Calculate the pH of a buffer solution prepared from 0.155 mol of phosphoric acid, 0.250 mole of KH₂PO₄, and enough water to make 0.500 L of solution.

In order to calculate the \(pH\)of this buffer solution, we need to use the Henderson-Hasselbach equation:

\(pH = p{K_a} + log\frac{{c\left( {{A^ - }} \right)}}{{c(HA)}}\)

We do not yet know the concentrations of the buffer components, but we can calculate them using the equation:

\(\begin{align}c &= \frac{n}{V}c\left( {{H_3}P{O_4}} \right)\\ &= \frac{{0.155\;mol}}{{0.500\;L}}c\left( {{H_3}P{O_4}} \right)\\ &= 0.310Mc\left( {{H_2}PO_4^ - } \right)\\ &= \frac{{0.250\;mol}}{{0.500\;L}}c\left( {{H_2}PO_4^ - } \right)\\ &= 0.500M\end{align}\)

We can calculate\(p{K_a}\)using the equation:

\(p{K_a} = - log{K_a}\)

We can look up the\({K_a}\)value for all acids in the table in the Appendix\(H\)in the book. The value for phosphoric acid is\(7.5 \times 1{0^{ - 3}}\).

\(p{K_a} = - log{K_a}\)

\(\begin{align}p{K_a} &= - log\left( {7.5 \times 1{0^{ - 3}}} \right)\\p{K_a} &= 2.1\end{align}\)

Now that we know the concentrations of the buffer components, we can calculate the pH using the Henderson-Hasselbach equation:

\(\begin{align}pH &= p{K_a} + log\frac{{c\left( {{A^ - }} \right)}}{{c(HA)}}\\pH &= 2.1 + log\frac{{0.500M}}{{0.310M}}\\pH &= 2.3\end{align}\)

The pH value of the buffer solution in the problem is 2.3