Page 54 - Physical chemistry understanding our chemical world

PROPERTIES OF GASES AND THE GAS LAWS 21

The small burner at the heart of the balloon heats the air within
‘Density’ ρ is defined as
the canvas hood of the balloon. The densities of all materials – mass per unit volume.
solid, liquid or gas – alter with temperature. Almost universally,
we find the density ρ increases with cooling. Density ρ is defined
as the ratio of mass m to volume V , according to
mass,m
density ρ = (1.3)
volume,V
It is not reasonable to suppose the mass m of a gas changes by heating or cooling it
(in the absence of chemical reactions, that is), so the changes in ρ caused by heating
must have been caused by changes in volume V . On the other hand, if the volume
were to decrease on heating, then the density would increase.
So the reason why the balloon floats is because the air inside its voluminous hood
has a lower density than the air outside. The exterior air, therefore, sinks lower
than the less-dense air inside. And the sinking of the cold air and the rising of the
warm air is effectively the same thing: it is movement of the one relative to the
other, so the balloon floats above the ground. Conversely, the balloon descends back
to earth when the air it contains cools to the same temperature as the air outside
the hood.

How was the absolute zero of temperature
determined?

Charles’s law

J. A. C. Charles (1746–1823) was an aristocratic amateur scientist of the 18th century.
He already knew that the volume V of a gas increased with increasing temperature T ,
and was determined to find a relationship between these variables.
The law that now bears his name can be stated as, ‘The ratio of
According to ‘Charles’s
volume and temperature for a fixed mass of gas remains constant’,
law’, a linear relation-
provided the external pressure is not altered. ship exists between
Stated mathematically, Charles demonstrated
V and T (at constant
pressure p).
V
= constant (1.4)
T
where the value of the constant depends on both the amount and A ‘straight line’ will
the identity of the gas. It also depends on the pressure, so the data always have an equa-
are obtained at constant pressure p. tion of the type y =
This is one form of ‘Charles’s law’. (Charles’s law is also called mx + c,where m is the
gradient and c is the
‘Gay–Lussac’s law’.) Alternatively, we could have multiplied both
intercept on the y-axis
sides of Equation (1.4) by T , and rewritten it as
(i.e. when the value of
x = 0).
V = constant × T (1.5)