Physical Chemistry , 1st ed.

equilibrium constant. Note that this is not the case in conditions of extreme
pressures or temperatures.
For chemical species that are dissolved in solution (usually water), activities
are defined in terms of the mole fraction:

aiixi (5.15)

where iis the activity coefficient.For solutes, the activity coefficient ap-
proaches 1 as the mole fraction approaches zero:

xlim

i→^0

i1limx

i→^0

(ai) xi

Mole fractions can be related to other defined concentration units. The
strictest mathematical relationship is between mole fraction and molality,mi,
and is

mi

(1

10

x

0

i

0

)

x

i

Mi



where Miis the molecular weight of the solute in grams per mole, and the 1000
factor in the numerator is for a conversion between grams and kilograms. For
dilute solutions, the mole fraction of the solute is small compared to 1, so the
xiin the denominator can be neglected. Solving for xi,we get

ximi 

1

M

00

i

0



Thus, the activity for solutes in dilute solution can be written as

aii mi 

1

M

00

i

0



Using equation 5.11, we substitute for the activity to get

ii°RTln i mi 

1

M

00

i

0



Since Miand 1000 are constants, the logarithm term can be separated into two
terms, one incorporating these constants and the other incorporating the ac-
tivity coefficient and the molality:

i°iRTln

1

M

00

i

0

RTln (i mi)

The first two terms on the right side of the equation can be combined to make
a “new” standard chemical potential, which we will designate i. The above
equation becomes
iiRTln (i mi)

Comparing this to equation 5.11 gives us a useful redefinition of the activity
of dissolved solutes:

aii mi (5.16)

Equation 5.16 implies that concentrations can be used to express the effect of
dissolved solutes in reaction quotient and equilibrium constant expressions. In
order that aibe unitless, we divide the expression by the standard molal con-
centration of 1 mol/kg, symbolized by m°:

ai

i

m

°

mi

 (5.17)

5.4 Solutions and Condensed Phases 131