Question #44982

2'-Deoxythymidine (initial concentration $0.066 \text{ M}$) is reacted with a phosphoric acid buffer (total analytical concentration $[P]_{total} = 0.4 \text{ M}$) in a specialized solvent system at $298 \text{ K}$. The medium is buffered such that the concentration of neutral $H_3PO_4$ is exactly equal to the concentration of its monoanion $H_2PO_4^-$ (assume higher deprotonations are negligible).\n\nIn this medium, only the fully protonated, neutral $H_3PO_4$ species acts as the active electrophile for the nucleophilic acyl-like substitution by the nucleoside hydroxyl groups. The equilibrium constants for the formation of the 5'-phosphoester and 3'-phosphoester from neutral $H_3PO_4$ are $K_5 = 2.0 \times 10^{-3}$ and $K_3 = 0.5 \times 10^{-3}$, respectively.\n\nTo drive the thermodynamically unfavorable phosphorylation, a molecular sieve apparatus continuously strips water, maintaining its steady-state concentration at $1.0 \times 10^{-4} \text{ M}$. Assuming no other side reactions occur, what is the equilibrium concentration of the 5'-nucleotide (thymidine-5'-monophosphate)?