Question #45003

A lipophilic B-vitamin analog creates a hydrophobic microenvironment (dielectric constant $\epsilon = 2.0$) around Thymine during DNA replication, altering its tautomeric equilibrium. Given the following thermodynamic data at $300\text{ K}$:

• Standard Gibbs free energy for the diketo $\rightleftharpoons$ enol tautomerization of Thymine in aqueous medium ($\epsilon = 80$): $\Delta G^\circ_{aq} = +26.75\text{ kJ/mol}$
• Standard free energy of transfer from aqueous to the hydrophobic microenvironment for the diketo form: $\Delta G^\circ_{tr}(\text{diketo}) = +19.00\text{ kJ/mol}$
• Standard free energy of transfer from aqueous to the hydrophobic microenvironment for the enol form: $\Delta G^\circ_{tr}(\text{enol}) = -2.00\text{ kJ/mol}$

Calculate the equilibrium constant ($K_{eq}$) for the tautomerization in the hydrophobic microenvironment at $300\text{ K}$. Additionally, identify the number of hydrogen bonds ($n$) the enol tautomer of Thymine will form with its new complementary purine base during a tautomeric shift mutation. (Take $2.303 RT = 5.75\text{ kJ/mol}$ at $300\text{ K}$)

Provide the answer in the format: $K_{eq}, n$.