  A binary solution with short-range ordering (SRO) exhibits characteristic
solution thermodynamics. The Modified Quasichemical Model in the Pair
Approximation (MQMPA) can effectively capture the thermodynamic features of a
binary solution with a onefold SRO. However, once the SRO occurs at multiple
compositions in a binary solution, the MQMPA is in principle inconvenient to
treat the solution thermodynamics. It usually requires a large number of model
parameters to fit the thermodynamic data of such a solution. The present work
proposes the Modified Quasichemical Model in the Distinguishable-Pair
Approximation (MQMDPA), which is a further improvement of the MQMPA. The MQMDPA
can more realistically describe the solution thermodynamics with manifold SROs
using fewer model parameters. It benefits from grouping the ordered pairs,
which were assumed to be indistinguishable within the MQMPA, into several
distinguishable types. Each kind of ordered pair has unique coordination
numbers and pair energy, which is responsible for describing one of the SROs at
the desired composition and strength. Interestingly, the MQMDPA can be
completely transformed into the MQMPA when all kinds of ordered pairs are
assigned the same pair energy and coordination numbers. The distinguishable
pairs have thus become indistinguishable. Several real liquids with at least
two observed SROs were successfully treated by the MQMDPA to demonstrate its
effectiveness and reliability.
