General Chemistry Principles, Patterns, and Applications, 2011

[1] A sample of gas cannot really have a volume of zero because any sample of matter must
have some volume. Furthermore, at 1 atm pressure all gases liquefy at temperatures well above
−273.15°C.
10.4 The Ideal Gas Law
L E A R N I N G O B JE C T I V E
1. To use the ideal gas law to describe the behavior of a gas.
In Section 10.3 "Relationships among Pressure, Temperature, Volume, and Amount", you learned how the volume of
a gas changes when its pressure, temperature, or amount is changed, as long as the other two variables are held
constant. In this section, we describe how these relationships can be combined to give a general expression that
describes the behavior of a gas.
Deriving the Ideal Gas Law
Any set of relationships between a single quantity (such as V) and several other variables (P, T, and n) can
be combined into a single expression that describes all the relationships simultaneously. The three
individual expressions derived in Section 10.3 "Relationships among Pressure, Temperature, Volume, and
Amount" are as follows:
Boyle’s law
V µ1P(at constant n, T )
Charles’s law
V µT(at constant n, P)
Avogadro’s law
V µ n(at constant T, P)
Combining these three expressions gives
Equation 10.9
V µ nTP
which shows that the volume of a gas is proportional to the number of moles and the temperature and
inversely proportional to the pressure. This expression can also be written as
Equation 10.10
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