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# How does $p{K_a}$ change with pH?

Last updated date: 19th Jul 2024
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Hint: The term pH and $p{K_a}$ are used in an equation known as Henderson-Hasselbalch equation. In the equation, the pH is equal to the sum of $p{K_a}$ value and log of the concentration of the conjugate base divided by the concentration of weak acid.
The pH is the measure of the hydrogen ion concentration.

Complete step by step answer:
The pH of the solution is defined as the measure of the concentration of hydrogen ions in the aqueous solution.
It is given as the negative logarithm of hydrogen ion concentration.
$pH = - \log [{H^ + }]$
The relationship between the pH and $p{K_a}$ is given by the Henderson-Hasselbalch equation. The equation which gives relation between the pH of an aqueous solution of an acid and the acid dissociation constant of the acid is described as the Henderson-Hasselbalch equation.
The equation is given as shown below.
$pH = p{K_a} + \log \left( {\dfrac{{[Conjugate\;base]}}{{[weak\;acid]}}} \right)$
$pH = p{K_a} + \log \left( {\dfrac{{[{A^ - }]}}{{[HA]}}} \right)$
The pH is the sum of $p{K_a}$ value and log of the concentration of the conjugate base divided by the concentration of weak acid.
At half of the equivalence point the pH of solution is equal to the $p{K_a}$.
$pH = p{K_a}$
The $p{K_a}$ value is equal to the negative logarithm of acid dissociation constant of the weak acid.
It is given as shown below.
$p{K_a} = - \log \left[ {{K_a}} \right]$
Where,
${K_a}$ is the acid dissociation constant of the weak acid.
Lower is the pH, higher will be the concentration of hydrogen ions. The lower will be the value of $p{K_a}$stronger will be the acid and it will have higher ability to donate protons.
The pH depends on the concentration of the solution whereas the $p{K_a}$ is constant of each molecule and cannot be affected by the concentration.

Note:
The Henderson-Hasselbalch equation is used to calculate the pH of the buffer solution and also the equilibrium pH in an acid-base reaction. The $p{K_a}$ value measures the strength of the acid in the solution.