(Solved): Including activity coefficients, derive Equation 10-11 for potassium hydrogen phthalate \( \left(\m ...

Including activity coefficients, derive Equation 10-11 for potassium hydrogen phthalate \( \left(\mathrm{K}^{+} \mathrm{HP}^{-}\right) \). \( \left[\mathrm{H}^{+}\right]=\sqrt{\frac{K_{1} K_{2}\left[\mathrm{HP}^{-}\right] \gamma_{\mathrm{HP}}+K_{1} K_{\mathrm{W}}}{K_{1}+\left[\mathrm{HP}^{-}\right] \gamma_{\mathrm{HP}}}} \) potassium hydrogen phthalate \( \left(\mathrm{K}^{+} \mathrm{HP}^{-}\right) \) \( \left[\mathrm{H}^{+}\right]=\sqrt{\frac{K_{1} K_{2}\left[\mathrm{HP}^{-}\right]+K_{1} K_{\mathrm{w}}}{K_{1}+\left[\mathrm{HP}^{-}\right]}} \) \( \mathrm{F} \) is the formal concentration of the intermediate species. Incorrect Calculate the \( \mathrm{pH} \) of \( 0.10 \mathrm{M} \mathrm{KHP} \), using the derived equation. Assume the sizes of both \( \mathrm{HP}^{-} \)and \( \mathrm{P}^{2-} \) are \( 600 \mathrm{pm} \). For comparison, Equation 10-11 gives \( \mathrm{pH}=4 \).18. Activity coefficients can be found in this table. The \( \mathrm{p} K_{a} \) values for phthalic acid are \( 2.950 \) and \( 5.408 \)