Why does RNA alone go into the aqueous phase when treated with phenol-chloroform at lower pH? At a neutral or basic pH, both DNA and RNA would escape into the aqueous phase. So how is DNA held back at acidic pH?
In this case there are two properties that determine the behaviour of RNA:
- Its polarity;
- Its acidity.
Because of its polarity, RNA tends to escape the phenol-clorophorm phase; actually, it can go into the aqueous phase even if the pH is neutral , but with a lower efficiency than if the pH is acidic. Here comes the second property, RNA acidity. Because of that, when RNA is in a neutral solution, it has a negative charge: the $-OH$s of the phosphate group dissociate to $-O^-$ and $H^+$. However, this does not happen in an acidic solution, where there are already too many $H^+$. Thus, at basic pH the $-OH$ groups are intact and have a neutral charge; this stabilizes the system.
Think about it: if the aqueous phase is at neutral pH and fills up with negatively charged RNA molecules, after a while no more negative molecules can enter that solution. On the other hand, if the RNA molecules that enter the aqueous phase stay electrostatically neutral, the number of molecules which go into the solution will be limited only by the availability of water molecules to dissolve them.
That is why you use acidic* pH, it is simply a matter of efficiency.
Disclaimer: This answer is based upon a comment by the OP under the OQ.
 You would never use a high-pH solution to extract RNA because such condition hydrolyses RNA.
The purpose of acid phenol extraction is to selectively retain RNA in the aqueous phase while DNA partitions to the organic phase or coalesces at the interphase. I have found many people on the internet say that this is due to protonation of DNA phosphates while RNA phosphates remain ionic, thus giving differing solubility. I do not buy this explanation because:
- The pKa of the phosphodiester moiety is several orders of magnitude lower than the pH used in acid phenol extractions, and so should be largely deprotonated.
- Given their similar structures, the drastic difference in pKa between RNA and DNA required for it to be preparatively useful, to me, seems implausible.
- I found no such claims in scientific literature.
The properties of DNA and RNA that come to mind and which may explain the differential solubility are:
- DNA is denatured in acid due to protonation of the nucleobases, which imparts positive charge. This could facilitate aggregation.
- DNA is generally longer.
- RNA has a 2' hydroxyl group which increase polarity of the molecule.
Somewhat supporting this is a FAQ from ThermoFisher:
Partitioning of the nucleic acids in phenol is pH dependent. At pH 7.0 or higher, both DNA and RNA partition into the aqueous phase. At an acidic pH (below 7.0) DNA is denatured and will move into the organic phase, but the RNA remains in the aqueous phase.
The exact biophysics escape me. I realize this is not an answer but, rather, more of a long comment. I thought it important to address what, in my mind, may be a misconception. Criticisms are welcome.