252
6 The Thermodynamics of Solutions
Exercise 6.10
Carry out the steps to obtain Eq. (6.2-6).
E X A M P L E 6.5
The value of the distribution coefficient for I 2 between water (phase B) and carbon tetrachloride (phase A) is approximately equal to 0.0022 at 25.0 ◦ C. If a solution containing 0.0100 mol
of I 2 and 1.000 mol of water is equilibrated with 1.000 mol of carbon tetrachloride at this
temperature, find the final mole fraction of iodine in each phase.
Solution
Denote I 2 by the subscript i. Since the mole fractions of I 2 are small, we can write to a good
approximation
x
(H 2 O)
i
+ x
(CCl 4 )
i
≈ 0.0100
x
(H 2 O)
i
x
(CCl 4 )
i
x
(H 2 O)
i
0.0100 − x
(H 2 O)
i
0.0022
x
(H 2 O)
i
(0.0022)(0.0100 − x
(H 2 O)
i
) 0.00022 − (0.0022)x
(H 2 O)
i
1.0022x
(H 2 O)
i
0.000022
x
(H 2 O)
i
0.000022
1.0022
0.000022
x
(CCl 4 )
i
0.0100 − 0.000022 0.009978
Other Measures of Composition
The molality of component i (a solute) in a solution is defined by
m i
n i
w 1
(definition of molality)
(6.2-7)
where n i is the amount of component i in moles and w 1 is the mass of the solvent
(component 1) in kilograms. The units of molality are mol kg −1 , sometimes referred
to as “molal.” If M 1 is the molar mass of the solvent, then
w 1 n 1 M 1
(6.2-8)
so that the mole fraction of component i is given by
x i
n i
n 1 + n 2 + · · · + n c
n i
(w 1 /M 1 ) + n 2 + · · · + n c
(6.2-9)
6 The Thermodynamics of Solutions
Exercise 6.10
Carry out the steps to obtain Eq. (6.2-6).
E X A M P L E 6.5
The value of the distribution coefficient for I 2 between water (phase B) and carbon tetrachloride (phase A) is approximately equal to 0.0022 at 25.0 ◦ C. If a solution containing 0.0100 mol
of I 2 and 1.000 mol of water is equilibrated with 1.000 mol of carbon tetrachloride at this
temperature, find the final mole fraction of iodine in each phase.
Solution
Denote I 2 by the subscript i. Since the mole fractions of I 2 are small, we can write to a good
approximation
x
(H 2 O)
i
+ x
(CCl 4 )
i
≈ 0.0100
x
(H 2 O)
i
x
(CCl 4 )
i
x
(H 2 O)
i
0.0100 − x
(H 2 O)
i
0.0022
x
(H 2 O)
i
(0.0022)(0.0100 − x
(H 2 O)
i
) 0.00022 − (0.0022)x
(H 2 O)
i
1.0022x
(H 2 O)
i
0.000022
x
(H 2 O)
i
0.000022
1.0022
0.000022
x
(CCl 4 )
i
0.0100 − 0.000022 0.009978
Other Measures of Composition
The molality of component i (a solute) in a solution is defined by
m i
n i
w 1
(definition of molality)
(6.2-7)
where n i is the amount of component i in moles and w 1 is the mass of the solvent
(component 1) in kilograms. The units of molality are mol kg −1 , sometimes referred
to as “molal.” If M 1 is the molar mass of the solvent, then
w 1 n 1 M 1
(6.2-8)
so that the mole fraction of component i is given by
x i
n i
n 1 + n 2 + · · · + n c
n i
(w 1 /M 1 ) + n 2 + · · · + n c
(6.2-9)