PHYSICAL CHEMISTRY IN BRIEF

CHAP. 6: THERMODYNAMICS OF HOMOGENEOUS MIXTURES [CONTENTS] 166

U Main unit:dimensionless quantity.

Example

For a solution of sucrose (2) in water (1), which at 100◦C contains one mole percent sucrose,

we haveγ 2 = 0. 0064 , γ[ 2 x]= 1. 108 andγ 2 [m]= 1. 097. Calculate the respective activities.

Solution

The molality of sucrose in the given solution is

m 2 = (1000× 0 .01)/(18. 015 × 0 .99) = 0. 5607 mol kg−^1 , and the activities are obtained from

relations (6.99), (6.100) and (6.102).

a 2 = 0. 01 × 0 .0064 = 0. 000064 ,

a

[x]

2 = 0.^01 ×^1 .108 = 0.^01108 ,

a[ 2 m] = (0. 5607 /1)× 1 .097 = 0. 6151.

Relation to the partial mole excess Gibbs energy

The activity coefficientγiis related to the partial molar excess Gibbs energy by

RTlnγi=G

E

i. (6.103)

Given thatRTlnγiis the partial molar quantity to ∆GE, we have

∆GE=RT

∑k

i=1

xilnγi. (6.104)

Example

Derive relation (6.103).