Physical Chemistry Third Edition

252 6 The Thermodynamics of Solutions

Exercise 6.10

Carry out the steps to obtain Eq. (6.2-6).

EXAMPLE 6.5

The value of the distribution coefficient for I 2 between water (phase B) and carbon tetrachlo-

ride (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 subscripti. Since the mole fractions of I 2 are small, we can write to a good

approximation

x(Hi^2 O)+x(CCli^4 )≈ 0. 0100

x(Hi^2 O)

x(CCli^4 )



x(Hi^2 O)

0. 0100 −x(Hi^2 O)

 0. 0022

xi(H^2 O)(0.0022)(0. 0100 −x(Hi^2 O)) 0. 00022 −(0.0022)x(Hi^2 O)

1. 0022 x(Hi^2 O) 0. 000022

x(Hi^2 O)

0. 000022

1. 0022

 0. 000022

x(CCli^4 ) 0. 0100 − 0. 000022  0. 009978

Other Measures of Composition

Themolalityof componenti(a solute) in a solution is defined by

mi

ni

w 1

(definition of molality) (6.2-7)

whereniis the amount of componentiin moles andw 1 is the mass of the solvent

(component 1) in kilograms. The units of molality are mol kg−^1 , sometimes referred

to as “molal.” IfM 1 is the molar mass of the solvent, then

w 1 n 1 M 1 (6.2-8)

so that the mole fraction of componentiis given by

xi

ni

n 1 +n 2 + ··· +nc



ni

(w 1 /M 1 )+n 2 + ··· +nc

(6.2-9)