Question

How do you calculate Keq from pKa values?

Answer 1

Hint: The $K_{eq}$ in case of the acid dissociation constant is given as $k_a$ where $k_a$ is the ionization constant for a weak acid. The strength of an acid is defined as the negative logarithm of the acid dissociation constant.

Complete step by step answer:
The general equation for the ionization (dissociation into ions) of the weak acids in water is shown below.
$HA(aq)+H_{2}O(l)\to H_3{O}^{+}(aq)+A^{-}(aq)$
Where,
HA is the parent acid
$A^{-}$ is the conjugate base
The equilibrium constant for the above reaction is given as shown below.
$k={\displaystyle \frac{[H_3{O}^{+}][A^{-}]}{[H_{2}O][HA]}}$
The concentration of the water is constant for the reaction taking place in aqueous solution, there the $H_{2}O$ is used as the new quantity known as acid ionization constant which is given as $K_a$. The acid ionization constant is also known as acid dissociation constant.
The acid dissociation constant for the reaction is shown below.
$K_a=K[H_{2}O]={\displaystyle \frac{[H_3{O}^{+}][A^{-}]}{[HA]}}$
The relation between the $K_{eq}$ which in case of acid dissociation constant is used as $K_a$ and the $p{k}_a$ is shown below.
The $p{k}_a$ is the negative logarithm of acid dissociation constant which is represented as shown below.
$p{k}_a=-{\log }_{10}{k}_a$
Where,
$p{k}_a$ is the strength of an acid.
So, acid dissociation constant can be written as
$k_a={10}^{-p{k}_a}$
So by using the above equation, the Keq can be calculated from pKa values.

Additional information:
There is a relation between the $p{k}_a$ and $p{k}_b$of the conjugate acid-base pair.
The relation is shown below.
$p{k}_a+p{k}_b=p{k}_w$
Where,
$p{k}_w$ is the constant used for water.
$p{k}_a+p{k}_b=14$

Note:
The value of K and $k_a$ differ from each other by the concentration of water. When the value of acid dissociation constant $k_a$ is large, stronger is the acid and higher will be the concentration of hydrogen ion $H^{+}$ at the equilibrium.