# Is there an actual specific heat for aluminum in its gaseous state? [closed]

I've scourged the internet and I can't seem to find it anywhere although I've found the specific heat values for aluminum in both solid and liquid states. I'm trying to construct a heating curve and I need the specific heat capacity of aluminum in its gaseous state in order to calculate the amount of energy that would be necessary to bring aluminum from its liquid state to a gaseous state.

By "bring aluminum from its liquid state to a gaseous state", I assume you mean to a gaseous state at a temperature above aluminum's boiling point—since to merely convert it from a liquid to a gas, you only need the enthalpy of vaporization.

According to https://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node18.html, most metallic vapors have molar heat capacities very close to those of ideal gases, i.e., $$C_v = 3/2 R = 12.47$$ J/(mol K) and $$C_p = 5/2 R = 20.79$$ J/(mol K). Thus you can obtain aluminum's specific heat capacity by dividing by the atomic mass, giving $$C_v = 0.46$$ J/(g K) and $$C_p = 0.77$$ J/(g K)

The reason for this is that metals don't form metallic bonds in the gaseous state (metallic bonding is a collective phenomenon that requires bulk metal), and are thus monatomic*. And the heat capacities of monatomic gases are simple, since they have only translational degrees of freedom.

[*As real gases, they may not be exactly monatomic, since they can still transiently associate via van der Waals forces. But treating them as monatomic is a good approximation.]

The exception to the above would occur when the temperature is sufficiently high to cause the metal to ionize, in which case you would have a higher heat capacity because you would now have two (or more) particles for every ionized aluminum atom. But since aluminum's first ionization energy is 5.985 eV/atom = $$577$$ kJ/mol, and $$RT$$ at $$3000$$ K is $$25$$ kJ/mol, I don't expect there to be significant ionization close to its $$2792$$ K boiling point. [Also, some might argue that, once it starts ionizing, it is no longer a gas, but a gas-plasma mixture.]

• I have read somewhere gaseous mercury is an exception among metals not forming diatomic molecules, being called for that pseudonoble gas. But it may be true that those diatomic molecules are just negligible parts for most metals and conditions. I remember posting recently some link about a study of temperature and pressure dependency of Rb2 occurrence. It was not negligible. Dec 7 '20 at 6:26
• en.wikipedia.org/wiki/Dirubidium Dirubidium is produced when rubidium vapour is chilled. The enthalpy of formation (ΔfH°) in the gas phase is 113.29 kJ/mol.[2] In practice, an oven heated to 600 to 800K with a nozzle can squirt out vapour that condenses into dimers.[3] The proportion of Rb2 in rubidium vapour varies with its density, which depends on the temperature. At 200° the partial pressure of Rb2 is only 0.4%, at 400 °C it constitutes 1.6% of the pressure, and at 677 °C the dimer has 7.4% of the vapour pressure (13.8% by mass). Dec 7 '20 at 7:05
• Practically no data there, but I guess the page would not exist if dialuminium was not a thing. Dec 7 '20 at 7:15
• @Poutnik Mercury does seem to be an exception. But as far as dialuminum being "a thing", that page is thin evidence. It could have been auto-generated purely as a placeholder by a computer algorithm after doing a webcrawl and finding articles like this, which specify "dialuminum trioxide", which is not Al2(g). spiedigitallibrary.org/conference-proceedings-of-spie/10035/… Dec 7 '20 at 8:38
• I have not done detailed research, so I was not going to make any hard claim about Al2(g). But I guess for majority, but not all, of metals and conditions, temperature is too high and/or vapour density too low to form considerable amount of dimers, affecting the heat capacity values. BTW there is no need to form metallic bonds that are a bulk property. The old good covalent bond is enough. I suppose noticable dimerization may occur mainly for metals with low boiling point like alkali metals, or just for sensitive spectroscopic methods, e.g. measuring vibration-rotation IR spectra. Dec 7 '20 at 9:05