Physical Chemistry , 1st ed.

point, (^) fusGMPequals zero, so we are simply adding zero to equation 7.38.
We g e t
ln xdissolved solute
R
fu
T
sG
M
M
P
P



ln xdissolved solute

R

fu

T

sH^ f

R

usS^

R

fu

T

sH

M

M

P

P^ fu

R

sSMP

Again, we are using the subscript MP to indicate that these Hand Svalues
are for the melting-point temperature. If, however, the changes in enthalpy and

entropy do not change much with temperature, we can approximate (^) fusH
(^) fusHMPand (^) fusS (^) fusSMP. We substitute to eliminate (^) fusHMPand (^) fusSMP.

ln xdissolved solute

R

fu

T

sH^ f

R

usS^

RT

fu

M

sH

P



(^) f
R
usS
Then, we note that the two terms in (^) fusScancel. The two terms in (^) fusHcan
be combined and factored; the final equation is

ln xdissolved solute

(^) f
R

usH

T

1



TM

1

P

 (7.39)

This is the basic equation for calculating solubilities of solids in solutions. As
usual, all temperatures must be in units of absolute temperature. Note that the
solubility is given in terms of the mole fraction of the dissolved solute in
the solution. If a solubility in terms ofmolarity or grams per liter is desired,
the appropriate conversions must be applied.

Example 7.10

Calculate the solubility of solid naphthalene, C 10 H 8 , in liquid toluene,

C 6 H 5 CH 3 , at 25.0°C if the heat of fusion of naphthalene is 19.123 kJ/mol and

its melting point is 78.2°C.

Solution

Using equation 7.39, we get

ln xdissolved solute 

298.

1

15 K



351.

1

35 K



Notice that we have converted the value for Rinto kJ units, and also the tem-

perature values into absolute temperature. All of the units cancel algebraically,

as they should. We get

ln xdissolved solute2300.1(0.0033542 0.0028461)

ln xdissolved solute1.1687

Now we take the inverse natural logarithm:

xdissolved solute0.311

Experimentally, the mole fraction xdissolved soluteis 0.294 for naphthalene

dissolved in toluene. Note the good agreement between the calculated and

19.123 mkoJl



0.008314 moklJK

(^) fusHMPTMP (^) fusSMP

RTMP
( (^) fusHT (^) fusS)

RT
( (^) fusHT (^) fusS)

RT
7.6 Liquid/Solid Solutions 187