Molecular structure and charge distribution
- Related Topics:
- liquid crystal
- solution
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- On the Web:
- PNAS - Significant structures in the liquid state (PDF) (Mar. 29, 2025)
If a molecule has no net electrical charge, its negative charge is equal to its positive charge. The forces experienced by such molecules depend on how the positive and negative charges are arranged in space. If the arrangement is spherically symmetric, the molecule is said to be nonpolar; if there is an excess of positive charge on one end of the molecule and an excess of negative charge on the other, the molecule has a dipole moment (i.e., a measurable tendency to rotate in an electric or magnetic field) and is therefore called polar. The dipole moment (μ) is defined as the product of the magnitude of the charge, e, and the distance separating the positive and negative charges, l: μ = el. Electrical charge is measured in electrostatic units (esu), and the typical charge at one end of a molecule is of the order of 10-10 esu; the distance between charges is of the order of 10-8 centimetres (cm). Dipole moments, therefore, usually are measured in debyes (one debye is 10-18 esu-cm). For nonpolar molecules, μ = 0.
Polar molecules
The force F between two polar molecules is directly proportional to the product of the two dipole moments (μ1 and μ2) and inversely proportional to the fourth power of the distance between them (r4): that is, F varies as μ1μ2/r4. The equation for this relationship contains a constant of proportionality (F = kμ1μ2/r4), the sign and magnitude of which depend on the mutual orientation of the two dipoles; if the positive end of one faces the negative end of the other, the constant of proportionality is negative (meaning that an attractive force exists), while it is positive (meaning that a repulsive force exists) when the positive end of one faces the positive end of the other. When polar molecules are free to rotate, they tend to favour those orientations that lead to attractive forces. To a first approximation, the force (averaged over all orientations) is inversely proportional to the temperature and to the seventh power of the distance of separation. Mixtures of polar molecules often exhibit only mild deviations from ideality, but mixtures containing polar and nonpolar molecules are frequently strongly nonideal. Because of the qualitative and quantitative differences in intermolecular forces, the molecules segregate: the polar molecules prefer to be with each other, and so do the nonpolar ones. Only at higher temperatures, such that the thermal energy of the molecules offsets the cohesion between identical molecules, do the two liquids mix in all proportions. In mixtures containing both polar and nonpolar components, deviations from Raoult’s law diminish as temperature rises.
Nonpolar molecules
A nonpolar molecule is one whose charge distribution is spherically symmetric when averaged over time; since the charges oscillate, a temporary dipole moment exists at any given instant in a so-called nonpolar molecule. These temporary dipole moments fluctuate rapidly in magnitude and direction, giving rise to intermolecular forces of attraction called London (or dispersion) forces. All molecules, charged or not, polar or not, interact by London forces. To a first approximation, the London force between two molecules is inversely proportional to the seventh power of the distance of separation; it is therefore short-range, decreasing rapidly as one molecule moves away from the other. The London theory indicates that for simple molecules positive deviations from Raoult’s law may be expected (i.e., the activity coefficient γi is greater than 1, as explained previously). Since the London theory suggests that the attractive forces between unlike simple molecules are smaller than those corresponding to an ideal solution, the escaping tendency of the molecules in solution is larger than that calculated by Raoult’s law. As a result, mixing of small nonpolar molecules is endothermic (absorbing heat from the surroundings) and the volume occupied by the liquid solution often exceeds that of the unmixed components—that is, the components expand on mixing.
In addition to the forces listed above, there are so-called induction forces set up when a charged or polar molecule induces a dipole in another molecule: the electric field of the inducing molecule distorts the charge distribution in the other. When a charged molecule induces a dipole in another, the force is always attractive and is inversely proportional to the fifth power of the distance of separation. When a polar molecule induces a dipole in another molecule, the force is also attractive and is inversely proportional to the seventh power of separation. Induction forces are usually small but may make a significant contribution to the energy of a mixture of molecules that are strongly dissimilar.
Effects of chemical interactions
In many cases the properties of a mixture are determined primarily by forces that are more properly classified as chemical rather than as physical. For example, when dinitrogen pentoxide is dissolved in water, a new substance, nitric acid, is formed; and it is necessary to interpret the behaviour of such a solution in terms of its chemical properties, which, in this case, are more important than its physical properties. This example is an extreme one, and there are many solutions for which the chemical effect is less severe but nevertheless dominant.
Hydrogen bonding: association
This dominance is especially important in those solutions that involve hydrogen bonding. Whenever a solution contains molecules with an electropositive hydrogen atom and with an electronegative atom (such as nitrogen, oxygen, sulfur, or fluorine), hydrogen bonding may occur and, when it does, the properties of the solution are affected profoundly. Hydrogen bonds may form between identical molecules or between dissimilar molecules; for example, methanol (CH3OH) has an electropositive (electron-attracting) hydrogen atom and also an electronegative (electron-donating) oxygen atom, and therefore two methanol molecules may hydrogen-bond (represented by the dashed line) singly to form the structure
or in chains to form
Hydrogen bonding between identical molecules is often called association.
Hydrogen bonding: solvation
In a mixture of methanol and, say, pyridine (C5H5N), hydrogen bonds can also form between the electropositive hydrogen atom in methanol and the electronegative nitrogen atom in pyridine. Hydrogen bonding between dissimilar molecules is an example of a type of interaction known as solvation. Since the extent of association or solvation or both depends on the concentrations of the solution’s components, the partial pressure of a component is not even approximately proportional to its mole fraction as given by Raoult’s law; therefore, large deviations from Raoult’s law are commonly observed in solutions in which hydrogen bonding is extensive. Broadly speaking, association of one component, but not the other, tends to produce positive deviations from Raoult’s law, because the associating component hydrogen-bonds to a smaller extent when it is surrounded by other molecules than it does in the pure state. On the other hand, solvation between dissimilar molecules tends to produce negative deviations from Raoult’s law.
Theories of solutions
Activity coefficients and excess functions
As has been explained previously, when actual concentrations do not give simple linear relations for the behaviour of a solution, activity coefficients, symbolized by γi, are used in expressing deviations from Raoult’s law. Activity coefficients are directly related to excess functions, and, in attempting to understand solution behaviour, it is convenient to characterize nonelectrolyte solutions in terms of these functions. In particular, it is useful to distinguish between two types of limiting behaviour: one corresponds to that of a regular solution; the other, to that of an athermal solution (i.e., when components are mixed, no heat is generated or absorbed).
In a binary mixture with mole fractions x1 and x2 and activity coefficients γ1 and γ2, these quantities can be related to a thermodynamic function designated by GE, called the excess Gibbs (or free) energy. The significance of the word excess lies in the fact that GE is the Gibbs energy of a solution in excess of what it would be if it were ideal.
In a binary solution the two activity coefficients are not independent but are related by an exact differential equation called the Gibbs-Duhem relation. If experimental data at constant temperature are available for γ1 and γ2 as a function of composition, it is possible to apply this equation to check the data for thermodynamic consistency: the data are said to be consistent only if they satisfy the Gibbs-Duhem relation. Experimental data that do not satisfy this relation are thermodynamically inconsistent and therefore must be erroneous.
To establish a theory of solutions, it is necessary to construct a theoretical (or semitheoretical) equation for the excess Gibbs energy as a function of absolute temperature (T ) and the mole fractions x1 and x2. After such an equation has been established, the individual activity coefficients can readily be calculated.
Gibbs energy, by definition, consists of two parts: one part is the enthalpy, which reflects the intermolecular forces between the molecules, which, in turn, are responsible for the heat effects that accompany the mixing process (enthalpy is, in a general sense, a measure of the heat content of a substance); and the other part is the entropy, which reflects the state of disorder (a measure of the random behaviour of particles) in the mixture. The excess Gibbs energy GE is given by the equation
where HE is the excess enthalpy and SE is the excess entropy. The word excess means in excess of that which would prevail if the solution were ideal. In the simplest case, both HE and SE are zero; in that case the solution is ideal and γ1 = γ2 = 1. In the general case, neither HE nor SE is zero, but two types of semi-ideal solutions can be designated: in the first, SE is zero but HE is not; this is called a regular solution. In the second, HE is zero but SE is not; this is called an athermal solution. An ideal solution is both regular and athermal.
