Which acid in Table 14.2 is most appropriate for preparation of a buffer solution with a pH of 3.7? Explain your choice.

Even though we could set up the concentration ratio of base : acid in such a way that basically any buffer could make up a solution of any pH, all of the buffers would work very well at just any pH. This is because the capacity of buffers is different if the ratio of base to acid is not the same. The capacity of the buffer is defined as the amount of acid or base that can be added to the buffer until the pH of the solution changes significantly. A buffer solution is the best when the concentration of its components is equal. That is why the buffer has the highest capacity or is the beset equal to the \(p{K_a}\)of the acid part of the buffer. Therefore, in order to pick the most suitable buffer we need to see from the table 14.2. which acid has the \(p{K_a}\)value which is the closest to 3.7. We can calculate the \(p{K_a}\) from the K_a value in the table using the formula,

\(\begin{align}p{K_a} &= - log{K_a}\\p{K_a}\left( {HSO_4^ - } \right) &= - log\left( {1.2 \times 1{0^{ - 2}}} \right) &= 1.9\\p{K_a}(HF) &= - log\left( {3.5 \times 1{0^{ - 4}}} \right) &= 3.5\\p{K_a}\left( {HN{O_2}} \right) &= - log\left( {4.6 \times 1{0^{ - 4}}} \right) &= 3.3\\p{K_a}(HCNO) &= - log\left( {2 \times 1{0^{ - 4}}} \right) &= 3.7\\p{K_a}\left( {HC{O_2}H} \right) &= - log\left( {1.8 \times 1{0^{ - 4}}} \right) &= 3.7\\p{K_a}\left( {C{H_3}C{O_2}H} \right) &= - log\left( {1.8 \times 1{0^{ - 5}}} \right) &= 4.7\\p{K_a}(HClO) &= - log\left( {2.9 \times 1{0^{ - 8}}} \right) &= 7.5\\p{K_a}(HBrO) &= - log\left( {2.8 \times 1{0^{ - 9}}} \right) &= 8.6\\p{K_a}(HCN) &= - log\left( {4.9 \times 1{0^{ - 10}}} \right) &= 9.3\end{align}\)

We can see from our calculations that both \(HCNO\)and \(HC{O_2}H\)have \(p\;{K_a}\) values of 3.7. They would both, therefore, be an excellent choice for our buffer.

\( Both HCNO and HC{O_2}H \) would be an excellent choice for buffer.