The molar heat capacity of a substance is the heat required to raise the temperature by 1 °C per mole of molecules or formula units of the substance. For a given substance, the more varieties of movement—such as vibrations—that the atoms in a lattice undergo, the greater the heat capacity. In 1819 the chemists Pierre Dulong and Thérèse Petit claimed (in modern language) that the molar heat capacity of a crystalline solid per atom is the same for all crystals.

(a) Verify this claim for metals by making a table of the molar heat capacities of Cu, Fe, Pb, and Zn.

(b) Verify this claim for ionic crystals by making a table of the heat capacity per mole of atoms in the compound for CuO, FeS, PbBr₂, and ZnO.

(c) Calculate the heat capacity per mole of atoms for CuSO₄ and PbSO₄. Do the atoms in a polyatomic ion act independently, or does the entire ion behave as one particle in the lattice?

Use your results to support your conclusion.