Chapter 5, Problem 5.101QE

In the 1880s, Frederick Trouton noted that the enthalpy of vaporization of 1 mol pure liquid is approximately 88 times the boiling point, T_b, of the liquid on the Kelvin scale. This relationship is called Trouton’s rule and is represented by the thermochemical equation

liquid → gas ΔH = 88 · T_b, joules

Combined with an empirical formula from chemical analysis, Trouton’s rule can be used to find the molecular formula of a compound, as illustrated here. A compound that contains only carbon and hydrogen is 85.6% C and 14.4% H. Its enthalpy of vaporization is 389 J/g, and it boils at a temperature of 322 K.

1. (a) What is the empirical formula of this compound?
2. (b) Use Trouton’s rule to calculate the approximate enthalpy or vaporization or one mole of the compound. Combine the enthalpy of vaporization per mole with that same quantity per gram to obtain an approximate molar mass of the compound.
3. (c) Use the results of parts (a) and (b) to find the molecular formula of this compound. Remember that the molecular mass must be exactly a whole-number multiple of the empirical formula mass, so considerable rounding may be needed.