Which acid in Table 14.2 is most appropriate for preparation of a buffer solution with a pH of 3.1? 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 pH, not 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 are equal. That is why the buffer has the highest capacity, or is the best, while preserving a pH 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 3.1. We can calculate the \(p{K_a}\)from the K_avalue 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 the calculations that \(HN{O_2}\)has a \(p{K_a}\)value (3.3) which is closest to the desired pH of our solution and would therefore be the best choice for our buffer.

\(HN{O_2} \) would be the best choice for buffer.