KEY2CHEM

Relationship of pH and Acidity

 

The \(pH\) (\(pH = -log[\require{mhchem}\ce{H3O+}]\)) of an aqueous solution is determined by the identity and concentration of the substance that is dissolved in water. For acid-base systems, pH characterizes the relative availability of protons. The ability of an acid, HA, to donate a proton in water is measured by its equilibrium constant, \(K_a\):

\(\require{mhchem}\ce{HA(aq) + H2O(l) <=>H3O+(aq) + A^{-}(aq)} \;\;\;\; K_a\)

 

The \( pK_a \) of an acid (\(pK_a = - log K_a\)) is another measure of acid strength. A smaller \(pK_a\) corresponds to a larger \(K_a\), which corresponds to greater proton transfer by the acid.

 


Example 1.

 

A weak acid, \(\require{mhchem}\ce{HX}\), has a \(pK_a\) of \(4.76\). If the \(pH\) of the solution is \(3.08\), which species is mostly present in solution?

 

A. \(\require{mhchem}\ce{HX}\)

B. \(\require{mhchem}\ce{X-}\)

C. equal mixture of \(\require{mhchem}\ce{HX}\) and \(\require{mhchem}\ce{X-}\)

 

 

Solution

A. \(\require{mhchem}\ce{HX} \)

Since \(pH < pK_a\), most of the acid is in its protonated form.


Example 2.

 

Which solution will have the lowest \(pH\)? The \(pK_a\) of each acid is listed.

 

A. \(0.1 \text{ M } \require{mhchem}\ce{HCl};\; pK_a = -7.00\)

B. \(0.1 \text{ M } \require{mhchem}\ce{HF}; \;pK_a = 3.47\)

C. \(0.1 \text{ M } \require{mhchem}\ce{CH3COOH};\; pK_a = 4.76\)

 

Solution

 

A. \(0.1 \text{ M } \require{mhchem}\ce{HCl}; \;pK_a = -7.00 \)

The acid with the lowest \(pK_a \) (which corresponds to the greatest proton transfer when dissolved in water) will have the lowest \(pH\).


Example 3.

 

A solution contains \(0.25\text{ M }\) of weak acid \(\require{mhchem}\ce{HA}\) and \(1.0 \text{ M}\) of its conjugate base \(\require{mhchem}\ce{A-}\). The \(pK_a \) of \(\require{mhchem}\ce{HA}\) is \(5.22\). What is true about the \(pH\) of the solution?

 

A. \(pH = 5.22\)

B. \(pH > 5.22\)

C. \(pH < 5.22\)

 

 

 

Solution

 

 

B. \(pH > 5.22\)

Most of the solution is composed of the deprotonated form of the acid (its conjugate base, \(\require{mhchem}\ce{A-}\)). As such, the solution’s \(pH\) is determined by the predominant form, which yields a solution with \(pH > pK_a\) of the acid. This could also be proved numerically with the Henderson-Hasselbalch equation.

\(pH = pK_a + log \frac{\require{mhchem}\ce{A-}}{\require{mhchem}\ce{HA}} \)

\(pH = 5.22 + log \frac{1.0\text{ M}}{0.25\text{ M}}\)

\(pH = 5.22 + log 4\)

\(pH = 5.82\)