Please help! The Law of DuLong and Petit states that the heat capacity per mole of many metals is ...?

Question

approximately 6.0 calories per mole-degree C. Knowing that the specific heat capacity of three metals in Joules per gram-degree C. is 0.45 for Fe, 0.24 for Ag, and 0.13 for Au. Do these metals agree with the Law of DuLong and Petit? How do you know this? Using your understanding of bonding in metals, explain why this law appears to hold.

Answer 1

(0.45 J/g°C)(55.85 g/mole)(1 Cal/4.184 J)" = 6.0068 Cal/mole-°C
(0.24 J/g°C)(107.9 g/mole)(1 Cal/4.184 J)" = 6.1893 Cal/mole-°C
(0.13 J/g°C)(197.0 g/mole)(1 Cal/4.184 J)" = 6.1209 Cal/mole-°C
These values are within 3.2% of the Law of DuLong and Petit.

Answer 2

I think D&Ps law states that the heat capacity of metals is about 6 (cal per mole) which is about 25.2 J per mole. In fact it works reasonably well for all solids. Solids only have vibrations to absorb energy and a mole of solid will have 3*Avogadro's constant vibrational degrees of freedom. So if these vibrational energies are accessible you would expect the heat capacity to be 3*R (R = gas constant = 8.314 J mole-1 K-1) approx 24.9 J.