Page 38 - Physical chemistry understanding our chemical world

WHAT IS PHYSICAL CHEMISTRY: VARIABLES, RELATIONSHIPS AND LAWS 5

Graph (c) in Figure 1.1 is a straight-line graph, but is horizontal. In other words,
whatever we do to the controlled variable x, the observed variable y will not change.
In this case, the variable y is not a function of x because changing x will not change
y. A simple example would be the position of a book on a shelf as a function of time.
In the absence of other forces and variables, the book will not move just because it
becomes evening.
Graph (d) in Figure 1.1 shows another situation, this time the
Data is plural; the sin-
data do not demonstrate a straightforward relationship; it might
gular is datum.
demonstrate there is no relationship at all. The magnitude of the
controlled variable x does not have any bearing on the observed
variable y. We say the observed variable y is independent of the When two variables are
controlled variable x. Nevertheless, there is a range of results for multiplied together, we
y as x varies. Perhaps x is a compound variable, and we are being call them a compound
simplistic in our analysis: an everyday example might be a stu- variable.
dent’s IQ as x and his exam performance as y, suggesting that,
while IQ is important, there must be another variable controlling the magnitude of
the exam result, such as effort and commitment. Conversely, the value of y might be
completely random (so repeating the graphs with the same values of x would gen-
erate a different value of y – we say it is irreproducible). An example of this latter
situation would be the number of people walking along a main road as a function
of time.

Why does the mercury in a barometer go up when the
air pressure increases?

Relationships between variables

The pressure p of the air above any point on the Earth’s surface relates ultimately
to the amount of air above it. If we are standing high up, for example on the top
of a tall mountain, there is less air between us and space for gravity to act upon.
Conversely, if we stand at the bottom of the Grand Canyon (one of the lowest places
on Earth) then more air separates us from space, causing the air pressure p to be
much greater.
A barometer is an instrument designed to measure air pressure p. It consists of
a pool of liquid mercury in a trough. A long, thin glass tube (sealed at one end)
is placed in the centre of the trough with its open-side beneath the surface of the
liquid; see Figure 1.2. The pressure of the air acts as a force on the surface of the
mercury, forcing it up and into the capillary within the tube. If the air pressure is
great, then the force of the air on the mercury is also great, causing much mer-
cury up the tube. A lower pressure is seen as a shorter length h of mercury in
the tube.
By performing experiments at different pressures, it is easy to prove the existence
of a relationship between the air pressure p and the height h of the mercury column