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Melting Point and Heat of Fusion The temperature at which a liquid passes into the solid state is known as the freezing point. It is also the melting point of a pure crystalline compound. The freezing point or melting point of a pure crystalline solid is strictly defined as the temperature at which the pure liquid and solid exist in equilibrium. In practice, it is taken as the temperature of the equilibrium mixture at an external pressure of 1 atm; this is sometimes known as the normal freezing or melting point. The student is reminded that different intermolecular forces are involved in holding the crystalline solid together and that the addition of heat to melt the crystal is actually the addition of energy. Recall that in a liquid, molecular motion occurs at a much greater rate than in a solid.
The heat (energy) absorbed when 1 g of a solid melts or the heat liberated when it freezes is known as the latent heat of fusion , and for water at 0Ā°C it is about 80 cal/g (1436 cal/mole). The heat added during the melting process does not bring about a change in temperature until all of the solid has disappeared because this heat is converted into the potential energy of the molecules that have escaped from the solid into the liquid state. The normal melting points of some compounds are collected in Table next together with the molar heats of fusion.
Substance Melting Point (K) Molar Heat of Fusion, ĪHf (cal/mole)
- H 2 O 273.15
- H 2 S 187.61
- NH 3 195.3
- PH 3 139.4
- CH 4 90.5
- C 2 H
- n-C 3 H 8 85.5
- C 6 H 6 278.5
- C 10 H 8 353.2
Melting Point and Intermolecular Forces The heat of fusion may be considered as the heat required to increase the interatomic or intermolecular distances in crystals, thus allowing melting (increased molecular motion) to occur. A crystal that is bound together by weak forces generally has a low heat of fusion and a low melting point, whereas one bound together by strong forces has a high heat of fusion and a high melting point.
Because polymorphic forms represent different molecular arrangements leading to different crystalline forms of the same compound, it is obvious that different intermolecular forces will account for these different forms. Then consider polymorph A, which is held together by higher attractive forces than is polymorph B. It is obvious that more heat will be required to break down the attractive forces in polymorph A, and thus its melting temperature will be higher than that of polymorph B.
Paraffins crystallize as thin leaflets composed of zigzag chains packed in a parallel arrangement. The melting points of normal saturated hydrocarbons increase with molecular weight because the van der Waals forces between the molecules of the crystal become greater with an increasing number of carbon atoms. The melting points of the alkanes with an even number of carbon atoms are higher than those of the hydrocarbons with an odd number of carbon atoms, as shown in Figure below. This phenomenon presumably is because alkanes with an odd number of carbon atoms are packed in the crystal less efficiently.
Solubilities, like melting points, are strongly influenced by intermolecular forces. This is readily observed in Table below, where the methylation of theophylline to form caffeine and the lengthening of the side chain from methyl (caffeine) to propyl in the 7 position result in a decrease of the melting point and an increase in solubility. These effects presumably are due to a progressive weakening of intermolecular forces.
R=H
The Liquid Crystalline State Three states of matter have been discussed thus far in this chapter: gas, liquid, and solid. A fourth state of matter is the liquid crystalline state or mesophase. The term liquid crystal is an apparent contradiction, but it is useful in a descriptive sense because materials in this state are in many ways intermediate between the liquid and solid states.
Properties and Significance of Liquid Crystals Because of their intermediate nature, liquid crystals have some of the properties of liquids and some of the properties of solids. 1-For example, liquid crystals are mobile and thus can be considered to have the flow properties of liquids. 2-At the same time they possess the property of being birefringent, a property associated with crystals. In birefringence, the light passing through a material is divided into two components with different velocities and hence different refractive indices. 3-Some liquid crystals show consistent color changes with temperature, and this characteristic has resulted in their being used to detect areas of elevated temperature under the skin that may be due to a disease process. 4-Nematic liquid crystals may be sensitive to electric fields, a property used to advantage in developing display systems. 5-The smectic mesophase has application in the solubilization of water-insoluble materials. It also appears that liquid crystalline phases of this type are frequently present in emulsions and may be responsible for enhanced physical stability owing to their highly viscous nature.
Differential scanning calorimetry is the most commonly used method and is generally a more useful technique because its measurements can be related more directly to thermodynamic properties. It appears that any analysis that can be carried out with DTA can be performed with DSC, the latter being the more versatile technique.
Differential Scanning Calorimetry In DSC, heat flows and temperatures are measured that relate to thermal transitions in materials. Typically, a sample and a reference material are placed in separate pans and the temperature of each pan is increased or decreased at a predetermined rate. When the sample, for example, benzoic acid, reaches its melting point, in this case 122.4Ā°C, it remains at this temperature until all the material has passed into the liquid state. because of the endothermic process of melting. A temperature difference therefore exists between benzoic acid and a reference, indium (melting point [mp] = 156.6Ā°C), as the temperature of the two materials is raised gradually through the range 122Ā°C to 123Ā°C. A second temperature circuit is used in DSC to provide a heat input to overcome this temperature difference. In this way the temperature of the sample, benzoic acid, is maintained at the same value as that of the reference, indium. The difference is heat input to the sample, and the reference per unit time is fed to a computer and plotted as dH/dt versus the average temperature to which the sample and reference are being raised. The data collected in a DSC run for a compound such as benzoic acid are shown in the thermogram in Figure below.
If the ice water is sealed in a bottle , evaporation effects are limited to the
available headspace, the ice melts to liquid, and evaporation becomes time and temperature dependent. For example, if the container is placed in a freezer, only one phase, ice, may be present after long-term storage. Heating of the container, provided the volume stays fixed, could potentially cause the formation of only a vapor phase. Opening and closing of the container would change the vapor phase composition and thus affect equilibrium. This one- component example can be extended to the two-component system of a drug suspension where solid drug is suspended and dissolved in solution and evaporation may take place in the headspace of the container. The suspended system will sit at equilibrium until the container is opened for administration of the drug, and then equilibrium would have to be reestablished for the new system. A new equilibrium or nonequilibrium state is established because dispensing of the suspension will decrease the volume of the liquid and solid in the container. Therefore, a new system is created after each opening, dispensing of the dose, and then resealing.
The Phase Rule In each of the examples just given, each phase can be defined by a series of independent variables (e.g., temperature) and their coexistence can only occur over a limited range. For example, ice does not last as long in boiling water as it does in cold water. Therefore, to understand and define the state of each phase, knowledge of several variables is required. J. Willard Gibbs formulated the phase rule , which is a relationship for determining the least number of intensive variables (independent variables that do not depend on the volume or size of the phase, e.g., temperature, pressure, density, and concentration) that can be changed without changing the equilibrium state of the system, or, alternately, the least number required to define the state of the system. This critical number is called F , the number of degrees of freedom of the system, and the rule is expressed as follows:
where C is the number of components and P is the number of phases present. Looking at these terms in more detail, we can define a phase as a homogeneous, physically distinct portion of a system that is separated from other portions of the system by bounding surfaces. Thus, a system containing water and its vapor is a two- phase system. An equilibrium mixture of ice, liquid water, and water vapor is a three- phase system.
Systems Containing One Component We have already considered a system containing one component, namely, that for water, which is illustrated in Figure beside. The curve OA in the PāT (pressureā temperature) diagram in is known as the vapor pressure curve. Its upper limit is at the critical temperature, 374Ā°C for water, and its lower end terminates at 0.0098Ā°C, called the triple point. Along the vapor pressure curve, vapor and liquid coexist in equilibrium. Curve OC is the sublimation curve, and here vapor and solid exist together in equilibrium. Curve OB is the melting point curve, at which liquid and solid are in equilibrium. The negative slope of OB shows that the freezing point of water decreases with increasing external pressure.
