Clausius-Clapeyron equation pure solid-vapor equilibrium

In general, when a solution freezes there is a separation of solute and solvent. That leads to the creation of a new triple point where the solvent, in solution, is in equilibrium with both its own pure vapor and pure solid. The relationship between the decrease in the freezing temperature and the lowering of the vapor pressure is given by the Clausius-Clapeyron equation for solid-liquid equilibria ... 

If the gas phase activity of the host is controlled by the presence of a pure condensed phase, solid or liquid, the equilibrium between host and guest in a stoichiometric clathrate can be described in terms of the gas phase pressure of the guest. This is, in effect, a vapor pressure for the guest. At higher pressures the guest will condense to form clathrate, and at lower pressures the clathrate will decompose. Temperature variation of this pressure will follow the Clapeyron equation which, with the usual assumptions (ideal gas behavior of the vapor and negligible volume of the condensed phase), reduces to the Clausius-Clapeyron equation ... 

Solids Below the triple point, the pressure at which the solid and vapor phases of a pure component are in equilibrium at any given temperature is the vapor pressure of the solid. It is a monotonic function of temperature with a maximum at the triple point. Solid vapor pressures can be correlated with the same equations used for liquids. Estimation of solid vapor pressure can be made from the integrated form of the Clausius-Clapeyron equation... 

The criteria for equilibria involving solid phases are exactly those given in 7.3.5 for any phase-equilibrium situation phases in equilibrium have the same temperatures, pressures, and fugacities. Moreover, pure-component solid-fluid equilibria obey the Clapeyron equation (8.2.27). This means the latent heat of melting is proportional to the slope of the melting curve on a PT diagram and the latent heat of sublimation is proportional to the slope of the sublimation curve. In the case of solid-gas equilibria, the Clausius-Clapeyron equation (8.2.30) often provides a reliable relation between temperature and sublimation pressures, analogous to that for vapor-liquid equilibria. 

Vapour pressure p represents the partial pressure of a compound above the pure solid or liquid phase at thermal equilibrium it corresponds to a steady state with a continuous exchange, but no net transfer, of molecules between the two phases. From thermodynamic considerations, the vapour pressure of a chemical is determined by its enthalpy of vaporization (A/f ) and the temperature (7) as described by the Clausius-Clapeyron equation ... 

The Clapeyron equation is rigorous and exact. It applies not only to gas-liquid equilibrium, but to any two-phase equilibrium of a pure species (e.g., liquid-solid, gas-solid) or change between two different crystal forms (e.g., graphite to diamonds, see Example 4.2). By adding some simplifications, we find the Clausius-Clapeyron (C-C) equation, which is only approximate but is a surprisingly good approximation of observed behavior for gas-liquid and gas-solid equilibria (vapor pressures) of single pure species. 

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