Concise Physical Chemistry

c12 JWBS043-Rogers September 13, 2010 11:27 Printer Name: Yet to Come

196 SOLUTION CHEMISTRY

TABLE 12.1 Vapor Pressures of

Acetone over Dilute Binary Solutions

of Acetone in Diethyl Ether.

X 2 p 2 (kPa)a

0.000 0.00

0.029 2.53

0.068 5.33

0.154 9.90

0.178 10.90

0.255 14.46

0.315 16.92

0.372 19.02

aThe units of pressure are kilopascals.

on the curve ofp 2 vs.X 2. This slope is the slope of the tangent linep 2 vs.X 2 for the

most dilute solutions and is approximately 2. 53 / 0. 0290 =87 kPa. Thus the Henry’s

law estimate ofp 2 atX 2 = 0 .20 is 0. 20 ( 87. 2 )= 17 .4kPa.

The interpolated value ofp 2 atX 2 = 0 .20 is

0. 255 − 0. 200

0. 255 − 0. 178

=

14. 5 −p 2

14. 5 − 10. 9

= 0. 71

p 2 = 14. 5 − 0 .71(3.6)= 11 .9kPa

The activity coefficient is the ratio of the actual value to the Henry’s law estimateγ=

11. 9 / 17. 4 = 0 .68 and the activity is the effective concentration of acetone relative to

the Henry’s law standarda=γX 2 = 0 .68 and( 0. 20 )= 0 .14.

Example 12.2

What are the mole fractions of solvent and solute in a 0.1000 molar solution of NaCl?

Solution 12.2 The number of grams of NaCl in 1 liter of the solution is

0. 1000 =

0. 1000 ( 22. 99 + 35. 45 )

1 .000 liter

=

5. 844

1 .000 dm^3

The densityρ=m/Vof pure solid NaCl is 2.17 g cm−^3 , so NaCl takes up

V=m/ρ= 5. 844 / 2. 17 = 2 .69 cm^3

This amount of the total volume of the solution is taken up by the solid NaCl, leaving

997.3 cm^3 of water in the 1.000 dm^3 of solution. Now that we know the volume of

solvent, we can calculate the mole fractions. Recall that we have 0.1000 mol of NaCl