Question

How does ${\text{p}}{{\text{K}}_{\text{a}}}$ change with temperature?

Answer 1

Hint: To solve this we must know that ${\text{p}}{{\text{K}}_{\text{a}}}$ is the negative logarithm to the base 10 of the acid dissociation constant i.e. ${{\text{K}}_{\text{a}}}$. The ${\text{p}}{{\text{K}}_{\text{a}}}$ value is used to indicate the strength of acids. To solve this we must know the relationship between acid dissociation constant and temperature.

Formula Used:
${\text{p}}{{\text{K}}_{\text{a}}} = - \log {{\text{K}}_{\text{a}}}$

Complete step by step answer:
We know that ${\text{p}}{{\text{K}}_{\text{a}}}$ is the negative logarithm to the base 10 of the acid dissociation constant i.e. ${{\text{K}}_{\text{a}}}$. The ${\text{p}}{{\text{K}}_{\text{a}}}$ value is used to indicate the strength of acids.
We know that ${{\text{K}}_{\text{a}}}$ i.e. the acid dissociation constant is the measure of strength of an acid in the solution. It measures the position of equilibrium for the dissociation of an acid.
Consider the reaction for the dissociation of acid,
${\text{HA}} \rightleftharpoons {{\text{H}}^ + } + {{\text{A}}^ - }$

The expression for the acid dissociation constant i.e. ${{\text{K}}_{\text{a}}}$ is as follows:
\[{{\text{K}}_{\text{a}}} = \dfrac{{[{{\text{A}}^ - }][{{\text{H}}^ + }]}}{{[{\text{HA}}]}}\]
- The dissociation of an acid is an endothermic process. In an endothermic process, the system absorbs heat from the surrounding. Thus, when heat is absorbed, the equilibrium shifts from left to right i.e. the rate of dissociation of acid increases. As the dissociation of acid increases, the acid dissociation constant i.e. ${{\text{K}}_{\text{a}}}$ also increases.
- We know that ${\text{p}}{{\text{K}}_{\text{a}}}$ is the negative logarithm to the base 10 of the acid dissociation constant i.e. ${{\text{K}}_{\text{a}}}$. The expression for ${\text{p}}{{\text{K}}_{\text{a}}}$ is as follows:
${\text{p}}{{\text{K}}_{\text{a}}} = - \log {{\text{K}}_{\text{a}}}$

From the above expression we can say that as the ${{\text{K}}_{\text{a}}}$ increases ${\text{p}}{{\text{K}}_{\text{a}}}$ decreases. Thus, as the temperature increases, ${\text{p}}{{\text{K}}_{\text{a}}}$ decreases.
Thus, ${\text{p}}{{\text{K}}_{\text{a}}}$ is inversely proportional to the temperature.

Note: When the ${\text{p}}{{\text{K}}_{\text{a}}}$ value is lower then the acid is stronger. This is because a low ${\text{p}}{{\text{K}}_{\text{a}}}$ value indicates that acid undergoes complete dissociation. Higher the dissociation stronger is the acid. Same is the case with ${\text{p}}{{\text{K}}_{\text{b}}}$ i.e. base dissociation constant. Higher the ${\text{p}}{{\text{K}}_{\text{b}}}$ value stronger is the base.