The vapor pressure, in mm of Hg , of solid ammonia is given...

The vapor pressure, in mm of Hg , of solid ammonia is given by the relation: $\ln p=23.03-3754 / T$ where $T=$ absolute temperature. The vapor pressure, in mm of Hg , of liquid ammonia is given by the relation: $\ln p=19.49-3063 / T$. (a) What is the temperature of the triple point? (b) Compute the latent heat of vaporization (boiling) at the triple point. Express your answer in $\mathrm{cal} / \mathrm{mole}$. (You may approximate the be-havior of the vapor by treating it as an ideal gas, and may use the fact that the density of the vapor is negligibly small compared to that of the liquid.) (c) The latent heat of sublimation at the triple point is $7508 \mathrm{cal} / \mathrm{mole}$. What is the latent heat of melting at the triple point?

The vapor pressure, in mm of Hg , of solid ammonia is given by the relation: $\ln p=23.03-3754 / T$ where $T=$ absolute temperature.

The vapor pressure, in mm of Hg , of liquid ammonia is given by the relation: $\ln p=19.49-3063 / T$.
(a) What is the temperature of the triple point?
(b) Compute the latent heat of vaporization (boiling) at the triple point. Express your answer in $\mathrm{cal} / \mathrm{mole}$. (You may approximate the be-havior of the vapor by treating it as an ideal gas, and may use the fact that the density of the vapor is negligibly small compared to that of the liquid.)
(c) The latent heat of sublimation at the triple point is $7508 \mathrm{cal} / \mathrm{mole}$. What is the latent heat of melting at the triple point?

Key Concepts

Triple Point

The triple point is the unique set of temperature and pressure conditions at which all three phases of a substance (solid, liquid, and gas) coexist in thermodynamic equilibrium. It is a fundamental concept in phase diagrams and phase equilibrium, playing a crucial role in defining the conditions for phase transitions.

Clausius-Clapeyron Equation

The Clausius-Clapeyron equation provides a relationship between the vapor pressure of a substance and its temperature during a phase change. It is used to derive important thermodynamic quantities such as the latent heat of transformation by relating the slope of a plot of the natural logarithm of vapor pressure versus the inverse absolute temperature to the enthalpy change associated with the phase transition.

Latent Heat

Latent heat is the amount of energy that must be added (or removed) per mole or unit mass of a substance to induce a phase change at constant temperature and pressure, without changing the temperature. It encompasses latent heat of vaporization, fusion (melting), and sublimation, and is an essential concept when analyzing energy changes in phase transitions.

Ideal Gas Approximation

The ideal gas approximation assumes that the vapor phase behaves as an ideal gas, meaning that the interactions between molecules are negligible and the volume occupied by the molecules themselves is small compared to the total volume. This simplification is useful in practical calculations of vapor pressures and latent heats when the density of the vapor is very low compared to that of the condensed phases.

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