (K).

Volume is measured in cubic metres (m³).

Pressure is measured in Pascals (Pa). Since Pressure = Force / Area, pressure may also be expressed in units of Nm^-2 and 1Pa = 1Nm^-2. Because this is a very small unit, it is common to see pressures measured in units of thousands of Pascals, kilo-Pascals or kPa.

Universal gas constant

For any sample of an ideal gas PV/T is a constant. In order to generalize this, we can say that for n moles of gas molecules, PV/T = nk where k is the 'Universal gas constant'. This is assigned the letter R and has a value of 8.31446261815324 JK⁻¹mol^-1.

The gas laws

The gas laws are simply expressions of the above equation.

Boyle's law

For a fixed mass of (ideal) gas at a contant temperature PV has a constant value.

Charles' law

For a fixed mass of (ideal) gas at a contant pressure V/T has a constant value.

Gay-Lussac's law

For a fixed mass of gas at a contant volume P/T has a constant value.

Dalton's law

Since the general gas law specifes only the number of mols of gas particles present, the nature of the actual gas or gases present are unimportant. If a gas mixture is present, then each individual gas produces an effect in propertion with with its presence in the overall mixture. For air, this appears as below:

Dalton's law

In each of the above equations, one parameter is fixed as the other two vary, but this is only achieved by actively controling the fixed parameter. When compressing a gas (altering P and V) work is done and this results in an increase in the temperature of the gas. To comply with Boyle's law we should have to cool the gas (thus maintaining a constant temperature) in order to measure the linear relationship between pressure and volume.

In real systems, this is not generally the case. Adiabetic systems are those which are 'closed' to the external world (i.e. no energy enters or leaves). In adiabatic compression, as volume decreases, both pressure and temperature increase. This is used in the diesel engine where the sudden compression of the fuel-air mixture raises its temperature above that required to cause combustion; no spark-plugs are needed. By contrast, when an oxygen cylinder is emptied rapidly, the temperature of the emerging gas falls very low. This is why maximum flow-rates are specified for gas-cylinders.

Real gases

Behaviour of a real gas (above critical pressure)

In the paragraphs above, I have referred to 'ideal' gases. These are notional gases which obey the general gas law. In reality, this cannot be true; as a gas is compressed further and further, its molecules are forced closer and closer together. At the most extreme compression, the molecules become so close that the 'gas' becomes indistinguishable from a liquid. Liquids are virtually incompressible, a tiny reduction in volume generates a huge increase in pressure. As a result, we should expect that as a gas is compressed from a low-pressure state (with behaviour closely approximating the gas laws) to a high pressure state, the relationship between volume and pressure will become non-linear (Fig. 3).

In Fig.3 the gas is compressed, but still behaves as a gas. If this process is continued, then we may see an interaction between gas and liquid phases (Fig. 4). In this plot, each line is a plot of pressure v volume at a fixed temperature (an expression of Boyle's law). As a result, it is referred to as an 'isotherm'. At higher temperatures (> 31°C), compression results in an increase in pressure. When the gas is relatively rarefied (right of the diagram) P∝1/V (Boyle's law). At more extreme compression, pressure rises much more rapidly.

Behaviour of CO₂

Below 31° something different happens. Initially, Boyle's law applies, but then as volume decreases, pressure becomes constant (points 1 and 2 in Fig 4) ! Remember - this is an isothermal diagram, so to maintain the constant temperature despite compression of the gas, energy must be removed from the system (contrast this with adibatic compression). This energy is the kinetic energy of the CO₂ molecules and as they slow, they eventually begin to liquefy. The green zone in Fig.4 represents a period in which gaseous CO₂ and liquid CO₂ exists in equilibrium. As compression increases, more gas turns to liquid and pressure remains constant. Eventually, when all of the gas has been liquefied, then pressure will rise very rapidly as we try to compress a liquid.