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The relationship between acid pH and pKa in aqueous solutions is described by the Henderson-Hasselbalch equation (acid dissociation constant). This equation can be used to forecast the pH of a buffer solution when the concentrations of such acid as well as its conjugate base, or the base and the related conjugate acid, are determined.

A weak acid and its conjugate base, or a weak base and its conjugate acid, make up a buffer solution.

Given data.

12.43gtris

5.67 gtris hydrochloride

$$\begin{gathered} \left[\mathrm{tris}\right]=\frac{12.43\mathrm{g}/\mathrm{L}}{121.135\mathrm{g}/\mathrm{mol}}=0.1026M \\ \left[\mathrm{tris}\mathrm{hydrochloride}\right] \\ =\frac{5.67\mathrm{g}/\mathrm{L}}{157.596\mathrm{g}/\mathrm{mol}} \\ =0.0359\mathrm{M} \end{gathered}$$

While mixing, the concentration remains constant, and pH may be calculated using the Henderson-Hasselbalch equation.

$$\begin{gathered} \mathrm{pH}={\mathrm{pK}}_{\mathrm{a}}+\log \frac{\mathrm{I}\mathrm{tris}}{\left[\mathrm{tris}\mathrm{hydrochloride}\right]} \\ \mathrm{pH}=8.072+\log \frac{0.1026}{0.0359} \\ \mathrm{pH}=8.072+0.456 \\ =8.53 \end{gathered}$$

Thus, the pH of buffered solution tris(hydroxymethyl)-aminomethane and tris hydrochloride is 8.53