AS-Level Chemistry Gases and the gas laws

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Gases and the gas laws

The Irish chemist Robert Boyle (1627–91) was one of the first people to investigate the effect of pressure on the volume of gases. About a hundred years after, in the late 18th century, the hot air balloon flights of the Montgolfier brothers stimulated scientists to study the behavior of gases. Two of these scientists were French: Joseph Gay-Lussac (1778–1850) and Jacques Charles (1746–1823). They were particularly interested in the variation of the volumes of gases with temperature. Jacques Charles put his theories to the test and in 1783 made the first ascent in a hydrogen balloon.

Meanwhile the Italian scientist Amedeo Avogadro (1776–1856) proposed the law that equal volumes of all gases, at the same temperature and pressure, contain the same number of molecules. These scientists discovered the gas laws that show how the volume, V, of a sample of gas depends on three things:

the temperature, T

the pressure, p

the amount of gas in moles, n.

Real and ideal gases

Scientists have the concept of an ‘ideal gas’ which obeys the gas laws perfectly. In practice, real gases do not obey the laws under all conditions. Under laboratory conditions, however, there are gases which are close to behaving like an ideal gas.

These are the gases which, at room temperature, are well above their boiling points, such as helium, nitrogen, oxygen and hydrogen. Chemists generally find that the gas laws predict the behaviour of real gases accurately enough to make them a useful practical guide, but it is important to bear in mind that gases such as ammonia, butane, sulfur dioxide and carbon dioxide can show marked deviations from ideal behaviour. These are the gases which boil only a little below room temperature and can be liquefied just by raising the pressure.

The ideal gas equation

The behaviour of an ideal gas can be summed up by combining the gas laws into a single equation called the ideal gas equation:

pV = nRT

This equation sums up all the gas laws.

When SI units are used, the pressure is measured in pascals, Pa, the volume in cubic metres, m3, and the temperature in kelvin, K. R, in the ideal gas equation, is the gas constant. R has the value 8.31 J mol–1 K–1 if all quantities are in SI units.

The molar volume of gases

The ideal gas equation shows that at a fixed temperature and fixed pressure, the volume of a gas depends only on the amount of gas in moles; the type or the formula of the gas does not matter. This is only strictly true for ideal gases but is nevertheless useful when dealing with real gases.

Substituting in the ideal gas equation makes it possible to calculate the volume of one mole of gas under any conditions. This shows that the volume of one mole of any gas occupies about 24 dm3 (24 000 cm3) at a typical room temperature of around 16 °C (298 K) and at atmospheric pressure (100 kPa). This volume of one mole of gas is called the molar volume under the stated conditions.

So, 1 mole of oxygen (O2) and 1 mole of carbon dioxide (CO2) each occupy 24 dm3 at room temperature. Therefore 2 moles of O2 occupy 48 dm3 and 0.5 moles of O2 occupy 12 dm3 at room temperature. Notice from these simple calculations that:

volume of gas/cm3 = amount of gas/mol × molar volume/cm3 mol–1

So, under laboratory conditions at room temperature:

volume of gas/cm3 = amount of gas/mol × 24 000/cm3 mol–1