Thermodynamics and Chemistry

CHAPTER 9 MIXTURES

9.1 COMPOSITIONVARIABLES 224

9.1.4 Binary solutions

We may write simplified equations for a binary solution of two substances, solvent A and
solute B. Equations9.1.1–9.1.4become

xBD

nB

nACnB

(9.1.5)

(binary solution)

wBD

nBMB

nAMACnBMB

(9.1.6)

(binary solution)

cBD

nB

V

D

nB

nAMACnBMB

(9.1.7)

(binary solution)

mBD

nB

nAMA

(9.1.8)

(binary solution)

The right sides of Eqs.9.1.5–9.1.8express the solute composition variables in terms of the
amounts and molar masses of the solvent and solute and the densityof the solution.
To be able to relate the values of these composition variables to one another, we solve
each equation fornBand divide bynAto obtain an expression for the mole rationB=nA:

from Eq.9.1.5

nB

nA

D

xB

1 xB

(9.1.9)

(binary solution)

from Eq.9.1.6

nB

nA

D

MAwB

MB.1wB/

(9.1.10)

(binary solution)

from Eq.9.1.7

nB

nA

D

MAcB

MBcB

(9.1.11)

(binary solution)

from Eq.9.1.8

nB

nA

DMAmB (9.1.12)

(binary solution)

These expressions fornB=nAallow us to find one composition variable as a function of
another. For example, to find molality as a function of concentration, we equate the expres-
sions fornB=nAon the right sides of Eqs.9.1.11and9.1.12and solve formBto obtain

mBD

cB

MBcB

(9.1.13)