Appendix B

Appendix B

Description of Material Omitted from the Preliminary Edition

Section VII extends the calculation of inter-atomic distances to chemical compounds. Part of this material was included in Section VI. The omitted portion completes the calculation of distances for all of the common inorganic binary compounds crystallizing in the normal structural forms, including both isotropic and anisotropic crystals. The normal distances between the atoms in complex crystals are also evaluated.

Section VIII takes up the subject of the specific volume of complex compounds in which the volume is not a direct function of the inter-atomic distances. An expression for the calculation of these volumes is derived from the general principles previously formulated, and this expression is applied to the calculation of specific volumes for a substantial number of typical inorganic compounds of this class. The applicability of the same expression to organic compounds is also indicated, but actual calculations are deferred to a later section.

Section IX develops from the inter-atomic force equation a general expression for the effect of compression on solid structures. It is shown that the inward force acting on the solid under equilibrium conditions is equivalent to an initial pressure, and the total effective pressure is the sum of this initial pressure and the applied external pressure. An equation for the calculation of the initial pressure is derived from the general pressure expression and initial pressures are calculated for the elements and a large number of compounds. A simple relation between the initial pressure and the initial compressibility is derived and initial compressibilities are calculated for the elements and many compounds. It is shown that these values agree with the experimental results within the probable margin of error. An additional equation is formulated from the general pressure expression to enable calculation of the relative volumes of solids under pressure. Values obtained from this equation are then compared with most of Bridgman’s data on solid compression, including practically all of his results on the elements and a large amount of the data on both organic and inorganic compounds.

Section X takes up the subject of valence. It is shown that the factors determining valence are entirely separate and distinct from those entering into the determination of the inter-atomic distance, and the valence equilibrium is something of a totally different nature from the inter-atomic force equilibrium. The various types of valences, their derivation, and characteristics are described and explained and the possible valences of each element are tabulated. The factors governing the relative stability of the alternate valence combinations are determined. The nature of radicals and their participation in the molecular structure are explained and the composition and characteristics of the common inorganic radicals are covered in detail.

Section XI extends the principles developed in the preceding section to the compounds of the organic division. It is shown that the accepted “bond” theory of organic structure is not a true representation of the nature of these compounds, and that they are in reality constructed in the same manner as the inorganic compounds, differing from the latter in some respects only because of the two-dimensional nature of most of the inter-atomic forces in the organic compounds. The effect of this factor on the characteristics of the organic radicals and the interior structural groups of the organic compounds is explained. A condensed, but substantially complete, discussion of the chain compounds then follows, indicating how the special structural features of the various classes of compounds of this type result from the operation of the general principles previously derived. It is pointed out that the new theory derived from the Fundamental Postulates not only accounts for the major structural features equally as well as the accepted “bond theory” but also explains many facts on which the bond theory is silent; for example, the difference between the hydroxyl hydrogen (replaceable by Na) and the methyl hydrogen (replaceable by Cl), the reason why CO exists as a separate compound but CH2 does not, and so on.

Section XII is a similar detailed discussion of the ring compounds. The reason for the existence of the ring structure is explained, together with such other factors as the unusual stability of the benzene ring, the ability of the aromatic rings to utilize structural groups which do not appear in the chain compounds, the structural relationships in the condensed rings, etc. Each of the principal families of cyclic, aromatic, and heterocyclic compounds is discussed and the special features of these various groups are shown to result from the operation of the applicable general principles. A number of revisions of chemical nomenclature are suggested to conform with the new relationships which are established.

Section XIII introduces the property of heat. The nature and characteristics of thermal motion are derived from the Fundamental Postulates. The concept of temperature is defined and the conversion constants relating the natural and Centigrade scales are evaluated. Mathematical expressions are developed for the heat content of the solid and its derivative, the specific heat. The general specific heat pattern for the elements is derived from the latter equation and the nature of the possible variations is determined. Values are calculated for the specific heats of elements of different types and a number of diagrams are presented to show the correlation between these theoretical specific heat curves and the observed values. It is shown that the specific heats of the simple inorganic compounds follow the same pattern as those of the elements and additional similar graphs are included for these compounds. The concept of the thermal group is introduced and the specific heats of representative organic and complex inorganic compounds are calculated with the assistance of this concept. These calculated values are also compared with the experimental data in appropriate diagrams.

Section XIV applies the relationships of the preceding section to the inter-atomic force equation to determine the nature and characteristics of thermal expansion. An equation is developed for calculating the expansion of different substances and the expansions thus obtained for a number of elements are compared with experimental values.

Section XV examines the effect of a continued increase in thermal energy on the force system of the individual molecule and shows that at a particular thermal level, which varies with the nature of the substance, this system experiences a drastic change. The transition temperature is identified as the melting point and the new condition beyond the transition is identified as the liquid state. It is made clear that physical state is a property of the individual molecule and not, as generally assumed, a “state of aggregation.” In the vicinity of the melting point the liquid aggregate is a mixture of solid molecules and liquid molecules in proportions determined by probability considerations (not a mixture of solid and liquid aggregates, but a liquid which contains some solid molecules). The existence of both kinds of molecules in the aggregates in this and the similar region in the vicinity of the critical temperature has a major effect on the properties of the aggregates in these regions and much of the mathematical development in the next few sections is devoted to a determination of the magnitude of these effects. At this time the effect on the liquid specific heat is examined. A general liquid specific heat expression is derived and it is shown that modification of this expression as required by the presence of solid molecules results in a curve which reproduces the experimental results. The nature of the heats of fusion and transition is explained and the method of calculating the heat of fusion is indicated. In order to obtain some information needed in the subsequent development, some further attention is given to the property of mass and the concept of secondary mass is introduced and explained. The mass of the H¹ atom and the mass equivalent of unit atomic weight are calculated and from the latter figure Avogadro’s number is derived.

Section XVI establishes the relation of the low temperature volume (or density) of the liquid to the solid volume and derives a mathematical expression for computation of this liquid volume. A liquid equivalent of Avogadro’s Law is formulated on the basis of this expression. The liquid volume at these temperatures is shown to consist of two separate components: a constant initial component and a temperature-dependent component. Densities of approximately 700 organic compounds and 100 other substances (elements, fused salts, etc.) calculated on the basis are shown to be in agreement with experimental values. The nature and magnitude of the structural factors involved in these calculations are discussed.

Section XVII considers the transition from liquid to gas at the upper end of the liquid temperature range and produces further evidence supporting the theoretical conclusion that physical state is a property of the individual molecule. The general nature of the gaseous state is considered and the Gas Laws are derived from the Fundamental Postulates. The molar gas volume is computed from the basic conversion constants by means of the Gas Laws. Equations for the specific heats of gases are derived and their scope of application is indicated. The critical temperature is defined and an expression for calculation of the values applicable to different substances is formulated. Critical temperatures are calculated for approximately 200 elements and compounds and the results are shown to be in agreement with experimental values.

Section XVIII extends the liquid volume relationships to the higher temperatures. It is demonstrated that these high temperature volumes include a third component in addition to the two which make up the low temperature volume. An equation for the orthobaric volume is developed and it is shown that the volumes of approximately 50 elements and compounds computed over the range of temperatures from the boiling point to the critical temperature are in agreement with the measured values. The computations for water are extended down to the freezing point in order to illustrate the effect of the increasing proportion of solid molecules on the liquid volume. The probability relations applying to this situation are developed and from the probability values the percentage of solid molecules in liquid water is computed for each temperature. A composite solid-liquid volume is then obtained in each case and the resulting values are shown to agree with the measured volumes of the liquid aggregate.

Section XIX is a discussion of liquid compressibility. Further elaboration of the relationships previously developed indicates that the compressive forces act on each of the three volume components separately, and a mathematical expression is derived for each effect. An equation for calculating the initial pressure applicable to the liquid (which is not the same as the solid initial pressure) is also formulated and the initial pressures for a large number of liquids are calculated. All of this information is then applied to a computation of the compressions of various liquids studied by Bridgman and calculated values for 25 compounds at several different temperatures and over a wide range of pressures are shown to be in agreement with Bridgman’s results. Following these comparisons, which apply to liquids in which the solid component is still negligible at the highest pressure of observation, the discussion is extended to those liquids which begin the transition to the solid state within the experimental range. The effect of pressure on the probability relations is evaluated, and the proportion of solid molecules in the liquid aggregate is calculated for each individual temperature and pressure of observation, using the same methods as in the water calculations of Section XVIII. A good correlation with Bridgman’s results is shown on 16 different liquids over a wide range of temperatures and pressures. A very extensive tabulation of values for liquid water is included.

Section XX examines the corresponding situation on the other side of the melting point: the modification of the solid volume due to the presence of liquid molecules. The percentages of these liquid molecules in the solid aggregates under pressure and the resulting aggregate volumes are calculated by the methods of Section XIX. The tabulated comparisons of that section are then extended into the solid state up to Bridgman’s experimental pressure limit. This section also examines the volume relations in the liquid-gas transition zone. An expression for the compression of the critical volume component is derived and applied to the volumes calculated by the methods of Section XVIII to determine the volumes of the high-temperature liquid under pressure. Values for water and six hydrocarbons are shown to be in agreement with experimental results.

Section XXI is a discussion of surface tension. This phenomenon is explained as another manifestation of the same force that is responsible for the liquid initial pressure, and the initial pressure equation is modified for application to the calculation of the surface tensions. Values are computed for more than 100 substances over the normal liquid temperature range and it is shown that these values agree with the experimental results. The nature of the structural factors which determine the individual values is discussed.

Section XXII extends the application of the principles developed in connection with the discussion of the melting point in Section XV and shows that a similar change of state of the individual molecule takes place at the critical temperature. The process of evaporation at temperatures below the critical point is indicated to be a result of the operation of the probability principles. The general nature of the vapor state is explained. A mathematical expression for the specific heat of the vapor is developed and a number of curves based on this expression are compared with experimental data. The relation of vapor volume to liquid volume is discussed and a general equation for saturated vapor volume is derived. Volumes calculated from this equation for 16 compounds over the normal liquid temperature range are shown to agree with experimental results. An equation is derived for the critical volume and calculated values are compared with experimental data. It is shown that the factors determining the total heat of liquids and vapors are the same as those determining the volume, and the volume equations are modified to apply to total heat. The total heat of liquid water and saturated steam is calculated at 20° intervals all the way from the melting point to the critical temperature and it is shown that the calculated values agree with the experimental results.

Section XXIII analyzes the results of superheating a vapor and develops an expression for calculating the superheated vapor volume. Because of the rather small amount of variation between substances and the large amount of tabular data required to cover the normal temperature and pressure range of each substance, the comparisons between calculated and experimental values are limited to five compounds at constant pressure over a range of temperatures and two more at constant temperature over a range of pressures, plus water vapor over a wide range of conditions. The relation of the superheated vapor volume to the volume of gases in the range above the critical volume is discussed and the superheated vapor equation is modified to apply to the volumes of real gases. Close agreement is shown between the experimental values and the volumes calculated from this equation for seven compounds. This comparison includes a very extensive tabulation of water volumes.

Section XXIV shows that the volumetric behavior of gases in the range below the critical volume is totally unlike that in the range covered in Section XXIII, and the condition existing below the critical volume and above the critical temperature is defined as a different state of matter: the condensed gas state. It is shown that the theoretical principles require condensed gases to follow volumetric relations analogous to those of the liquid, and values calculated on this basis for representative compounds are shown to agree with the observed volumes. As in the preceding sections very extensive comparisons of water volumes are included, covering the entire range up to 2500 atm. and 1000° C at 50° intervals.

Section XXVI is a discussion of the phenomena originating from the presence of electrons in the material environment. A portion of this material is included with Section XXV. In the omitted portion a mathematical expression for the calculation of resistivities of conductors is derived from the basic principles and resistivities computed for the elements are compared with such experimental values as are available. The nature of superconductivity at low temperatures is explained. An equation is developed for the effect of compression on resistivity and the values calculated from this expression are shown to be in agreement with Bridgman’s results on 23 elements.

Section XXXIV is devoted to refraction. A portion of this material is included with Section XXXIII to show the general nature of the refraction phenomenon and the method of calculation of the refractivity where the factors involved are relatively simple. The omitted portions include a discussion of the more complex refraction patterns and numerical calculations of both refraction and dispersion for approximately 500 substances.

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