For one of the following liquids, determinethe heat of...

For one of the following liquids, determinethe heat of vaporization at its normal boiling point by application of the Clapeyron equation to the given vapor-pressure equation. Use generalized correlations from Chap. 3 to estimate AV. (a) Benzene: $$ \ln P^{\text {sat }} / \mathrm{kPa}=13.8594-\frac{2773.78}{T / \mathrm{K}-53.00} $$ (b) Ethylbenzene: $$ \ln \mathrm{P}^{\text {sat }} / \mathrm{kPa}=14.0045-\frac{3279.47}{T / \mathrm{K}-59.95} $$ (c) n-Heptane: $$ \text { In } \mathrm{P}^{\text {sat }} / \mathrm{kPa}=13.8587-\frac{2911.32}{T / \mathrm{K}-56.51} $$ (d) n-Pentane: $$ \ln P^{\text {sat }} / \mathrm{kPa}=13.8183-\frac{2447.07}{T / \mathrm{K}-39.94} $$ (e) Toluene: $$ \ln P^{\text {sat }} / \mathrm{kPa}=14.0098-\frac{3103.01}{T / \mathrm{K}-53.36} $$

For one of the following liquids, determinethe heat of vaporization at its normal boiling point by application of the Clapeyron equation to the given vapor-pressure equation. Use generalized correlations from Chap. 3 to estimate AV.
(a) Benzene:
$$
\ln P^{\text {sat }} / \mathrm{kPa}=13.8594-\frac{2773.78}{T / \mathrm{K}-53.00}
$$
(b) Ethylbenzene:
$$
\ln \mathrm{P}^{\text {sat }} / \mathrm{kPa}=14.0045-\frac{3279.47}{T / \mathrm{K}-59.95}
$$
(c) n-Heptane:
$$
\text { In } \mathrm{P}^{\text {sat }} / \mathrm{kPa}=13.8587-\frac{2911.32}{T / \mathrm{K}-56.51}
$$
(d) n-Pentane:
$$
\ln P^{\text {sat }} / \mathrm{kPa}=13.8183-\frac{2447.07}{T / \mathrm{K}-39.94}
$$
(e) Toluene:
$$
\ln P^{\text {sat }} / \mathrm{kPa}=14.0098-\frac{3103.01}{T / \mathrm{K}-53.36}
$$

Key Concepts

Clapeyron Equation

The Clapeyron equation relates the rate of change of vapor pressure with respect to temperature to the latent heat of phase change and the difference in molar volumes between the vapor and condensed phases. This thermodynamic relation is essential for determining properties like the heat of vaporization from experimental vapor pressure data.

Heat of Vaporization

The heat of vaporization is the energy required to convert one mole of a liquid into vapor at constant pressure. It is a key thermodynamic property that quantifies the energy barrier associated with the phase change from liquid to vapor, especially at the normal boiling point where the transition occurs under equilibrium conditions.

Normal Boiling Point

The normal boiling point is the temperature at which a liquid's vapor pressure equals a standard atmospheric pressure, typically 101.3 kPa. This well-defined condition is widely used in thermodynamic calculations since many properties, like the heat of vaporization, are characterized at this specific point.

Vapor Pressure Equation

Vapor pressure equations, such as those in the form of the Antoine equation, establish an empirical relationship between the natural logarithm of the vapor pressure and the inverse of temperature (or a modified temperature term). These equations are crucial for determining equilibrium vapor pressures over a range of temperatures, which in turn are used in applying the Clapeyron equation.

Generalized Correlations

Generalized correlations in thermodynamics refer to empirical or semi-empirical relationships used to estimate thermodynamic properties that are not directly measured. In the context of vaporization, these correlations can be used to estimate molar volumes or other parameters that are needed to apply the Clapeyron equation effectively for calculating quantities like the heat of vaporization.

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