Page 338 - Physical Chemistry

lev38627_ch10.qxd 3/14/08 1:07 PM Page 319

319
Section 10.9
where g and m are the sucrose activity coefficient and molality in the sat-
m,i,sat i,sat Standard-State Thermodynamic
urated solution, m° 1 mol/kg, and G* is the molar G of pure sucrose. Properties of Solution Components
m,i
Subtraction of G (T, P°) from each side of (10.80) gives
elem
G* G elem m° G elem RT ln 1g m,i,sat m i,sat >m°2
m,i
m,i
The left side of this equation is by definition G° of pure sucrose; m° G
f m,i elem
on the right side is G° of sucrose(aq) [Eq. (10.78)]. Therefore
f
¢ G°1i*2 ¢ G°1i, sln2 RT ln 1g m,i,sat m i,sat >m°2 (10.81)
f
f
1544 kJ>mol ¢ G°1sucrose, aq2 38.314 J>1mol K241298 K2 ln12.87
6.052
f
¢ G° 1sucrose, aq2 1551 kJ>mol
298
f
To find H°of sucrose(aq), we start with H q of sucrose, which is the dif-
f diff
ference at 1 bar between the partial molar enthalpy of sucrose in water at infinite
q
dilution and the molar enthalpy of pure sucrose: H q H i H* [Eq. (9.38)].
m,i

diff,i
q
But H i H° m,i (Prob. 10.22), so

q
q
¢H diff,i H i H* H° H* 1H° H° elem 2 1H* H° elem 2
m,i
m,i
m,i
m,i
m,i
¢H q ¢ H°1i, sln2 ¢ H°1i*2 (10.82)
f
f
diff,i
5.9 kJ>mol ¢ H°1sucrose, aq2 1 2221 kJ>mol2
f
¢ H°1sucrose, aq2 2215 kJ>mol
f
Using
¢ G°1i, sln2 ¢ H°1i, sln2 T ¢ S°1i, sln2 (10.83)
f
f
f

one finds S ° 298 (sucrose, aq) 408 J/(mol K) (Prob. 10.48).
Exercise
Subtract standard-state thermodynamic properties of the elements from m°

i
H° i TS ° i [Eq. (9.28)] to derive Eq. (10.83).
Electrolyte Solutions
Standard-state thermodynamic properties for electrolyte solutes can be found by the
same method as used for sucrose(aq) in the preceding example. For an electrolyte in
solution, m m° nRT ln (n g m /m°) [Eq. (10.51)]. Equating m in a saturated so-
i m,i i i
lution to m of the pure solid electrolyte leads to the following equation [analogous to
(10.81)] for electrolyte i:
¢ G°1i*2 ¢ G°1i, sln2 nRT ln 1n g m i,sat >m°2 (10.84)
,sat
f
f

From (10.82) and (10.83), we can find H° and S° of electrolyte i in solution.
f
For electrolyte solutions, we can work with thermodynamic properties (m , H , S ,
i
i
i
etc.) of the electrolyte as a whole, and these properties are experimentally deter-
minable. Suppose we have 30 common cations and 30 common anions. This means
we must measure thermodynamic properties for 900 electrolytes in water. If we could
determine single-ion chemical potentials m and m , we would then need to mea-

sure values for only 60 ions, since m for an electrolyte can be determined from m
i
i
n m n m [Eq. (10.38)]. Unfortunately, single-ion chemical potentials cannot

readily be measured. What is done is to assign arbitrary values for thermodynamic

properties to the aqueous H ion. Thermodynamic properties of other aqueous ions

are then tabulated relative to H (aq).