are using subscripts to denote the component, and superscripts to denote the phase; aq denotes the liquid aqueous solution). We define our standard state as that of the pure substance. According to eqn. 3.48, the chemical potential of water in the solution can be expressed as:
(3.59)
where
(3.60)
Ice will incorporate very little salt; if we assume it is a pure phase, we may write eqn. 3.60 as:
(3.60a)
or
(3.61)
(The order is important: eqn. 3.60a describes the freezing process, 3.61 the melting process. These processes will have equal and opposite entropies, enthalpies, and free energies.) The left-hand side of eqn. 3.61 is the Gibbs free energy of melting for pure water, which we denote as
We may rewrite eqn. 3.61 as:
(3.62)
If we assume that ΔH and ΔS are independent of temperature (which is not unreasonable over a limited temperature range) and we assume pressure is constant as well, the left-hand side of the equation may also be written as:
(3.63)
Substituting eqn. 3.63 into 3.62:
(3.64)
At the melting temperature of pure water,
Substituting this into eqn. 3.64 and rearranging:
(3.65)
Further rearrangement yields:
For a reasonably dilute solution, the activity of water will approximately equal its mole fraction, so that:
(3.66)
The entropy of melting is always positive, and since X is always less than 1, the left-hand side of eqn. 3.66 must always be positive. Thus, the ratio
3.7 ELECTROLYTE SOLUTIONS
Electrolyte solutions are solutions in which the solute dissociates to form ions, which facilitate electric conduction. Seawater is an obvious example of a natural electrolyte solution, but all natural waters are also electrolytes, though generally more dilute ones. These solutions, which Lavoisier* called the “rinsings of the Earth,” are of enormous importance in many geologic processes.
3.7.1 The nature of water and water–electrolyte interaction
There is perhaps no compound more familiar to us than H2O. Commonplace though it might be, H2O is the most remarkable compound in nature. Its unusual properties include: the highest heat capacity of all solids and liquids except ammonia, the highest latent heat of vaporization of all substances, the highest surface tension of all liquids, its maximum density is at 4°C, with density decreasing below that temperature (negative coefficient of thermal expansion), the solid form is less dense than the liquid (negative Clapeyron slope), and finally, it is the best solvent known, dissolving more substances and in greater quantity than any other liquid. We will digress here briefly to consider the structure and properties of H2O and the nature of water–electrolyte interactions from a microscopic perspective.
Many of the unusual properties of water arise from its nonlinear polar structure, which is illustrated in Figure 3.9a. The polar nature of water gives rise to van der Waals forces and the hydrogen bond discussed in Chapter 1. The hydrogen bond, which forms between hydrogen and oxygen atoms of adjacent molecules, imposes a dynamic partial structure on liquid water (Figure 3.9b). These bonds continually break and new ones reform, and there is always some fraction of unassociated molecules. On average, each water molecule is coordinated by four other water molecules. When water boils, all hydrogen bonds are broken. The energy involved in breaking these bonds accounts for the high heat of vaporization.
