Acidity of HCl v HF, Is it really entropy?

The following is a message I sent referring to the difference in acidity of HCl and HF.

Another student and I were discussing the differences between solution phase and gas phase data. He has been a strong advocate of gas phase acidity. Anslyn and Dougherty report that ionization is a high energy reaction in the gas phase and homolytic cleavage is a lower energy process. They say one must calculate a gas phase acidity from the ionization potential and electron affinity. I have been nervous about whether these calculations measure what we think they measure. My friend sent a photocopy of a page from the textbook, “Chemical Structure and Reactivity: An Integrated Approach.” Some time has passed since we had first discussed this. My argument then was that HF was not a weaker acid because of a lower entropy, but that a lower entropy was the result of its being a weaker acid. I believe the argument on an entropy basis is circular. Entropy is only a force for randomization and should not be implied as a force for aggregation. 

I’ve had to take some time to think about this problem. My initial argument had been that the entropy term of HF should be similar to that of HCl, provided HF also ionized. Clearly the entropy of molecular and ionic HF would be quite different, but ionic HF and HCl may be similar. I reasoned the entropy for HF competes with the affinity of fluoride for its proton. If the net increase in entropy is small, it is due to the greater affinity of fluoride for its proton. 

My objective was to show that bonds are not made up of covalent and ionic portions. I argue that homolytic and heterolytic energies reflect the gas phase and solution phase energies and they are simply different (though they may be similar). The Hess’s Law cycle in the book addresses this point in a way. The pKa gives direct data for the energy of the ionization reaction. HF is the weakest acid. The Hess’s Law cycle attempts to determine the same result by a different mechanism. Although I have some anxiety about step 3, it may be okay for hydrogen. However, I really have a problem with step 4. Step 4 assumes HF forms ions in solution in the same manner as HCl. The solution phase data tells you HF is only partly ionic. Step 4 is actually returning to the start of the Hess’s Law cycle with a fraction being siphoned off in an ionization step. 

A reason I have some anxiety about step 3 is that the gas phase ionization of lithium or sodium is endothermic while solution phase it is very exothermic. If the gas phase result reflected the inherent atomic properties of lithium or sodium, then we should expect to find metallic lithium and sodium in their natural state. I argue the gas phase endothermic reaction is simply different than the solution phase reaction. A solution phase Born-Haber cycle for NaCl goes from elemental sodium and chlorine and gives solvent separated ions. Therefore, ion affinity is not a factor and this type of Born-Haber cycle is simply a measure of the redox energy of this reaction. 

I think I have the ideas correct, though my explanations may be muddled. Can you comment? 

Thank you,
PW
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