Question #44514

An aqueous buffer solution at $298\text{ K}$ is prepared by dissolving $0.144\text{ mol}$ of a neutral amino acid zwitterion ($\ce{HA^\pm}$) and $0.144\text{ mol}$ of its sodium salt ($\ce{NaA}$) in water, along with an inert non-electrolyte. The total mass of the resulting solution is exactly $2000\text{ g}$ and the mass of the water solvent is $1.00\text{ kg}$. The density of the solution is $1.250\text{ g mL}^{-1}$.

The thermodynamic acid dissociation constant for the zwitterion is $pK_{a2} = 9.60$. Assuming the Debye-Hückel limiting law applies, what is the $pH$ of this buffer solution?

(Given: Debye-Hückel constant $A = 0.50\text{ L}^{1/2}\text{ mol}^{-1/2}$ at $298\text{ K}$. The limiting law is $\log \gamma_i = -A z_i^2 \sqrt{I_c}$, where $I_c$ is the ionic strength in molarity).