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28 INTRODUCTION TO PHYSICAL CHEMISTRY

If there is exactly 1 mol of gas, the pressure is expressed in pascals (Pa), the
temperature is in kelvin and the volume is in cubic metres (both SI units), then the
−1
value of the constant is 8.314 J K −1 mol . We call it the gas constant and give it
the symbol R. (Some old books may call R the ‘universal gas constant’, ‘molar gas
constant’ or just ‘the gas constant’. You will find a discussion about R on p. 54)
More generally, Equation (1.12) is rewritten as

Equation (1.13) tells us
the constant in Boyle’s pV = nRT (1.13)
law is ‘nRT’and the
(different) constant in
where n is the number of moles of gas. Equation (1.13) is called
Charles’s law is the ideal-gas equation (or, sometimes, in older books the ‘universal
‘nR ÷ p’.
gas equation’). The word ‘ideal’ here usually suggests that the gas
in question obeys Equation (1.13).

Worked Example 1.3 What is the volume of 1 mol of gas at a room temperature of
◦
5
25 C at an atmospheric pressure of 10 Pa?
First, we convert the data into the correct SI units. In this example, only the temperature
needs to be converted. From Equation (1.7), the temperature is 298 K.
Secondly, we rearrange Equation (1.13) to make V the subject, by dividing both sides
by p:
nRT
V =
p

and then insert values:

1mol × 8.314 J K −1 mol −1 × 298 K
V =
5
10 Pa
3
So the volume V = 0.0248 m .
3
3
If we remember how there are 1000 dm in 1 m , we see how 1 mol of gas at room
3
temperature and standard pressure has a volume of 24.8dm .
SAQ 1.9 2 mol of gas occupy a volume V = 0.4m 3 at a temperature
T = 330 K. What is the pressure p of the gas?

An alternative form of Equation (1.13) is given as

p 1 V 1 p 2 V 2
= (1.14)
T 1 T 2

and is used when we have to start with a constant number of moles of gas n housed in a
volume V 1 . Its initial pressure is p 1 when the temperature is T 1 . Changing one variable
causes at least one of the two to change. We say the new temperature is T 2 , the new