Answer to Question #156570 in General Chemistry for shane javier

Question

If the oxygen gas sample in #1 passed through a drier that decreased the pressure of the  mixture to 750 Torr and the pressure exerted by the water vapour is only 80% of the  saturated vapour pressure at the given temperature, what would be the pressure of the dry

oxygen?

Answer 1

Skills to Develop

To determine the contribution of each component gas to the total pressure of a mixture of gases

In our use of the ideal gas law thus far, we have focused entirely on the properties of pure gases with only a single chemical species. But what happens when two or more gases are mixed? In this section, we describe how to determine the contribution of each gas present to the total pressure of the mixture.

Partial Pressures

The ideal gas law assumes that all gases behave identically and that their behavior is independent of attractive and repulsive forces. If volume and temperature are held constant, the ideal gas equation can be rearranged to show that the pressure of a sample of gas is directly proportional to the number of moles of gas present:

P=n(RTV)=n×const.(1.6.1)

(1.6.1) P=n

(

R

T

V

)

=n×const.

Nothing in the equation depends on the identity of the gas—only the amount.

With this assumption, let’s suppose we have a mixture of two ideal gases that are present in equal amounts. What is the total pressure of the mixture? Because the pressure depends on only the total number of particles of gas present, the total pressure of the mixture will simply be twice the pressure of either component. More generally, the total pressure exerted by a mixture of gases at a given temperature and volume is the sum of the pressures exerted by each gas alone. Furthermore, if we know the volume, the temperature, and the number of moles of each gas in a mixture, then we can calculate the pressure exerted by each gas individually, which is its partial pressure, the pressure the gas would exert if it were the only one present (at the same temperature and volume).

To summarize, the total pressure exerted by a mixture of gases is the sum of the partial pressures of component gases. This law was first discovered by John Dalton, the father of the atomic theory of matter. It is now known as Dalton’s law of partial pressures. We can write it mathematically as

Ptot=P1+P2+P3+P4...=∑i=1nPi(1.6.2)

(1.6.2)

P

t

o

t

=

P

1

+

P

2

+

P

3

+

P

4

...=

∑

i

=

1

n

P

i

where Ptot

P

t

o

t

is the total pressure and the other terms are the partial pressures of the individual gases (up to n

n

component gases).