Page 39 - Physical chemistry understanding our chemical world

6 INTRODUCTION TO PHYSICAL CHEMISTRY

Vacuum

Thick-walled
glass tube
h

Trough of mercury

Figure 1.2 A barometer is a device for measuring pressures. A vacuum-filled glass tube (sealed
at one end) is placed in a trough of mercury with its open end beneath the surface of the liquid
metal. When the tube is erected, the pressure of the external air presses on the surface and forces
mercury up the tube. The height of the mercury column h is directly proportional to the external
pressure p

in the tube. This relationship follows Equation (1.1):
In fact, the value
of the constant c in h = c × p (1.1)
Equation (1.1) com-
prises several natural where c is merely a proportionality constant.
constants, including In practice, a barometer is merely an instrument on which
the acceleration due we look at the length of the column of mercury h and, via
gravity g and the den- Equation (1.1), calculate the air pressure p. The magnitude of h is
sity ρ of the mercury.
in direct relation to the pressure p. We ascertain the magnitude of
h if we need to know the air pressure p.
While physical chemistry can appear to be horribly mathematical, in fact the mathe-
matics we employ are simply one way (of many) to describe the relationships between
variables. Often, we do not know the exact nature of the function until a later stage
of our investigation, so the complete form of the relationship has to be discerned
in several stages. For example, perhaps we first determine the existence of a linear
equation, like Equation (1.1), and only then do we seek to measure
an accurate value of the constant c.
We might see this
situation written math- But we do know a relationship holds, because there is a response.
ematically as, h = f(p), We would say there was no relationship if there was no response.
where the ‘ =’means For example, imagine we had constructed a poor-quality barometer
‘is not equal to’. In (meaning it does not follow Equation (1.1)) and gave it a test run. If
other words, h is not a we could independently verify that the pressure p had been varied
function of p in a poor over a wide range of values yet the length of the mercury h in
barometer. the barometer did not change, then we would say no relationship
existed between p and h.