Concise Physical Chemistry

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

PROBLEMS, EXAMPLES, AND EXERCISE 195

Ammonia

Molality

0 5 10 15 20 25 30 35

Freezing Point

-100

-80

-60

-40

-20

0

FIGURE 12.7 Lowering of the freezing point of water by ammonia (CRC Handbook

of Chemistry and Physics, 2008–2009). The straight line has the theoretical slope of

–1.86 K mol−^1. Open circles have had their molality corrected for hydration of NH 3.

The straight line in Fig. 12.7 was calculated from
Tf=− 1. 86 m, and the three

open circles were calculated by correction of the molality for a hydration number of

1.8 by the Zavitsas method. The small deviation of the open circles from the straight

line is due to failures in some of the approximations made in the derivation ofKf(for

example, lnX 1 ∼=−X 2 ). They can be corrected in a more rigorous derivation (see

Problems). Hydration numbers for many other solutes are known and are usually

higher than 1.8, meaning that the departure of the actual colligative property from

its ideal estimate is correspondingly greater. The approach to ideal behavior at small

NH 3 concentrations in Fig. 12.7 shows the meaning of the term “limiting law” quite

graphically. The phenomenon described here is not restricted to any one colligative

property or to water as a solvent; it is general.

PROBLEMS, EXAMPLES, AND EXERCISE

Example 12.1 Partial Pressures

If we carry out experimental determinations of the partial pressure of acetone over

solutions of acetone in diethyl ether, results for small values ofX 2 will be something

like Fig. 12.3. Some typical experimental data are given in Table 12.1. Examine

the data for the pressure of acetone over diethyl ether and obtain an estimate of the

activity coefficient for acetone at mole fractionX 2 = 0 .20.

Solution 12.1 A first estimate of the Henry’s law constant, which is a limiting law,

can be found from the limiting slope ofp 2 as a function ofX 2 for the first few points