A student measures the equilibrium concentration of hydronium ion in a \(0.10 \text{ M}\) aqueous solution of a weak monoprotic acid, \(\text{HA(aq)}\), at \(298 \text{ K}\).

\[ \text{HA(aq)} + \text{H}_2\text{O(l)} \rightleftharpoons \text{H}_3\text{O}^+\text{(aq)} + \text{A}^-\text{(aq)} \]

At equilibrium, \([\text{H}_3\text{O}^+] = 1.0 \times 10^{-3} \text{ M}\).

Useful information at \(298 \text{ K}\):

• \(RT \approx 2.48 \text{ kJ/mol}\)
• \(\ln(1.0 \times 10^{-6}) \approx -13.8\)
• \(\ln(1.0 \times 10^{-5}) \approx -11.5\)
• \(\ln(1.0 \times 10^{-3}) \approx -6.9\)

Based on these data, what is the value of \(\Delta G^\circ\) for the ionization of \(\text{HA(aq)}\) at \(298 \text{ K}\)?