The Foundations of Chemistry

and vapor are present. Table 12-4 displays the vapor pressure of water near room temper-
ature.
The relevant point here is that a gas collected over water is “moist”; that is, it is satu-
rated with water vapor. Measuring the atmospheric pressure at which the gas is collected,
we can write

PatmPgasPH 2 O or PgasPatm
PH 2 O

Example 12-19 provides a detailed illustration.

EXAMPLE 12-19 Gas Collected Over Water

Hydrogen was collected over water (Figure 12-7) at 21°C on a day when the atmospheric pres-
sure was 748 torr. The volume of the gas sample collected was 300. mL. (a) How many moles
of H 2 were present? (b) How many moles of water vapor were present in the moist gas mixture?
(c) What is the mole fraction of hydrogen in the moist gas mixture? (d) What would be the
mass of the gas sample if it were dry?

Plan

(a) The vapor pressure of H 2 O, PH 2 O19 torr at 21°C, is obtained from Table 12-4. Applying
Dalton’s Law, PH 2 Patm
PH 2 O. We then use the partial pressure of H 2 in the ideal gas equa-
tion to find the number of moles of H 2 present. (b) The partial pressure of water vapor (the
vapor pressure of water at the stated temperature) is used in the ideal gas equation to find the
number of moles of water vapor present. (c) The mole fraction of H 2 is the ratio of its partial
pressure to the total pressure. (d) The number of moles found in part (a) can be converted to
mass of H 2.

Solution

(a)PH 2 Patm
PH 2 O(748
19) torr729 torr0.959 atm

We also know

V300. mL0.300 L and T21°C273°294 K

Solving the ideal gas equation for nH 2 gives

nH 2 1.19 10 
^2 mol H 2

(b)PH 2 O19 torr0.025 atm

Vand Thave the same values as in part (a).

nH 2 O3.1 10 
^4 mol H 2 O vapor

(c)XH 2 0.974

(d) _?_g H 2 1.19 10
^2 mol2.40 10
^2 g H 2

You should now work Exercise 64.

2.02 g



1 mol

729 torr



748 torr

PH 2



Ptotal

(0.025 atm)(0.300 L)




0.0821 m

L

o

a

l

t



m

K

(294 K)

PH 2 OV



RT

1 atm



760 torr

(0.959 atm)(0.300 L)




0.0821 m

L

o

a

l

t



m

K

(294 K)

PH 2 V



RT

1 atm



760 torr

Remember that eachgas occupies the

totalvolume of the container.

At STP, this dry hydrogen would

occupy 267 mL. Can you calculate

this?

12-11 Dalton’s Law of Partial Pressures 461

TABLE 12-4 Vapor Pressure

of Water

Near Room

Temperature

Vapor Pressure

Temperature of Water

(°C) (torr)

19 16.48

20 17.54

21 18.65

22 19.83

23 21.07

24 22.38

25 23.76

26 25.21

27 26.74

28 28.35