The French chemists Pierre L. Dulong and Alexis T. Petit noted in 1819 that the

Question

The French chemists Pierre L. Dulong and Alexis T. Petit noted in 1819 that the molar heat capacity of many solids at ordinary temperatures is proportional to the number of atoms per formula unit of the solid. They quantified their observations in what is known as Dulong and Petit's rule, which says that the molar heat capacity, Cp, of a solid can be expressed as where N is the number of atoms per formula unit and R is the universal gas constant. The observed heat capacity per gram of a compound containing thallium and chlorine is 0.21 J* K g. Use Dulong and Petit's rule to determine the empirical formula of the compound.

Explanation / Answer

Here Cp= N (3R)

And the value of, R gas constant= 8.3144621 J/K·mol
3R = 24.94 J/K·mol

Now we calculate the heat capacity of Ti and Cl compound with different-different formulas:

Now calculate the N for TiCl as follows:

N= 2 because of 2 atoms

molar mass of TiCl = 239.8365 g/mol

Now determine the heat capacity of TiCl per gram by dividing with its molar mass as follows:

2 x (24.94 J/K·mol) / (239.8365 g/mol)

= 0.2079 J/K·g
= 0.21 J/K.g

This values is same as observed values thus the molecular formula of the Ti and Cl compound is TiCl only.

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