BioPHYSICAL chemistry

of gas in a chamber the pressure will increase. These observations lead
to the ideal gas law:

PV=nRT (1.12)

In this equation, R is the gas constant. The value of this constant
depends upon the units for the various variables, with some values given
in Table 1.2.
To gain an understanding of the ideal gas law, we consider how a hot-
air balloon works first at a macroscopic level (Figure 1.1). Consider the
four different parameters of the gas law, T, P, n, and V. The volume is
simply defined by the size of the balloon. What about the temperature?
The temperature inside the balloon is much greater than the temperature
outside the balloon (hence the name hot-air
balloon). The pressure inside and outside the
balloon must be the same because there is a large
opening at the bottom of the balloon. Hot-air
balloons do not work by expansion, rather the
balloon material simply captures the hot air. An
important aspect is that the relative number
of air molecules inside the balloon (per unit
volume) is less than the number outside. For the
balloonto rise into the air the density of the
air inside the balloon must be less than that
of the air outside the balloon. In fact, the major
reasonfor heating the air inside the balloon is
to trap air that has less density, providing an upward hydrostatic force that
pushes the balloon up when this force is greater than the gravitational
force due to the mass of the balloon.
The motion upward of the hot-air balloon can also be viewed from an
equivalent molecular viewpoint. Consider a single air molecule inside the
balloon. This molecule will travel through the air until it hits the side of
the balloon, at which point it bounces away. Eventually, the air molecule
will travel down through the opening and leave the balloon. As the

CHAPTER 1 BASIC THERMODYNAMIC AND BIOCHEMICAL CONCEPTS 7

Table 1.2

The gas constant Rexpressed in different units.

R 8.314472 J K−^1 mol−^1

8.314472 × 103 Pa L K−^1 mol−^1

62.364 L Torr K−^1 mol−^1

1.98722 cal K−^1 mol−^1

PV  nRT

Figure 1.1The

ability of hot-air

balloons to travel

through the air

can be understood

in terms of the

interactions of the

air molecules against

the balloon wall.