Question

What is the \[{\text{pH}}\] of a solution of \[{\text{0}}{\text{.28M}}\] acid and \[{\text{0}}{\text{.84M}}\] of its conjugate base if the ionization constant of acid is \[{\text{4}} \times {\text{1}}{{\text{0}}^{ - 4}}\]?
A. $3.88$
B. $3.34$
C. $7$
D. $10.12$

Answer 1

Hint: We should know that the pH of an aqueous solution is a measurement of the concentration of hydrogen ions in the solution. While \[{\text{pH}}\] and \[{\text{p}}{{\text{K}}_a}\] are connected, \[{\text{p}}{{\text{K}}_a}\] is more specific in that it lets you forecast what a molecule will do at a certain pH. \[{\text{p}}{{\text{K}}_a}\]essentially informs you what \[{\text{pH}}\]a chemical species must have in order to donate or take a proton. The relationship between \[{\text{pH}}\] and $p{K_a}$ is described by the Henderson-Hasselbalch equation.

Complete answer:
The relation to be used for this question is the Henderson-Hasselbalch equation.
We can solve for the other value using an approximation known as the Henderson-Hasselbalch equation if you know either \[{\text{pH}}\] or \[{\text{p}}{{\text{K}}_a}\]:
\[pH = p{K_a} + \log \dfrac{{\left[ {conjugate base} \right]}}{{\left[ {weak acid} \right]}}\]
\[pH = p{K_a} + \log \dfrac{{\left[ {{A^ - }} \right]}}{{\left[ {HA} \right]}}\]
\[{\text{pH}}\] is equal to the sum of the \[{\text{p}}{{\text{K}}_a}\]value and the log of the conjugate base concentration divided by the weak acid concentration.
Given,
Concentration of acid \[ = 0.28\]
Concentration of base \[ = 0.84\]
And, ionization constant, \[{\text{p}}{{\text{K}}_{\text{a}}}{\text{ = 4 \times 1}}{{\text{0}}^{{\text{ - 4}}}}\]
Now we can substitute the known values we get,
Thus, \[{\text{pH = 4}} \times {\text{1}}{{\text{0}}^{ - 4}} + \log \dfrac{{\left[ {0.38} \right]}}{{\left[ {{\text{0}}{\text{.84}}} \right]}}\]
On simplification we get,
                 \[ = 3.88\]

So, the correct answer is “Option A”.

Note:
 It should be noted that when we have \[{\text{pH}}\]or \[{\text{p}}{{\text{K}}_a}\] values for a solution, we can tell a lot about it and how it compares to other solutions: The higher the concentration of hydrogen ions\[\left[ {{{\text{H}}^{\text{ + }}}} \right]\], the lower the\[{\text{pH}}\]. We need to know that the lower the\[{\text{p}}{{\text{K}}_a}\], the more powerful the acid is and the more protons it can contribute. The \[{\text{pH}}\]of a solution is determined by its concentration. This is significant since it implies that a weak acid has a lower pH than a dilute strong acid.