Why does $\ce{PCl_5}$ exists in the solid state as $\ce{[PCl_6]^{-}[PCl_4]^{+}}$? What is the problem with it that it doesn't exist in its original form in solid state? Like why isn't it just $\ce{PCl_5}$ in solid state as well?
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In the gas phase ions cannot be stabilized through solvation or lattice forces so ions are destabilized relative to non-ionic entities in the gas phase. $\ce{NaCl}$ is a case in point, in the gas phase it exists as an equilibrium of monomers and dimers. Yet in the solid phase it exists as a highly ionic crystal. This example demonstrates that going from a gas to a solid can dramatically affect the relative stabilities of ionic and covalent structures.
The same is true in the case of $\ce{PCl_5}$. In the gas phase it exists as a covalent compound with a trigonal bipyramid structure. However, in the solid phase, it turns out that enthalpic affects favor the ionic tetrahedral/octahedral structure $\ce{[PCl4]^{+}[PCl6]^{-}}$. Simply said, the ionic structure turns out to be thermodynamically more stable in the solid phase where positive and negative charges can be arranged to stabilize the entire lattice; whereas in the gas phase the positive and negative ions cannot be stabilized so the covalent form is favored since it is now lower in energy than the ionic form.
Another reason why the ionic form is preferred in the solid phase is that packing regular geometric shapes such as tetrahedra and octahedra together allows for a more stable arrangement since they can be packed closer together and in a more ordered arrangement than non-regular (kind of an odd shape) trigonal bipyramids can be arranged.
Edit: Response to OP's comment on ion stabilization
If we generate an ion in the gas phase, it will have a certain energy associated with it. If we put that ion in a solution its energy will be much less. We say the ion has been stabilized by placing it in solution. Some solvents will stabilize the ion more than other solvents. This relates to the dielectric constant of the solvent which is a measure of the solvent's polarity. The higher the dielectric constant for a solvent, the more polar the solvent and the better its ability to stabilize and lower the energy of an ion dissolved in it.
Here is a picture showing a sodium ion dissolved in water. Note how the negative ends of the dipoles in the water (the negatively polarized oxygen end of the water molecule) molecules congregate and orient themselves around the positive ion. This orientation of the negative ends of multiple water molecules around a positive sodium ion is what stabilizes the ion in solution. There is no such stabilization in the gas phase. In the gas phase it is just a "naked" ion without any external stabilization, so in the gas phase an ion will have a higher energy.
image source see the "Solvation od Ions" section
Here is another picture showing showing (on the right) sodium chloride in a crystal lattice. The sodium and chloride ions pack around each other to perform the same function as a solvent. The opposite charges arrange themselves around each other to minimize electrostatic repulsion between like ions and maximize the stabilizing electrostatic attraction between oppositely charged ions. Through these types of arrangements, the "lattice" can stabilize ions much like a solvent can stabilize ions. Consequently, both solvents and crystal lattices stabilize ions and lower their energy compared to the ion's energy in the gas phase where no such stabilization exists.
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Could you please elaborate on the thermodynamic stability attained by making it exist as $[PCl_4]^+[PCl_6]^-$? And moreover why is closed packing of tetrahedral and octahedral so favorable? I do get that charge separation may make the bond stronger but won't the chlorines repel with each other more? – Rohinb97 Feb 22 '15 at 21:35
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I've edited my answer to address your comment. But basically ions aren't very stable in the gas phase and can be very stable in the solid phase. As to the packing question, regular shapes with high symmetry can be arranged in a more ordered fashion than an irregular shape like a trigonal bipyramid. The more ordered an ionic solid, the lower its energy because this allows multiple positive charges to be arranged around a negative charge and vice versa. – ron Feb 22 '15 at 21:52
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"But basically ions aren't very stable in gas phase and can be very stable in solid phase". I didn't get this. The entropy increases when we convert a solid to a gas. It is more thermodynamically favorable for stability. And the axial bonds aren't so irregular. The molecules could be stacked a little sideways to accommodate them. As I said before, I do get that charge separation is favorable, since negative will attract positive and vice versa. I'm asking about the fact that how do the new shapes make packing more efficient. – Rohinb97 Feb 22 '15 at 22:10
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Are you saying you don't understand why ions are destabilized in the gas phase and stabilized in the solid phase? – ron Feb 22 '15 at 22:16
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Also look at the figure at the top of page 620 here. Notice how the octahedron tucks in snugly between the two tetrahedrons, I don't think you could have any similarly efficient arrangement with only trigonal bipyramid structures. – ron Feb 22 '15 at 22:48
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I understood your packing point. Thanks for the link. And yes I didn't get why ions are destabilized in gas phase but stabilized in solid phase. – Rohinb97 Feb 23 '15 at 07:03
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I've edited my question to try and better address the stabilization question – ron Feb 23 '15 at 17:02
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Solvents make the liquid state stable because they try to bear the strain present in the bond if any. There is a lot of difference between ions in a solvent and in solid state. An ion in solid state "only has to face itself" and there is no external factor to make it more stable. In a liquid, presence of other ions makes the liquid state stable. I fail to understand your analogy between the "lattice" stabilizing the ions and the solvent stabilizing the ions. – Rohinb97 Feb 23 '15 at 17:15
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"An ion in solid state "only has to face itself" and there is no external factor to make it more stable." No, it also faces other ions or other molecular dipoles and the electrostatic attraction stabilizes the ion. "In a liquid, presence of other ions makes the liquid state stable." No other ions don't make the liquid stable, other ions make the other ions stable and the liquid stabilizes all ions through various (dipole H-bonding, etc.) interactions. Read the articles linked to my image sources. – ron Feb 23 '15 at 17:23
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The links go towards Diels-Alder reaction and solubility of liquids. They nowhere touch this topic. And how can a solid face other ions/molecular dipoles ? I am not talking about the solid in a solvent. I'm saying that a solid, just in air, not in any solvent or anything. There is no external factor to make it more stable. And in my above comment the "in presence of other ions" meant the ions of the solvent. The solvent makes the solute stable. Just wanted to clarify that out because I didn't get your last statement. – Rohinb97 Feb 23 '15 at 17:54
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As I wrote next to the link, you need to look further down the page at the "Solvation of Ions" section. A solid faces other ions internally, within its structure. – ron Feb 23 '15 at 18:12
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Would chatting perhaps be helpful? – ron Feb 23 '15 at 18:24
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Let us continue this discussion in chat. – Rohinb97 Feb 23 '15 at 20:36
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OK I'll see you there. – ron Feb 23 '15 at 20:40
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Sorry @ron I had to leave the chat. Please see my messages in the chatroom. – Rohinb97 Feb 25 '15 at 07:22
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see my response in chat – ron Feb 25 '15 at 16:04