PHYSICAL CHEMISTRY IN BRIEF

CHAP. 6: THERMODYNAMICS OF HOMOGENEOUS MIXTURES [CONTENTS] 165

Example

A mixture of light and heavy water in the liquid phase behaves ideally. Calculate the activities of

heavy wateraD 2 O, a[Dx 2 ]O, anda[Dm 2 ]Oin a mixture resulting from the addition of 1 g D 2 O to 500

g H 2 O.

Solution

We first calculate the mole fraction and molality of heavy water

xD 2 O =

1 / 20. 027

500 / 18 .015 + 1/ 20. 027

= 0. 001796

mD 2 O =

1 / 20. 027

0. 5

= 0. 09987 mol kg−^1.

The activities of heavy water in the given mixture are

aD 2 O = a

[x]

D 2 O=xD 2 O= 0.^001796 ,

a[Dm 2 ]O =

mD 2 O

mst

= 0. 09987.

6.5.5 Activity coefficient

The value of theactivity coefficientdepends on the chosen standard state. The following
activity coefficients are used most often

γi =

ai

xi

, (6.99)

γi[x] =

a[ix]

xi

, (6.100)

γi[c] =

a[ic]

ci/cst

, (6.101)

γi[m] =

a[im]

mi/mst

. (6.102)