A student wants the dissociation constant of a new weak monobasic acid HA. She makes the cell $\displaystyle \text{Pt}\,|\,\text{H}_2(g,\ 0.500\ \text{bar})\,|\,\text{HA}(aq,\ 0.0500\ \text{mol L}^{-1})\,\|\,\text{Cu}^{2+}(aq,\ 0.0100\ \text{mol L}^{-1})\,|\,\text{Cu}(s)$ Her hydrogen supply gives only $0.500\ \text{bar}$, so the gas at the platinum is not at the standard pressure. At $298\ \text{K}$ the emf is $0.449\ \text{V}$, and the copper electrode is the cathode. Take $E^\circ(\text{Cu}^{2+}/\text{Cu}) = 0.34\ \text{V}$ and $\dfrac{2.303RT}{F} = 0.059\ \text{V}$. Treat the solutions as ideal, and take the acid as the only source of hydrogen ions on the left. The salt bridge removes any junction potential. What is $K_a$ of HA?