Explanation:
It is known that the relation between pH and hydrogen ion concentration is as follows.
pH = [tex]-log [H^{+}][/tex]
3 = [tex]-log [H^{+}][/tex]
antilog (-3) = [tex]1 \times 10^{-3}[/tex]
[tex][H^{+}] = 1 \times 10^{-3}[/tex] M
Now, let the given acid is HA and it dissociates as follows.
[tex]HA \rightarrow H^{+} + A^{-}[/tex]
0.1 0 0
0.1 - x x x
We know that relation between [tex]K_{a}[/tex], [tex][H^{+}][/tex] and HA is as follows.
[tex]K_{a} = \frac{[H^{+}][A^{-}]}{[HA]}[/tex]
= [tex]\frac{x \times x}{(c - x)}[/tex]
= [tex]\frac{1 \times 10^{-3} \times 1 \times 10^{-3}}{(0.1 - 1 \times 10^{-3})}[/tex]
= [tex]1.01 \times 10^{-5}[/tex]
Also, [tex]pK_{a} = -log K_{a}[/tex]
= [tex]-log (1.01 \times 10^{-5})[/tex]
= 5.00
Thus, we can conclude that the [tex]pK_{a}[/tex] of given acid is 5.0.
