Question

A buffer consists of 0.50M ${\mathbf{\text{NaH}}}_{\mathbf{\text{2}}}{\mathbf{\text{PO}}}_{\mathbf{\text{4}}}$and 0.40M ${\mathbf{\text{Na}}}_{\mathbf{\text{2}}}{\mathbf{\text{HPO}}}_{\mathbf{\text{4}}}$. Phosphoric acid is a triprotic acid (${\mathbf{\text{K}}}_{\mathbf{\text{a1}}}{\mathbf{\text{= 7.2×10}}}^{\mathbf{-}\mathbf{3}}{\mathbf{\text{,K}}}_{\mathbf{\text{a2}}}{\mathbf{\text{= 6.3×10}}}^{\mathbf{-}\mathbf{8}}$and${\mathbf{\text{K}}}_{\mathbf{\text{a3}}}{\mathbf{\text{= 4.2×10}}}^{\mathbf{-}\mathbf{1}}$).

(a) Which${\mathbf{\text{K}}}_{\mathbf{\text{a}}}$value is most important to this buffer?

(b) What is the buffer pH?

Short answer

(a) The value important to this buffer is${\text{K}}_{\text{a2}}$.

(b) The buffer pH obtained as is 7.10.

Step-by-step solution

Phosphoric acid buffer

The basicity of a phosphoric acid is three. The mixture of mono sodium phosphate and disodium phosphate forms a buffer mixture.

Subpart (a)

First, write the phosphoric acid dissociation process.

$$\begin{gathered} {\text{H}}_{\text{3}}{\text{PO}}_{\text{4}}{\text{+H}}_{\text{2}}\text{O}\rightleftharpoons {\text{H}}_{\text{2}}{\text{PO}}_{\text{4}}^{\text{-}}{\text{+H}}_{\text{3}}{\text{O}}^{\text{+}} \\ {\text{H}}_{\text{2}}{\text{PO}}_{\text{4}}^{\text{-}}{\text{+H}}_{\text{2}}\text{O}\rightleftharpoons {\text{HPO}}_{\text{4}}^{\text{2 -}}{\text{+H}}_{\text{3}}{\text{O}}^{\text{+}} \\ {\text{HPO}}_{\text{4}}^{\text{2 -}}{\text{+H}}_{\text{2}}\text{O}\rightleftharpoons {\text{PO}}_{\text{4}}^{\text{3 -}}{\text{+H}}_{\text{3}}{\text{O}}^{\text{+}} \end{gathered}$$

Write the sodium salt's dissolution.

$$\begin{gathered} {\text{NaH}}_{\text{2}}{\text{PO}}_{\text{4}}\to {\text{Na}}^{\text{+}}{\text{+H}}_{\text{2}}{\text{PO}}_{\text{4}}^{\text{-}} \\ {\text{Na}}_{\text{2}}{\text{HPO}}_{\text{4}}\to {\text{2Na}}^{\text{+}}{\text{+ HPO}}_{\text{4}}^{\text{2 -}} \end{gathered}$$

${\text{H}}_{\text{2}}{\text{PO}}_{\text{4}}^{\text{-}}$and ${\text{HPO}}_{\text{4}}^{\text{-}}$were both generated by salts. Both sides of the phosphoric acid's second dissociation include these chemical entities.

Therefore, for this buffer solution, we'll utilize${\text{K}}_{\text{a2}}$.

Subpart (b)

The given dihydrogen phosphate and hydrogen phosphate concentrations are:

$$\begin{gathered} {\text{[H}}_{\text{2}}{\text{PO}}_{\text{4}}^{\text{-}}\text{]=0.50M} \\ {\text{[HPO}}_{\text{4}}^{\text{2 -}}\text{]=0.40M} \end{gathered}$$

To find the pH, we may utilize the Henderson-Hasselbalch equation. First, use${\text{K}}_{\text{a2}}$to solve for the${\text{pK}}_{\text{a}}$ .

role="math" localid="1663392419506" $$\begin{gathered} {\text{pK}}_{\text{a}}{\text{= - logK}}_{\text{a}} \\ {\text{= - log(6.3×10}}^{-8}\text{)} \\ =7.20 \\ {\text{pH = pK}}_{\text{a}}\text{+ log}\frac{\text{[base]}}{\text{[ acid ]}} \\ {\text{= pK}}_{\text{a}}\text{+ log}\frac{\left[{\text{HPO}}_{\text{4}}^{\text{2 -}}\right]}{\left[{\text{H}}_{\text{2}}{\text{PO}}_{\text{4}}^{\text{-}}\right]} \\ \text{= 7.20 + log}\frac{\text{0.40M}}{\text{0.50M}} \\ \text{= 7.10.} \end{gathered}$$

Therefore, the value of the buffer pH is 7.10.