Page 56 - Physical chemistry understanding our chemical world

PROPERTIES OF GASES AND THE GAS LAWS 23

SAQ 1.3 What is the temperature T expressed in kelvin We divide each tem-
if the temperature is 30 C?
◦
perature, both kelvin
and centigrade, by
SAQ 1.4 What is the centigrade temperature correspon- its respective unit
ding to 287.2 K? to obtain a number,
rather than the tem-
SAQ 1.5 The data in the table below relate to gaseous perature.
helium. Demonstrate the linear relationship between the
volume V and the temperature T.

Temperature T/K 280 300 320 340 360 380 400 420 440
Volume V /m 3 0.023 0.025 0.027 0.028 0.030 0.032 0.033 0.035 0.037

Charles’s law is often expressed in a slightly different form than
Note how we write
Equation (1.4), as
the controlled vari-
V 1 V 2 able along the top row
= (1.8)
T 1 T 2 of a table, with the
observed following. (If
which is generally regarded as superior to Equation (1.4) because the table is vertical,
we do not need to know the value of the constant. we write the controlled
variable on the far left.)
Equation (1.8) is also preferred in situations where the volume of
a fixed amount of gas changes in response to temperature changes
(but at constant pressure). The subscripts refer to the two situations;
The subscripts written
so, for example, the volume at temperature T 1 is V 1 and the volume
to the right of a variable
at temperature T 2 is V 2 .
are called ‘descriptors’.
They are always written
SAQ 1.6 The gas inside a balloon has a volume V 1 of as a subscript, because
3
1dm at 298 K. It is warmed to 350 K. What is the vol- a superscripted number
ume following warming? Assume the pressure remained means a power, i.e. V 2
constant. means V × V.

Why pressurize the contents of a gas canister?

The effect of pressure on gas volume: Boyle’s law

It is easy to buy canisters of gas of many sizes, e.g. as fuel when we wish to camp
in the country, or for a portable welding kit. The gas will be n-butane if the gas is
for heating purposes, but might be oxygen or acetylene if the gas is to achieve the
higher temperatures needed for welding.
Typically, the components within the can are gaseous at most temperatures. The
3
3
typical volume of an aerosol can is about 0.3dm (3 × 10 −4 m ), so it could contain
very little gas if stored at normal pressure. But if we purchase a canister of gas and
release its entire contents at once, the gas would occupy a volume similar that of