PHYSICAL CHEMISTRY IN BRIEF

CHAP. 1: BASIC TERMS [CONTENTS] 38

The sum of mass fractions of all components equals one

∑k

i=1

wi= 1. (1.9)

We convert mole and mass fractions using the relations:

xi=

wi/Mi

∑k

j=1

wj/Mj

, wi=

xiMi

∑k

j=1

xjMj

. (1.10)

Example

A mixture contains 5 g of substance A with a molar massMA= 25 g mol−^1 , and 15 g of substance

B with a molar massMB= 75 g mol−^1. Calculate the mass fractions and the mole fractions.

Solution

Substituting into (1.8) gives

wA=

5

5 + 15

= 0. 25 , wB=

15

5 + 15

= 0. 75.

We calculate the mole fractions using the first of equations (1.10)

xA=

0. 25 / 25

0. 25 /25 + 0. 75 / 75

= 0. 5 , xB=

0. 75 / 75

0. 25 /25 + 0. 75 / 75

= 0. 5.

1.6.3 Volume fractionφi

Definition

φi=

Vi•

∑k

j=1

Vj•

=

xiVm,i•

∑k

j=1

xjVm,j•

, (1.11)