charge and the oxygen retains a partial positive charge. (b) Partial structure present in liquid water. Lines connecting adjacent molecules illustrate hydrogen bonds."/>
Figure 3.9 (a) Structure of the water molecule. Bond angle in the liquid phase is 108°, and 105° in the gas. The hydrogens retain a partial positive charge and the oxygen retains a partial positive charge. (b) Partial structure present in liquid water. Lines connecting adjacent molecules illustrate hydrogen bonds.
The dissolving power of water is due to its dielectric nature. A dielectric substance is one that reduces the forces acting between electric charges. When placed between two electrically charged plates (a capacitor), water molecules will align themselves in the direction of the electric field. As a result, the molecules oppose the charge on the plates and effectively reduce the transmission of the electric field. The permittivity, ε, of a substance is the measure of this effect. The relative permittivity, or dielectric constant, εr, of a substance is defined as the ratio of the capacitance observed when the substance is placed between the plates of a capacitor to the capacitance of the same capacitor when a vacuum is present between the plates:
(3.67)
where ε0 is the permittivity of a vacuum (8.85 × 10−12 C2/J m). The relative permittivity of water is 78.54 at 25°C and 1 atm. For comparison, the relative permittivity of methane, a typical nonpolar molecule, is 1.7.
Water molecules surrounding a dissolved ion will tend to align themselves to oppose the charge of the ion. This insulates the ion from the electric field of other ions. This property of water accounts in large measure for its dissolving power. For example, we could easily calculate that the energy required to dissociate NaCl (i.e., the energy required to move Na+ and Cl– ions from their normal interatomic distance in a lattice, 236 pm, to infinite separation) is about 585 kJ/mol. Because water has a dielectric constant of about 80, this energy is reduced by a factor of 80, so only 7.45 kJ are required for dissociation.
The charged nature of ions and the polar nature of water result in the solvation of dissolved ions. Immediately adjacent to the ion, water molecules align themselves to oppose the charge on the ion, such that the oxygen of the water molecule will be closest to a cation (Figure 3.10). These water molecules are called the first solvation shell or layer and they are effectively bound to the ion, moving with it as it moves. Beyond the first solvation shell is a region of more loosely bound molecules that are only partially oriented, called the second solvation shell or layer. The boundary of this latter shell is diffuse: there is no sharp transition between oriented and unaffected water molecules. The energy liberated in this process, called the solvation energy, is considerable. For NaCl, for example, it is −765kJ/mol (it is not possible to deduce the solvation energies of Na+ and Cl– independently). The total number of water molecules bound to the ion is called the solvation number. Solvation effectively increases the electrostatic radius of cations by about 90 pm and of anions by about 10 pm per unit of charge.
Figure 3.10 Solvation of a cation in aqueous solution. In the first solvation shell, water molecules are bound to the cation and oriented so that the partial negative charge on the oxygen faces the cation. In the second solvation shell, molecules are only loosely bound and partially oriented.
An additional effect of solvation is electrostriction. Water molecules in the first solvation sphere are packed more tightly than they would otherwise be. This is true, to a lesser extent, of molecules in the secondary shell. In addition, removal of molecules from the liquid water structure causes partial collapse of this structure. The net effect is that the volume occupied by water in an electrolyte solution is less than in pure water, which can lead to negative apparent molar volumes of solutes, as we shall see. The extent of electrostriction depends strongly on temperature and pressure.
A final interesting property of water is that some fraction of water molecules will autodissociate. In pure water at standard state conditions, one in every 10−7 molecules will dissociate to form H+ and OH– ions. Although in most thermodynamic treatments the protons produced in this process are assumed to be free ions, most will combine with water molecules to form H3O+ ions. OH− is called the hydroxyl ion; the H3O+ is called hydronium.
3.7.2 Some definitions and conventions
The first two terms we need to define are solvent and solute. Solvent is the substance present in greatest abundance in a solution; in the electrolyte solutions that we will discuss here, water is always the solvent. Solute refers to the remaining substances present in solution. Thus, in seawater, water is the solvent and NaCl, CaSO4, and so on, are the solutes. We may also refer to the individual ions as solutes.
3.7.2.1 Concentration units
Geochemists concerned with aqueous solutions commonly use a variety of concentration units other than mole fraction. The first is molality (abbreviated as lower-case m), which is moles of solute per kg of solvent (H2O). Molality can be converted to moles solute per moles solvent units by dividing by 55.51 mol/kg. A second unit is molarity (abbreviated as uppercase M), which is moles of solute per liter of solution. To convert molality to mole fraction, we would divide by the molecular weight of solvent and use the rational activity coefficient. Natural solutions are often sufficiently dilute that the difference between molality and molarity is trivial (seawater, a relatively concentrated natural solution, contains only 3.5 weight percent dissolved solids). Another common unit is weight fraction (i.e., grams per gram solution), which may take several forms, such as weight percentage, parts per thousand, or parts per million (abbreviated %, ppt or ‰, ppm or mg/kg). To convert to mole fraction, one simply divides the weight of solute and H2O by the respective molecular weights.
3.7.2.2 pH
One of the most common parameters in aqueous geochemistry is pH. pH is defined as the negative logarithm of the hydrogen ion activity:
(3.68)
3.7.2.3 Standard state and other conventions
The first problem we must face in determining activities in electrolyte solutions is specifying the standard state. With gases, the standard state is generally the pure substance (generally at 298 K and 1 atm), but this is generally not a reasonable choice for electrolytes. A NaCl solution will become saturated at about 0.1 XNaCl, and crystalline NaCl has very different properties from NaCl in aqueous solution. By convention, a hypothetical standard state of unit activity at 1 molal concentration is chosen:
(3.69)
