I knew while learning about electrolysis that if the ionic compound is molten it becomes free moving ions.
If that is the case, what will happen if I continued heating till it reaches the boiling point so that the ionic compound evaporates?
Will it still be free moving ions?
Also, shouldn't the result be more efficient at electrolysis than in the liquid state due to increased mobility of ions? If not, why?
Usually not. Boiling point rarely exceeds 4-5 thousand kelvin. A typical ionic bound energy is about 5 eV. 1 eV is roughly 11 thousand kelvin, so ions in low-temperature vapors exist as molecules. When the temperature becomes enough to break ionic molecules, it is enough to strip one or two electrons from atoms, so high-temperature vapors will be plasma with electrons and positive ions.
To complete the previous answers: according to this article http://www.ncbi.nlm.nih.gov/pubmed/17579381 NaCl exists in the gas phase both as a monomer (NaCl), about 73% of atoms at 943K, and as a dimer where the four atoms are arranged in a wobbly square (the remaining 27%). Traces of Na${}_2$ and Cl${}_2$ are also observed. I expect that as the temperature goes up the proportion of the dimer drops.
Since the boiling point of NaCl is 1,686 K at 1atm the study must have been conducted at low pressure or with the NaCl vapor mixed in with other gases.
The article also says (GED = gas-phase electron diffraction) :
The determination of the structure of sodium chloride vapor by GED dates back as far as 1937, when it was studied by heating salt to around 1000 K. As a consequence of the visual analysis methods in use at the time, only the predominant and expected monomer species was detected. It was not until the 1950s that the existence of associated species such as dimers (Na2Cl2) were discovered using mass spectrometry. Microwave spectroscopy has provided detailed information on the structure of the monomer, but the lack of a permanent dipole moment makes this impossible for the dimer.
I believe that gaseous ionic compounds such as NaCl are in fact diatomic NaCl. One can't create a plasma by simply boiling ordinary compounds. The forces between ions are way too strong.
In liquid state, NaCl become free moving ions but the overall system is stable because of the attractions between the oppositely charged ions. I believe that gaseous NaCl would exists as very polar covalent or ionic molecules with their overall affect being electrically neutral (no plasma).
This is a purely intuited answer and should be taken with a grain of salt as I could find no numbers to back it up. If someone could change this into a comment for me I would be much obliged.
