Thermodynamics and Chemistry

CHAPTER 11 REACTIONS AND OTHER CHEMICAL PROCESSES

11.1 MIXINGPROCESSES 305

TSmid(mix)

Hmid(mix)

Gidm(mix)

 2

 1

0

1

2

0:0 0:2 0:4 0:6 0:8 1:0

xA

quantity / kJ mol

^1

Figure 11.2 Molar mixing quantities for a binary ideal mixture at298:15K.

11.1.3 Excess quantities

Anexcess quantityXEof a mixture is defined as the difference between the value of the
extensive propertyXof the real mixture andXid, the value for a hypothetical ideal mixture
at the same temperature, pressure, and composition.
Anexcess molar quantityXmEis the excess quantity divided byn, the total amount of
all constituents of the mixture. Examining the dependence of excess molar quantities on
composition is a convenient way to characterize deviations from ideal-mixture behavior.
Excess molar quantities are related to molar mixing quantities as follows:

XmED.XXid/=nD

X

i

niXi

X

i

niXiid

!

=n

D

X

i

xi

XiXiid

D

X

i

xi.XiXi/

X

i

xi.XiidXi/

DÅXm(mix)ÅXmid(mix) (11.1.13)

By substituting expressions forÅXmid(mix) from Eqs.11.1.8–11.1.12in Eq.11.1.13, we ob-
tain the following expressions for the excess molar Gibbs energy, entropy, enthalpy, internal
energy, and volume:

GmEDÅGm(mix)RT

X

i

xilnxi (11.1.14)

SmEDÅSm(mix)CR

X

i

xilnxi (11.1.15)

HmEDÅHm(mix) (11.1.16)