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

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.