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CHAPTER
10 Nonideal Solutions

CHAPTER OUTLINE

10.1 Activities and Activity Using molecular arguments and experimental data, we obtained expressions for the
Coefficients chemical potentials m in ideal gas mixtures (Chapter 6) and in ideal and ideally dilute
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solutions (Chapter 9). All thermodynamic properties follow from these chemical
10.2 Excess Functions potentials. For example, we derived the reaction-equilibrium conditions for ideal gases
and ideally dilute solutions (the K° and K equilibrium constants), the conditions for
x
P
10.3 Determination of Activities phase equilibrium between an ideal or ideally dilute solution and its vapor (Raoult’s
and Activity Coefficients
law, Henry’s law), and the differences between the thermodynamic properties of an
10.4 Activity Coefficients on the ideal solution and the properties of the pure components ( mix V, mix H, mix S, mix G).
Molality and Molar We therefore know how to deal with ideal solutions. However, all solutions in the
Concentration Scales real world are nonideal. What happens when the system is not ideal? This chapter
deals with (a) nonideal liquid and solid solutions of nonelectrolytes (Secs. 10.1 to
10.5 Solutions of Electrolytes 10.4), (b) solutions of electrolytes (Secs. 10.5 to 10.9), and (c) nonideal gas mixtures
(Sec. 10.10). Chapter 11 considers reaction equilibrium in nonideal systems. Devia-
10.6 Determination of Electrolyte tions from ideality are often quite large and must be included for accurate results in
Activity Coefficients biochemical, environmental, and industrial applications of thermodynamics.
The chemical potentials in nonideal systems are usually expressed in terms of
10.7 The Debye–Hückel Theory of activities and activity coefficients, so our first task is to define these quantities and tell
Electrolyte Solutions
how they are measured.
10.8 Ionic Association
10.9 Standard-State 10.1 ACTIVITIES AND ACTIVITY COEFFICIENTS
Thermodynamic Properties of The chemical potentials are the key thermodynamic properties, since all other ther-
Solution Components
modynamic properties can be derived from the m ’s. For an ideal (id) or ideally dilute
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10.10 Nonideal Gas Mixtures liquid or solid solution of nonelectrolytes, the chemical potential of each component
is [Eqs. (9.42), (9.43), (9.58), and (9.59)]
10.11 Summary id
m m° RT ln x ideal or ideally dil. soln. (10.1)*
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where m° is the chemical potential in the appropriately defined standard state.
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id
Equation (10.1) gives ln x (m m°)/RT, or
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id
x exp31m m°2>RT 4 ideal or ideally dil. soln. (10.2)
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A nonideal solution is defined as one that is neither ideal nor ideally dilute. We
shall discuss the behavior of nonideal-solution components in terms of departures
from ideal or ideally dilute behavior. To make it easy to compare nonideal and ideal
behavior, we choose to express the nonideal chemical potentials m in a form that
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closely resembles the ideal chemical potentials in (10.1). For each component i of a
nonideal solution, we choose a standard state and symbolize the standard-state
chemical potential of i by m°. (The standard state will be chosen to correspond to the
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standard state used in either an ideal or ideally dilute solution; see below.) We then
define the activity a of substance i in any solution (nonideal or ideal) by
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a exp31m m°2>RT4 every soln. (10.3)
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