1.1 What is Chemistry?

14.3. Gas Mixtures http://www.ck12.org

a.Moles of each gas:

nF 2 =380 g F 2 ×

1 mol F 2

38 g F 2

= 10 .mol F 2

nNe=100 g Ne×

1 mol Ne

20 g Ne

=5 mol Ne

b.Total moles of all gases:

nt=nF 2 +nNe

nt= 10 + 5 = 15

c.Mole fraction of each gas:

XF 2 =

10 mol

15 mol

= 0. 67

XNe=

5 mol

15 mol

= 0. 33

d.Total pressure of the mixture:

Pt=

nRT

V

=

(15 mol)( 0 .08206 L·atm·K−^1 ·mol−^1 )(273 K)

(112 L)

Pt= 3 .0 atm

e.Partial pressure of each gas:

PF 2 =XF 2 Pt= ( 0. 67 )( 3 .0 atm) = 2 .0 atm

PNe=XNePt= ( 0. 33 )( 3 .0 atm) = 0 .99 atm

Diffusion and Effusion

Gas molecules are always in motion. We can measure the movement of gases in various ways. We have already seen
that the temperature is related to the average speed of the gas particles. Because individual particles are all moving
in random directions, the sample as a whole does not move this fast from place to place. However, we can also look
at the speed at which an entire gas sample moves. What if a gas is transferred to a larger container? Eventually,
the random motions of the gas particles will result in an even distribution throughout all the available space. This
process is referred to asdiffusion.

Another related process is effusion. Effusionis the process of a confined gas escaping through a tiny hole in its
container. Effusion can be observed by the fact that a helium-filled balloon will stop floating and sink to the floor
after a day or so. This is because the helium gas effuses through tiny pores in the balloon. Both diffusion and
effusion are related to the speed at which various gas molecules move. Gases that have a lower molar mass effuse
and diffuse at a faster rate than gases that have a higher molar mass. While they are similar processes, there is a
key difference between diffusion and effusion. Diffusion describes the process of a gas spreading out at a constant
pressure, such as throughout a room. Effusion, on the other hand, describes the process of a gas spreading out from
a high pressure surroundings to lower pressure surroundings.

Scottish chemist Thomas Graham (1805-1869) studied the rates of effusion and diffusion for various gases. Gra-
ham’s Law of Effusionstates that the rate of effusion or diffusion of a gas is inversely proportional to the square
root of the molar mass of the gas.

Ratee f f usion∝√^1
MM

Relative rates of effusion for gases of different molecular masses can be studied by looking at the time needed for a
given gas to effuse through a pinhole in a vacuum (Figure14.10). The lighter the gas molecules are, the smaller the
number in the denominator, and the faster the gas effuses and diffuses.