Page 49 - Essentials of physical chemistry

Ideal and Real Gas Behavior 11

DALTON’S LAW OF PARTIAL PRESSURES

One curious physical phenomenon associated with gases is the fact that when there is a mixture of
gases in a given volume they behave independently so that their pressures are additive. In fact this
raises the issue of what we mean by ‘‘pressure.’’ Common sense may lead us to expect that volumes
are additive as indeed they are for macroscopic objects such as bricks. Thus, it is somewhat thought
provoking that several gases can be easily confined in the same volume. This same sort of question
also arises for mixtures of liquids to a much less extent as discussed later in Chapter 6. These
considerations go to the very heart of the concept of the size of atoms and molecules and how much
space is between them in a liquid or gas. As we will soon see, the space between gas molecules is
about 100 times their size at 1 atm so there is plenty of space for other molecules. In addition, it will
soon become evident that pressure is (force=area) caused by many collisions of gas molecules with
the wall of the container. Cavendish in 1781 and Dalton in 1810 contributed to the concept now
known as ‘‘Dalton’s law.’’
The total pressure exerted by a mixture of gases is equal to the sum of the pressures that each
component would exert if placed separately into the container.
X
P i but if the gases act as ideal gases, we have
i
Thus, P tot ¼ P 1 þ P 2 þ P 3 þ ¼

RT RT RT RT X RT
P tot ¼ n 1 þ n 2 þ n 3 þ ¼ n i ¼ n tot . Now consider the
V V V V i V
mole fractions (n i =n tot ) x . We see that the ratios of the partial pressures to the total pressure
i

RT
P i n i V n i P i
are equal to the mole fractions ¼ ¼ ¼ x ¼ . As a corollary we note
i
RT
P tot n tot n tot P tot
V
additional conclusions as
n 1 n 2 n 3 P 1 P 2 P 3
þ ¼ 1, þ ¼ 1, and x þ x þ x þ ¼ 1:
þ þ þ þ 1 2 3
n tot n tot n tot P tot P tot P tot
The most common use of Dalton’s law is when gases are measured ‘‘over water,’’ that is, when a
pressure is measured in the presence of moisture, which produces a partial pressure of water vapor
as a gas, which in turn contributes a small pressure to the total pressure. This can occur when a
reaction produces a gas and the gas is trapped in a container inverted over water. Tables of the vapor
pressure of water are readily available in handbooks. Water is often in natural settings where gas
pressure is measured in the presence of dew or a layer of water as may occur in ‘‘wet’’ forensic
samples. In the distant past chemists often isolated gases as the product of a reaction and allowed the
gas to bubble through a water trap, thereby introducing water vapor pressure into the total pressure.
Example: Given a small amount of benzenediazonium chloride that is warmed gently in a closed
container to form chlorobenzene and N 2 . A tube is attached to the top of the container and inserted
under an inverted flask initially filled with water. As the reaction proceeds, most of the N 2 flows
through the tube and bubbles up under the water in the flask. After a while an estimated 450 mL of
the gas is trapped in the bubble and the pressure at the surface of the water is 750 mmHg and the
water temperature is 238C. Assuming we trapped most of the released N 2 (some is left in the original
flask and the tube) and there is a 1:1 stoichiometry of the moles of gas produced to the moles of
chlorobenzene, we can estimate the moles of chlorobenzene formed to be equal or greater than the
moles of N 2 . In a handbook we find that the vapor pressure of water is 2.8104 kPa at 238C because
all modern handbooks report data in SI units but if we have a manometer attached to the reaction
flask we can read the pressure in mmHg.

3
2:8104 10 Pa
(760 mm=atm) ffi 21:08 mmHg
P H 2 O ¼ 5
1:01325 10 Pa=atm