Chapter 5
05
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To relate this to our previous work and equation, we return to physics and a different expression
for pressure:
gdh
P
=
where
g
is given above,
d
is the density of the liquid in kg/m
3
and
h
is the height of the liquid
column in m. The pressure is then in Pa.
However, we can also use this equation to compare different liquids in the column measuring the
same pressure:
2
2
1
1
h
gd
h
gd
=
2
2
1
1
h
d
h
d
=
This means that density and the height of the column are inversely related. Thus, the more dense
the liquid, the shorter the column, and vice versa.
2.
Empirical Gas Laws
What follows are relationships between two of the four gas variables. These were determined
experimentally and, thus, are empirical.
Gas Variables
Amount, n, in moles
Pressure, P, usually in atm
Volume, V, usually in L
Temperature, T, in K
a.
Boyle’s Law: Relating Volume and Pressure
Boyle
’
s Law is illustrated in the diagram to the right. As
mercury is added to the J-tube, increasing the pressure, the
volume of the gas in the tip of the “J” decreases. We can
even look at this more quantitatively.
The J-tube on the left shows the gas at atmospheric pressure,
760 mmHg or 1 atm, where the volume is 100 mL.
In the J-tube in the center, the pressure in the tube is
atmospheric plus 760 mmHg for a total of 2 atm. Thus, the
pressure has been doubled. The volume is now 50 mL or
one-half the original volume.
In the J-tube on the right, the pressure is now atmospheric plus 1560 mmHg or a total of 3
atm. The volume is now 33 mL or one-third the original volume.
The same relationship is illustrated to the left.