Derivation of Troutons rule

We know experimentally that vapor molecules will condense when their cohesive energy with all the other surrounding molecules in the condensed phase exceeds about 9 kT. Since 6VT T) for close-packed structures, from Equation (261), then if we equalize these two quantities, we will find V d) (9/6)k / (3/2)kT, and we may conclude that when the 

This idea may be tested by examining the evaporation of liquids. We can try to calculate how strong the intermolecular attraction should be if it will allow vapor (gas) molecules to condense into a liquid at a particular temperature and pressure. Since we know from the Gibbs phase equation that the chemical potentials for gas and liquid molecules in equilibrium with each other are equal, we may write 

the volume of an ideal gas at standard atmospheric pressure (1 atm) and temperature (273.15 K) is approximately 22400 cm3, and the same gas occupies approximately 20 cm3 when condensed it is obvious that the cohesive energy of the liquid greatly exceeds the cohesive energy of the gas, At i aG so we may neglect, aCL and rearrange the above equation so that 

From the ideal gas equation, it is determined that the In term changes by only 13% in the range T = 100-500 K. Since this range includes most boiling temperatures of liquids, we may write approximately for the cohesive energy of the liquid 

This equation shows that the boiling point of any liquid is simply proportional to the energy needed to evaporate the molecule. As the internal energy of vaporization is given by 

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