How to calculate the dissociation constant.

Hint: As we know that Arrhenius is one of the concepts for acid and bases. Swedish chemist Arrhenius is the world's first chemist to talk about acid and bases. Depending on his concept and limitation later so many concepts are developed. Even Arrhenius is the birthplace of the concept of acids and bases. Followed by Arrhenius chemist the concept of acids and bases discuss Bronsted and Lowry in the world.
According to the Arrhenius concept one substance said to acid means, acid is nothing but a substance that dissociates to give hydrogen ion when decomposed in the water.
Examples of Arrhenius acids are hydrochloric acid (\[{\text{HCl}}\]), sulphuric acid (\[{{\text{H}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{4}}}\]), nitric acid (\[{\text{HN}}{{\text{O}}_{\text{3}}}\]) etc,.
According to Arrhenius concept one substance said to base means, bases is nothing but a substance that dissociates to give hydroxyl ion when decomposed in water.
Examples of Arrhenius bases are sodium hydroxide (\[{\text{NaOH}}\]), calcium hydroxide (\[{\text{Ca(OH}}{{\text{)}}_{\text{2}}}\]) etc,.

Complete answer:
When acid dissolve in water, it from \[{{\text{H}}^{\text{ + }}}\] or \[{{\text{H}}_{\text{3}}}{{\text{O}}^{\text{ + }}}\] in water. When the base dissolves in water, it forms \[{\text{O}}{{\text{H}}^{\text{ - }}}\] in water. The concentration of \[{{\text{H}}_{\text{3}}}{{\text{O}}^{\text{ + }}}\]is used to calculate the strength of acid in water. The concentration of \[{\text{O}}{{\text{H}}^{\text{ - }}}\]is used to calculate the strength of the base in water.
The reaction for acid in water.
\[{\text{HA + }}{{\text{H}}_{\text{2}}}{\text{O}} \to {{\text{H}}_{\text{3}}}{{\text{O}}^{\text{ + }}} + {{\text{A}}^{\text{ - }}}\]
HA is consider as acid. It react with water to from conjugate base\[{{\text{H}}_{\text{3}}}{{\text{O}}^{\text{ + }}}\].
The relationship between the concentration of acid and conjugate base is known as the dissociation constant.
\[{{\text{K}}_{\text{a}}}{\text{ = }}\dfrac{{{\text{[}}{{\text{H}}_{\text{3}}}{{\text{O}}^{\text{ + }}}{\text{][}}{{\text{A}}^{\text{ - }}}{\text{]}}}}{{{\text{[HA]}}}}\]
Here,${K_a}$ is considered as the dissociation constant of acid.
The concentration of acid is \[{\text{[HA]}}\].
The concentration of conjugate base is \[{\text{[}}{{\text{H}}_{\text{3}}}{{\text{O}}^{\text{ + }}}{\text{]}}\].
${K_a}$ is the dissociation constant of acid that is used for known weak or strong acid.

Note:
In general, pH values of all acids are in between \[{\text{0}}{\text{.9}}\]-\[6.9\] and all the bases are in between\[7.1 - 14.0\]. But, Arrhenius theory has some limitations. One of the main limitations is not being able to explain the behaviour of acids and bases in non-aqueous solvents such as acetone etc,. It is not able to explain the acid which doesn't contain hydrogen and bases don’t contain hydroxyl ion in the formula. Ammonia is a well known base and is not accepted as base in Arrhenius base. These limitations are recovered by further coming theories like the Bronsted and Lowry concept of acids and bases.