Physical Chemistry Third Edition

254 6 The Thermodynamics of Solutions

Themolar concentrationof componentiis defined by

ci

ni

V

(6.2-14)

whereniis the amount of the solute in moles andVis the volume of the solution. In SI

units the molar concentration is measured in moles per cubic meter (mol m−^3 ). If the

molar concentration is measured in moles per liter (mol L−^1 , sometimes abbreviated

as M), it is called themolarity. A common symbol for the molarity is the formula for

the substance inside square brackets:

ci[Fi] (6.2-15)

whereFiis an abbreviation for the formula of substancei. The molar concentra-

tion depends on the temperature because of thermal expansion, although the molality

does not.

EXAMPLE 6.7

Assuming that the coefficient of thermal expansion of an aqueous solution is the same as that

of water, 2. 07 × 10 −^4 K−^1 , find the molarity at 25.0◦C of a solution that has a molarity of

0.1000 mol L−^1 at 20.0◦C.

Solution

Consider a quantity of solution that has a volume at 20◦C of 1.000 L. The amount of solute is

n 2 (0.1000 mol L−^1 )(1.000 L) 0 .1000 mol

At 25◦C, the volume of the solution is

V(1.000 L)

[

1 +(2. 0661 × 10 −^4 K−^1 )(5.0K)

]

 1 .0010 L

The molarity (molar concentration) at 25.0◦Cis

c 2 

0 .1000 mol

1 .0010 L

 0 .0999 mol L−^1

In a dilute solution, the amounts of solutes are small and the volume of the solution

is nearly equal to the volume of the solvent used to make the solution

V≈n 1 Vm,1∗ (6.2-16)

whereVm,1∗ is the molar volume of the pure solvent (substance number 1). In this case

ci≈

ni

n 1 Vm,1∗

≈

xi

Vm,1∗

(dilute solution) (6.2-17)

EXAMPLE 6.8

Show that for a dilute solution, Henry’s law becomes

PikiVm,1∗ cik(c)i ci (6.2-18)