CHAP. 6: THERMODYNAMICS OF HOMOGENEOUS MIXTURES [CONTENTS] 164
- Dependence of activity on composition
Activity can be written as a product of dimensionless concentration (xi, ci/cst, mi/mst)
and the activity coefficient [see6.5.5], which is the function of temperature, pressure
and composition.
- For the standard state of a pure component at the temperature and pressure of the
system we have
lim
xi→ 1
ai/xi= 1. (6.95)
It follows from this relation that when choosing the given standard state, we can replace
activity with a mole fraction in the component prevailing in the mixture.
- For the standard states of infinite dilution we have
lim
xi→ 0
a[ix]
xi
= 1, (6.96)
lim
ci→ 0
a[ic]cst
ci
= 1, (6.97)
lim
mi→ 0
a[im]mst
mi
= 1. (6.98)
It follows from these limits that when choosing the standard states of infinite dilution, we
can replace activity with the respective concentration quantity in the component which
is enough diluted in the solution.
- For an ideal mixture, activity equals dimensionless concentration (xi, ci/cstormi/mst)
for an arbitrary composition.
Example
A mixture of benzene and toluene in the liquid phase behaves as an ideal mixture. Calculate the
activity of benzene in a mixture that results from the mixing of one mole of benzene with nine
moles of toluene at 25◦C.
Solution
The mole fraction of benzene and its activity are
xbenzene=nbenzene/(nbenzene+ntoluene)= 1/(1 + 9) = 0.1,abenzene= 0.1.
