Page 48 - Essentials of physical chemistry

10 Essentials of Physical Chemistry

It is very important at this point to note that the product of pressure and volume is always energy:
PV ¼ (force=area) (volume) ¼ force distance ¼ energy. One way to remember this is to chant
the rhyme ‘‘PV ¼ energy! PV ¼ energy! PV ¼ energy! etc.’’.
2
The most common practical unit of pressure is (pounds=inch ) abbreviated as psi (pounds per
square inch). In these units we get

6
1:01325 10 dyne=cm 2 2
¼ 14:70 lb=in: ¼ 14:7 psi

453:6 g=lb 2
(980 cm=s )
2
2
(2:54) cm =in 2
Note here that the unit lb (pound) is in the denominator of the denominator and so flips up to the
numerator in the answer.
Finally, a unit that occurs when reading the instructions for inflating the tires of a British or
European racing bicycle is that of a ‘‘bar.’’ Apparently someone noticed that the 1.01325 constant is
close to 1.0 so why not define a ‘‘bar’’ as a clean unit.
2
6
1 bar ¼ 1:0 10 dyne=cm ¼ (1:0=1:01325)(760 mmHg) ¼ 750:06 mmHg
To a good approximation 1 bar is 750 mmHg while 1 atm ¼ 760 mmHg. The name ‘‘bar’’ is
appropriate because pressure is what a ‘‘barometer’’ measures. To use a common service station air

750
14:7 psi ¼ 14:5 psi since
pump to inflate tires in bars just use the simple conversion 1 bar ¼
760
a bar is a smaller unit than an atm.
MOLECULAR WEIGHT FROM GAS DENSITY (THE DUMAS BULB METHOD)
In bygone days chemists used a simple method of first weighing an empty container and weighing
that known volume again with gas inside at a known temperature and pressure. The internal volume
could be obtained by the difference in mass of the container empty and filled with water using the
density of water. However, when it came time to weigh the container with the unknown gas in it the
weight of the empty container (often a glass bulb of about 400 mL volume) the difference in weight
(mass) was usually very small compared to the weight (mass) of the empty container. Thus, this
method has a very large uncertainty but it can be used with rounded estimates from assumed
molecular structures. The method works fairly well for high-molecular weight gases but would be
very uncertain for He or H 2 . The key idea is to use the mole concept with the ideal gas law.
w

RT
M
PV ¼ nRT ¼
so

wRT RT
w RT
¼ r
M ¼ ¼
PV V P P
Here
‘‘w’’ is the weight of the gas
r the density
M is the unknown molecular weight

This method is not very accurate and really only works well for a few gases that are of high
molecular weight (CCl 4 , CHCl 3 , etc.).