Molar heat capacity in metals and ionic solids

[indie452]

I am doing my revision and noticed that metals all have a molar heat capacity ~25 J/mol/K = 3R. Ionic solids such as NaCl and CaF2 however have different molar heat capacities. (~51 and 72 respectively)

Why is this? there is no explanation that my lecturer gave and I can't find it online but it seems like it probably comes from the basic physics.

I know that the observed values of c are not the theorized ones so not exactly 3R. But the values above are at room temp and so should just be the Dulong-Petit law.

So why are they different and is there a way to calculate what it could be via equation? Is it to do with the bonds producing different degrees of freedom?

any hints/help would be appreciated

 

[member 553083]

! The difference in molar heat capacities between metals and ionic solids is due to the different types of bonds present. Metals have strong metallic bonds, whereas ionic solids have strong electrostatic bonds. These different types of bonds lead to different vibrational frequencies, which in turn cause different amounts of kinetic energy to be stored in the lattice. Since molar heat capacity is related to the amount of energy stored in the lattice, this explains why the molar heat capacities of metals and ionic solids are different. To calculate the molar heat capacity of an ionic solid, you can use the Debye model of solids, which takes into account the vibrational frequencies of the lattice.