Chemistry, Third edition

10 · GASES, LIQUIDS AND SOLIDS

Charles’ law

The expansion of a fixed mass of gas at constant pressure as its temperature is raised

is predicted by Charles’ law:

The volume of a gas is directly proportional to its temperature in kelvin.

One way of allowing a sealed mass of gas to expand is to use a piston (Fig. 10.6).

Since the piston handle is free to move, the pressure of the gas inside the piston will

adjust itself so that it equals the pressure on the piston handle (the ‘external pres-

sure’). For example, if the external pressure (due to the air) is 1 atm, the gas inside

the piston will remain at a pressure of 1 atm throughout the expansion.

Mathematically, Charles’ law may be expressed as

VT

whereVis the volume of gas and Tis its temperature in kelvin. The symbol means

‘proportional to’ and shows (for example) that if Tdoubles,Valso doubles.

Charles’ law can be used only where the volume of a gas is allowedto change. For

example, heating a sample of gas in a sealed metal tube will not alter the volume of

the gas because the rigid walls of the container prevent expansion.

Suppose a piston contains 100 cm^3 of hydrogen gas at 300 K (the temperature of

the laboratory) and is under an external air pressure of 1 atm. Imagine that the piston

is heated so that the gas eventually reaches a constant temperature of 600 K. Heating

causes the temperature of the gas to rise. This causes the gas molecules to collide more

often and more violently with the inner wall of the piston handle, resulting in a

momentary increase in hydrogen gas pressure above 1 atm. Since the pressure of the

hydrogen gas is greater than the pressure on the piston handle, the gas forces the

piston handle back. In this way the gas increases its volume, but since the same

number of molecules of hydrogen gas are now spread out in a larger space, the

number of collisions per second on the inner wall of the piston handle falls and the

pressure of the hydrogen gas begins to fall back towards 1 atm. The piston handle

stops moving when the volume of the gas in the piston has been increased so that the

pressure of the hydrogen equals 1 atm. Charles’ law predicts that a doubling of the

hydrogen gas temperature doubles the volume of the gas – see Fig. 10.6.

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Fig. 10.6Charles’ law.

Charles’ law

A sample of nitrogen at 500 K occupies 73.0 cm^3. Predict the volume of the gas at 2500 K.

(Assume that its pressure has not changed.)

Exercise 10E