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, ????P , of a solid can be expressed as ????P=????⋅3???? where ???? is the number of atoms per formula unit and ???? is the universal gas constant. The observed heat capacity per gram of a compound containing rubidium and oxygen is 0.64 J·K−1·g−1 . Use Dulong and Petit's rule to determine the empirical formula of the compound.

Answer 1

The empirical formula of the compound : RbO₂

Further explanation

Dulong and Petit's rule's rule, which says that the molar heat capacity, Cp, of a solid can be expressed as

$\large{\boxed{\bold{Cp=N(3R)}}$

Where N is the number of atoms per formula unit and R is the universal gas constant

While the value of R is:

R = 8.3144621 J / K · mol

then:

3R = 24.94 J / K · mol

Heat capactiy per gram of a compound containing rubidium and oxygen is 0.64 J · K⁻¹ · g⁻¹

We try the possible empirical formula from the composition of Rb and O

• Rb₂O

So the number of atoms: 3 (Rb = 2 atoms, O = 1 atom)

Then the value of the Cp:

Molar mass Rb₂O = 2.85.5 + 1.16 = 187 g/mol

$\displaystyle Cp=N(3R)\\\\0.64=\frac{3.24.94}{187}\\\\0.64\neq0.4$

Then this empirical formula Rb₂O  is not appropriate

• RbO₂

So the number of atoms: 3 (Rb = 1 atom, O = 2 atoms)

Then the value of the Cp:

Molar mass RbO₂ = 1.85.5 + 2.16 = 117.5 g / mol

$\displaystyle Cp=N(3R)\\\\0.64=\frac{3.24.94}{117.5}\\\\0.64=0.64$

Then this empirical formula RbO₂  is appropriate

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Keywords:  an empirical formula,compound, gas constant, Dulong and Petit's rule,the molar heat capacity

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