This chapter considers the reasons that substances are liquids and solids (as opposed to gases) and looks at the properties of these states of matter.

In chapter 5, you learned that gases represent the most disorganized state of matter and that gases retain neither volume nor shape. Solids, considered in this chapter, are the most organized form of matter. Liquids are between the two other states in terms of organization.

Properties of liquids:

• Liquids retain volume but not shape.
• Liquids are practically non-compressible because the molecules are already close together.
• Liquids have much higher densities than gases, and usually (water is a notable exception) have lower densities than the corresponding solid.
• Liquids exhibit a resistance to flow called viscosity. Viscosity depends on temperature (higher temperature reduces viscosity) and the nature of the liquid.
• Liquids exhibit a resistance to an increase in their surface area called surface free energy (an older, but still commonly-used term is surface tension). Surface free energy, like viscosity, depends on temperature (higher temperatures reduce surface free energy) and the nature of the liquid.
• Viscosity and surface tension are related to the forces of attraction between molecules. This will be discussed later in this document.

Properties of Solids

• Solids are even less compressible than liquids.
• Solids retain both volume and shape.
• Solids exist in two forms: amorphous (literally, without shape) and crystalline. Amorphous forms are rather unusual, although one of the most common examples of this form is ordinary glass. The crystalline form is by far the more common of the two.
• A crystalline solid exists in a regular, three-dimensional form called a crystal. The actual 3-D arrangement of the atoms, molecules, or ions is called the crystal lattice, and the building block (fundamental unit) of the crystal lattice is called the unit cell.

Intermolecular Forces
Substances which are gases have relatively weak forces of attraction between molecules. Remember that the weak forces are the cause for the gaseous state, not the effect of a substance being a gas. Intermolecular forces are stronger for liquids (that's why they are liquids!), and even stronger for solids. Even within different substances in the same state, intermolecular forces differ. For example, the forces of attraction between two water molecules are stronger than the forces between two pentane molecules.

Likewise, water and pentane have different surface free energies and viscosities. Keep in mind that macroscopic properties are, ultimately, the result of microscopic effects.

Remember that intermolecular means between molecules, while intramolecular forces are forces within molecules, i.e., ionic and covalent bonds. There are three main types of intermolecular attractive forces:

• dipole-dipole forces. Dipole-dipole forces are classified as permanent dipole-permanent dipole forces, and can only exist between molecules which have a permanent dipole moment. Recall from chapter 8 that a combination of Lewis electron-dot structures and VSEPR can be used to decide whether a molecule has a permanent dipole moment. Carbon tetrachloride, which has no permanent dipole moment because the individual C-Cl bond dipoles cancel one another in the tetrahedral arrangement, cannot have dipole-dipole attractions with other CCl₄ molecules (or any other molecules, for that matter.) On the other hand, HCl molecules have a permanent dipole moment and are attracted to one another by dipole-dipole attractions.
• London dispersion forces (sometimes simply called London forces.) London forces are classified as instantaneous dipole-induced dipole forces. These forces of attraction are present between all substances, even those which have other types of intermolecular attractive forces. They arise when a temporary, instantaneous dipole in one molecule induces a dipole moment in an adjacent molecule. Figure 10.5 in the text illustrates this type of attraction. For molecules without a permanent dipole moment, London forces are the only type of intermolecular attractive forces possible. All other factors being equal, London forces become stronger with increasing molar mass because the molecule, being larger or made up of larger atoms, is more polarizable (able to have a temporary dipole moment induced in it.)
• Hydrogen bonding is an especially strong form of dipole-dipole forces. Hydrogen bonding occurs when the polar hydrogen atom from one molecule is attracted to the oxygen, nitrogen, or fluorine atom of another molecule. Despite the name, remember that hydrogen bonds are not real chemical bonds; it takes only a fraction of the energy to overcome hydrogen "bonds" that it takes to break an honest-to-goodness covalent bond. Hydrogen bonds are much stronger than ordinary dipole-dipole forces for two reasons:
  1. because of the large electronegativity of N, O, and F, N-H, O-H, and H-F bonds are quite polar, which means that there is a relatively large partial positive charge on the hydrogen.
  2. the very small size of the hydrogen atom allows it to get very close to the N, O, or F atom of the adjacent molecule. This results in a much lower energy (greater stability.)

Types of crystalline solids
The major types of crystalline solids are shown in Table 10.3, page 455. (Also see the summary in Table 10.7, page 474.) They are:

1. Molecular solids: lattice points are made up of molecules. The attractive forces between molecules can be dipole-dipole, H-bonds, or London forces, depending on the nature of the molecules. For example, ice is a molecular solid because it contains water molecules at the lattice points. The attractions between water molecules are hydrogen bonds. Remember that when ice melts or water boils, no covalent bonds are broken (if they were, the water would chemically decompose.) Melting or boiling water simply involves overcoming the hydrogen bonds between water molecules. Dry ice (solid carbon dioxide) is also a molecular solid because it contains carbon dioxide molecules at the lattice points. Unlike water, however, the attractive forces between the nonpolar CO₂ molecules in dry ice are weaker London forces.
2. Ionic solids: lattice points are made up of ions. The attractive forces are real chemical bonds -- ionic bonds. This is why ionic solids generally have very high melting points -- to melt the solid, ionic bonds need to be broken.
3. Atomic solids: lattice points are atoms. There are three sub-classes of atomic solids, determined by the attractive forces between atoms in the solid:
   • Metallic: atoms participate in the metallic bond. All elemental metals fall into this category.
   • Network (sometimes called Covalent): atoms are bonded together with covalent bonds, which extend throughout the crystal. Two good examples of this class are diamond (see figure 10.22(a)) and quartz (see figures 10.26 and 10.28.)
   • Group VIIIA: interatomic forces between atoms are London forces. All solid noble gases fall into this category.

X-Ray Diffraction and Crystal Morphology
Scientists know the details of unit cells (bond lengths, angles, and overall geometry) by looking at how x-radiation interacts with crystals. Since the wavelength of x-rays is on the same order of magnitude as the distances between the atoms, ions, or molecules in a crystal, the x-rays are diffracted by the crystal. By measuring the angles by which the x-radiation is diffracted, and by knowing the wavelength of the x-rays, the Bragg equation can be used to determine spacings between crystal planes:

where lambda is the wavelength of the x-radiation, d is the spacing between crystal planes, and theta is the angle of reflection. The variable n is known as the order and is an integer (usually 1, since first-order reflections are more intense.)

Crystal lattices can be pictured as macroscopic assemblies which arise from a microscopic stacking of building blocks called unit cells, in three dimensions. There are many types of unit cells, categorized by the angles between faces on the unit cell and the relative lengths of the sides of the unit cell. The simplest class of unit cell is called the cubic unit cell. This cell, as the name suggests, has the shape of a cube; specifically, the lengths of all three sides (usually designated a, b, and c) are equal, and all bond angles between sides of the cube are right angles.

There are several important points to keep in mind when models of unit cells are considered:

• Simple ball-and-stick models are not realistic because they suggest that there is a lot of empty space between the balls in the model. Space-filling models are better in this respect, because they show that there is actually contact between some of the spheres in the model (more on this later.)
• The spheres in these models can represent atoms, ions, or molecules, depending on what type of crystalline solid is represented by the model. For example, the spheres in a model of NaCl represent sodium and chloride ions, but the spheres in a model of ice represent water molecules.
• Unit cells are stacked on top of one another in the crystal: front and back, left and right, and top and bottom, for an infinitely large distance (from the atom's perspective; obviously there must be some limit, since otherwise the macroscopic crystal would be infinitely large.) Because of the stacking, the lattice points in a unit cell may be shared with adjacent cells. This point will be used later in deciding how many atoms, ions, or molecules are contained in a unit cell.

The three sub-types of cubic unit cells are

1. Simple cubic - this structure contains lattice points at each corner of the cube. The spheres representing the atoms, ions, or molecules of the unit cell touch along the edge of the cube. For this reason, the length of the edge of the unit cell is twice the radius of the atom, molecule, or ion. The following figure shows this relationship by displaying one edge of a simple cubic unit cell:
   
   

   Naturally, the above diagram should be pictured as three-dimensional, with spheres instead of circles. Since a sphere at the corner of a simple cubic unit cell is shared by a total of eight unit cells (see Fig. 10.17(a) on page 457), each corner of a cubic unit cell contributes one-eighth to a particular unit cell. Since there are eight corners on a simple cube, the result is that a simple cubic unit cell contains one atom, molecule, or ion per unit cell. ( 1 = eight corners at 1/8 per corner.)
   
   

2. Face-centered cubic - this structure contains lattice points at each corner of a cube (as in the simple cubic structure) and a lattice point in the center of each face of the cube. The lattice point in the center of the face is shared with one other unit cell (see Fig. 10.17(b), page 457), with the result that a face-centered cubic unit cell contains four atoms, ions, or molecules per unit cell. ( 4 = eight corners at 1/8 per corner plus six face centers at ½ per face center.) The spheres in a face-centered cubic unit cell touch along the face diagonal, as shown in the following figure:
   
   

   The relationship between the length of the edge of the unit cell and the radius of the sphere is derived in Sample Exercise 10.2 on page 457. Make sure you understand the geometry concepts used in this derivation.
   

3. Body-centered cubic - this structure consists of lattice points at the corners of the cube and a lattice point in the center of the cube. The lattice point in the center of the cube is not shared by other unit cells, giving the result that a body-centered unit cell contains two atoms, molecules, or ions per unit cell. ( 2 = eight corners at 1/8 per corner plus 1 unshared.) The spheres in a body-centered unit cell touch along the body diagonal of the cube (in other words, the upper-left rear corner sphere touches the center sphere, which touches the lower-right front corner sphere, etc.) You should derive the relationship between the length of the edge and the radius of a sphere, by using ideas similar to those in Sample Exercise 10.2.

Closest Packing and Packing Efficiency
Crystals made up of identical atoms (metals or frozen noble gases) tend to pack in a manner which places atoms as close as possible, with little wasted space. We can calculate the percentage of wasted space (the volume of the unit cell not taken up by "spheres" [=atoms, molecules, or ions]) in a unit cell.

Let's first consider a simple cubic unit cell. The volume of this unit cell is the length of the edge cubed: V = e³. Since the edge length is equal to two atomic, molecular or ionic radii, we have V = (2r)³ = 8r³. The unit cell contains one net "sphere" (see above), so the volume occupied by atoms, molecules, or ions is the volume of a sphere, or (4/3)(pi)(r³). Thus, the percentage of total volume which is occupied by matter is simply

This is not a very efficient packing arrangement, since 48% of the unit cell is wasted space. For this reason, metals and frozen noble gases do not generally crystallize in a simple cubic arrangement.

Consider now a face-centered unit cell. The relationship between the length of the edge of the unit cell and the radius is

(see Sample Exercise 10.2, p. 457.

Thus, the total volume of the unit cell is

and the unit cell contains four net spheres, meaning that the volume occupied by atoms, molecules, or ions is

Therefore, the percentage of total volume which is occupied by matter is given by the expression

This means that only 26% of the unit cell volume is empty space, making a face-centered unit cell a more efficient arrangement than a simple cubic unit cell. Another name for face-centered cubic (fcc) closest packing is cubic closest packing. An equally efficient method of packing (with the same fraction of occupied volume) is known as hexagonal closest packing. See figures 10.13 through 10.15 to see the difference between these two types of closest packing.

• You should calculate, as an exercise, the occupied fraction for a body-centered unit cell and decide how the efficiency of body-centered cubic packing compares to those for simple cubic and face-centered cubic.

Ionic Solids
Sometimes it is useful to describe ionic solids as close-packed arrangements of anions (or cations) with cations (or anions) filling holes in the crystal lattice. The three types of holes available are

• trigonal hole: the hole created in a plane when three spheres touch each other. This is the smallest of the types of holes and neither cations nor anions can fit in this hole. See Fig. 10.33(a) for a diagram of a trigonal hole.
• tetrahedral hole: this hole is created when a fourth sphere sits over the trigonal hole formed by three spheres in an adjacent layer. It is called a tetrahedral hole because the hole is surrounded by four spheres (see Fig. 10.33 (b).) It is larger than a trigonal hole, but smaller than an octahedral hole. The number of tetrahedral holes is equal to twice the number of packed spheres. Since fcc packing results in four net spheres per unit cell, there are eight tetrahedral holes per unit cell. See figure 10.34, page 472.
• octahedral hole: this hole is created by the packing of six spheres: three in each of two adjacent layers. Essentially, it can be viewed as the hole which is surrounded by a trigonal hole above it and another trigonal hole below it. Since it is surrounded by six spheres, it is called an octahedral hole. It is larger than a tetrahedral hole. The number of octahedral holes is equal to the number of packed spheres. Since fcc packing results in four net spheres per unit cell, there are four octahedral holes per unit cell. See figure 10.35, page 473.

Vapor Pressure and Changes of State
When a liquid in a closed container is allowed to reach equilibrium such that the rate of evaporation (vaporization) is equal to the rate of condensation, the pressure of the vapor remains constant. This pressure is called the vapor pressure and depends on only two things: the nature of the liquid and the temperature. The energy needed to vaporize one mole of a liquid at the normal boiling point is called the enthalpy of vaporization (or the heat of vaporization.) The enthalpy of vaporization is a direct measure of the intermolecular forces of attraction in the liquid. Stronger forces are correlated with a larger enthalpy of vaporization (and a lower vapor pressure), while weaker intermolecular forces are associated with a smaller enthalpy of vaporization (and a higher vapor pressure). The mathematical relationship between the vapor pressure and temperature is given by the Clausius-Clapeyron equation (equation 10.4). Equation 10.5 is a combination of two Clausius-Clapeyron equations and relates the vapor pressures of a given liquid at two different temperatures. The enthalpy of vaporization for a liquid can be determined by measuring the vapor pressure as a function of temperature. A plot of logarithm of vapor pressure versus reciprocal absolute temperature is linear, with a slope of

where R is the gas constant, 8.314 J/mol-K.

When a substance changes state, there is always an energy change. The following table illustrates these changes of state:

Note that although there is a change in energy, there is not a change in temperature for state changes. Study Figure 10.42 to make sure you understand this point. When heat is added to or removed from a substance in a given state, there is a change in temperature. The heat changes for these two different types of processes is given by these equations:

For both equations, "amount" depends on the units for the heat capacity or the enthalpy value for the state change: a heat capacity for water of 4.184 Joules/g-deg C dictates that the amount of water be expressed in grams, whereas an enthalpy of vaporization for water expressed as 43.9 kJ/mole (see Sample Exercise 10.6) dictates that the amount of water be expressed in moles.

Phase Diagrams
Phase diagrams are extensions of the vapor pressure type of diagram shown in Fig. 10.40(a), page 477. The difference is that the latter figure shows only the relationship between pressure and temperature for a given state, whereas a phase diagram contains information about P/T relationships for all three states. A phase diagram consists of three curves: a vapor pressure curve (like that shown in Fig 10.40(a)), a sublimation curve, and a melting point curve. A point along any one of these curves represents equilibrium between the two states associated with the curve (see the Table above.). Points A, B, and C in the figure below are these types of points. A point which is not on one of the curves (like point D below) means that the system is not in equilibrium and that the state is predominately that shown on the figure (liquid, in this case.) The point at which all three curves intersect represents the triple point, which is the one P/T combination where all three states coexist at equilibrium.

Last modified November 28, 1997