Solid state empty space

If a chemical is placed in an empty vessel that is greater in volume than the chemical itself, a portion of the chemical volatilizes to fill the remaining free space of the vessel with vapors. The pressure in the vessel at eqnilibrium is affected only by the temperature and is independent of the vessel volnme. The pressure that develops, called vapor pressure, characterizes any chemical in the liquid or solid state. 

This chapter continues to explore states of matter by focusing on the gas state. Table 8.1 summarized the main features of gases. In the gaseous state, molecules are much farther apart than in either solid or liquids. Because of this distance molecules in the gaseous state have virtually no influence on each other. The independent nature of gas molecules means intermolecular forces in this state are minimal. A gas expands to fill the volume of its container. Most of the volume occupied by the gas consists of empty space. This characteristic allows gases to be compressible, and gases have only about 1/1,000 the density of solids and liquids. 

Most recently, Gavezzotti (4) has analyzed theoretically certain solid state processes in terms of the volume of the constituent molecules and the size and location of the empty and filled spaces in the crystal lattice. With a statement that will be seen to be directly pertinent to the results of our investigation, he concludes that "a prerequisite for crystal reactivity is the availability of free space around the reaction site". 

Gases are mostly empty space at normal pressures. At standard temperature and pressure (STP 1 atm pressure, temperature 273K), the same amount of matter will occupy about 1000 times more volume if it is in the gaseous state than if it is a solid or liquid. At much higher densities (for example, pressures of several hundred atmospheres at 273K) this assumption will not be valid. 

In previous courses, you learned about the properties of the different states of matter. You may recall that both solids and liquids are incompressible. That is, the particles cannot squeeze closer together, or compress. The incompressible nature of solids and liquids is not due to the fact that particles are touching. On the contrary, the particle theory states that there is empty space between all particles of matter. 

In protein crystals, due to the large size of the molecule, the empty space can have cross sections of 10-15 A or greater. The empty space between the protein molecules is occupied by mother liquor. This property of protein crystals, shared by nucleic acids and viruses, is otherwise unique among the crystal structures. In fact, the values of the packing coefficient of protein crystals range from 0.7 to 0.2, but the solvent molecules occupy the empty space so that the total packing coefficient is close to 1 [37]. Nevertheless, a detailed theoretical study has been carried out to examine the models of DNA-DNA molecular interactions on the basis of hard-sphere contact criteria. The hard-sphere computations are insufficient for qualitative interpretation of the packing of DNA helices in the solid state, but... 

Fig. 3 shows the state of subsurface stress. The empty space in this figure shows a pore surrounded by solid rock. The vertical overburden pressure, S, is supported by two unequal forces the formation fluid (pore) pressure, p, and the vertical effective stress acting on the rock frame, o. By Newton s third law of motion... 

Liquids and solids are quite a different story. The principal difference between the condensed states (liquids and solids) and the gaseous state is the distance between molecules. In a liquid the molecules are so close together that there is very httle empty space. Thus liquids are much more difficult to compress than gases, and they are also much denser under normal conditions. Molecules in a liquid are held together by one or more types of attractive forces, which will be discussed in the next section. A liquid also has a definite volume, since molecules in a liquid do not break away from the attractive forces. The molecules can, however, move past one another freely, and so a liquid can flow, can be poured, and assumes the shape of its container. 

Modern chemistry is aided profoundly by the advancement of x-ray techniques, and crown ether chemistry is no exception. Our understanding of solution coinplexaiion has been augmented by numerous solid-state structures. Among the earliest crown ether complexes to appear were those reported by Truter and Bush. Numerous other contributions to this area were reviewed by Dobler. In brief, many crown ethers are solid and form regular crystals. Because they possess an empty central space, one or more methylene residues typically turns inward to fill the molecular void. When complexation of a cation occurs, the methylene rotates outward so that the bound cation will be accessible to all of the macroring donors. 

Crystalline solids consist of atoms, ions, or molecules that are arrayed into a long-range, regularly ordered structure known as a crystalline lattice. A crystal consists of a pattern of objects that repeats itself periodically in three-dimensional space, so that it has the property of translational symmetry. A lattice is simply a three-dimensional array of lattice points, where the atoms, ions, or molecules are held together in the solid state by a balance of attractive and repulsive forces. Lattice points are geometrical constructs it is not a necessary condition for a physical entity, such as an atom or ion, to actually occupy the lattice point Indeed, many lattice points are simply empty space, around which a basis, or motif, of particles is centered. Two examples of two-dimensional lattices are shown in Figure 11.1. 

The same quantify of a substance occupies a much greater volume as a gas than it does as a liquid or a solid. For example, 1 mol of water (18.02 g) has a volume of 18 mL at 4°C. This same amount of liquid water would occupy about 22,400 mL in the gaseous state—more than a 1200-fold increase in volume. We may assume from this difference in volume that (1) gas molecules are relatively far apart, (2) gases can be greatly compressed, and (3) the volume occupied by a gas is mostly empty space. 

As discussed in Section 0.1, most substances and mixtures can exist in three states solid, liquid, and gas. The physical properties of these states of matter are very different. In gases, the distances between molecules are so large compared to molecular size that the effect of molecular interaction is negligibly small at ordinary temperatures and pressures. Because there is a great deal of empty space in a gas—that is, space that is not occupied by molecules—gases can be readily compressed. The lack of strong forces between molecules also allows a gas to expand to flU the volume of its container. Furthermore, the large amount of empty space results in very low densities under normal conditions. 

The most efficient solid-state packing is usually preferred in order to minimize the amount of "empty" space in a structure. The exact crystal structure type, however, can vary depending on the shapes and sizes of the ions, atoms, or molecules making up the solid. 

Gases consist of large numbers of tiny particles that are far apart relative to their size. These particles, usually molecules or atoms, typically occupy a volume that is about 1000 times greater than the volume occupied by an equal number of particles in the liquid or solid state. Thus, molecules of gases are much farther apart than molecules of liquids or solids. Most of the volume occupied by a gas is empty space, which is the reason that gases have a lower density than liquids and solids do. This also explains the fact that gases are easily compressed. 

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