Thermodynamics and Chemistry

CHAPTER 9 MIXTURES

9.7 ACTIVITY OF ANUNCHARGEDSPECIES 271

components:

Substanceiin a gas mixture iDi(g)CRTlnai(g) (9.7.3)

Substanceiin a liquid or solid mixture iDiCRTlnai (9.7.4)

Solvent A of a solution ADACRTlnaA (9.7.5)

Solute B, mole fraction basis BDx;BCRTlnax;B (9.7.6)

Solute B, concentration basis BDc;BCRTlnac;B (9.7.7)

Solute B, molality basis BDm;BCRTlnam;B (9.7.8)

9.7.2 Activities and composition

We need to be able to relate the activity of componentito the mixture composition. We
can do this by finding the relation between the chemical potential of componenti in its
reference state and in its standard state, both at the same temperature. These two chemical
potentials,refi andi, are equal only if the mixture is at the standard pressurep.
It will be useful to define the following dimensionless quantity:

i

def

D exp

refi i

RT

!

(9.7.9)

The symbolifor this quantity was introduced by Pitzer and Brewer.^11 They called it
the activity in a reference state. To see why, compare the definition of activity given by
iDiCRTlnaiwith a rearrangement of Eq.9.7.9:refi DiCRTlni.
At a given temperature, the differencerefi idepends only on the pressurepof the
mixture, and is zero whenpis equal top. Thusiis a function ofpwith a value of 1
whenpis equal top. This book will callithepressure factorof speciesi.
To understand how activity is related to composition, let us take as an example the
activityam;Bof solute B based on molality. From Eqs.9.5.18and9.7.8, we have

BDrefm;BCRTln



(^) m;B
mB
m



Dm;BCRTlnam;B (9.7.10)

The activity is then given by

lnam;BD

refm;Bm;B

RT

Cln



(^) m;B
mB
m



Dlnm;BCln



(^) m;B
mB
m



(9.7.11)

am;BDm;B (^) m;B
mB
m

(9.7.12)

The activity of a constituent of a condensed-phase mixture is in general equal to the product
of the pressure factor, the activity coefficient, and the composition variable divided by the
standard composition.
Table9.5on the next page gives explicit expressions for the activities of various kinds
of nonelectrolyte substances.

(^11) Ref. [ 105 ], p. 249.