Question

How do you determine the ${{\text{K}}_{\text{a}}}$ of weak acid and ${{\text{K}}_{\text{b}}}$ of weak base?

Answer 1

To answer this question we should know what is ${{\text{K}}_{\text{a}}}$ ,${{\text{K}}_{\text{b}}}$ .These are used to determine the strength of acids and bases. ${{\text{K}}_{\text{a}}}$ is ionization constant for weak acids and ${{\text{K}}_{\text{b}}}$ is ionization constant for weak base. So depending on these acids and bases can be weak and strong. If an acid or base is completely ionized in aqueous solution it is a strong acid or strong base. But if it is slightly ionized then it is a weak acid or weak base.

Complete step by step answer:
As we know that the reaction of weak acid with water produces ${{\text{H}}_{\text{3}}}{{\text{O}}^{\text{ + }}}$ or ${{\text{H}}^{\text{ + }}}$
To determine acid ionization constant ${{\text{K}}_{\text{a}}}$ , following is the equation for ionization of weak acid $\left[ {HA} \right]$
in water and [${{\text{A}}^{\text{ - }}}$] is the conjugate base.
${\text{HA(aq) + }}{{\text{H}}_{\text{2}}}{\text{O(l)}} \rightleftarrows {{\text{H}}_{\text{3}}}{{\text{O}}^{\text{ + }}}{\text{(aq) + }}{{\text{A}}^{\text{ - }}}{\text{(aq)}}$
The equilibrium constant for the equation can be written as,
${\text{K = }}\dfrac{{{\text{[}}{{\text{H}}_{\text{3}}}{{\text{O}}^{\text{ + }}}{\text{][}}{{\text{A}}^{\text{ - }}}{\text{]}}}}{{{\text{[}}{{\text{H}}_{\text{2}}}{\text{O][HA]}}}}$
Since concentration of water is constant so ${\text{K}}$ can be written as ${\text{K[}}{{\text{H}}_{\text{2}}}{\text{O]}}$ and new constant form is ${{\text{K}}_{\text{a}}}$and also known as acid dissociation constant.
${{\text{K}}_{\text{a}}}{\text{ = K[}}{{\text{H}}_{\text{2}}}{\text{O] = }}\dfrac{{{\text{[}}{{\text{H}}_{\text{3}}}{{\text{O}}^{\text{ + }}}{\text{][}}{{\text{A}}^{\text{ - }}}{\text{]}}}}{{{\text{[HA]}}}}$
We can write ${{\text{H}}_{\text{3}}}{{\text{O}}^{\text{ + }}}$ as ${{\text{H}}^{\text{ + }}}$ but no ${{\text{H}}^{\text{ + }}}$ ion exist in aqueous medium so we use ${{\text{H}}_{\text{3}}}{{\text{O}}^{\text{ + }}}$.
Now weak bases on reaction with water produces ${\text{O}}{{\text{H}}^{\text{ - }}}$ (hydroxide) ions.
To determine base ionization constant ${{\text{K}}_{\text{b}}}$ ,following is the equation for ionization of weak base $\left[ B \right]$ in water and [${\text{B}}{{\text{H}}^{\text{ + }}}$] is conjugate acid.
${\text{B(aq) + }}{{\text{H}}_{\text{2}}}{\text{O(l)}} \rightleftarrows {\text{B}}{{\text{H}}^{\text{ + }}}{\text{(aq) + O}}{{\text{H}}^{\text{ - }}}{\text{(aq)}}$
The equilibrium constant for the equation can be written as,
${{\text{K}}_b}{\text{ = K[}}{{\text{H}}_{\text{2}}}{\text{O] = }}\dfrac{{{\text{[B}}{{\text{H}}^{\text{ + }}}{\text{][O}}{{\text{H}}^{\text{ - }}}{\text{]}}}}{{{\text{[B]}}}}$
If we know the value of ${{\text{K}}_{\text{a}}}$ and ${{\text{K}}_{\text{b}}}$ we can calculate ${\text{p}}{{\text{K}}_{\text{a}}}$ and ${\text{p}}{{\text{K}}_{\text{b}}}$

Note:
We should be noted that acid- base ionization constants are measured in terms of ${{\text{H}}^{\text{ + }}}$ and ${\text{O}}{{\text{H}}^{\text{ - }}}$ and therefore they don’t have any unit. Example of strong acid is ${\text{HCl}}$ and ${\text{C}}{{\text{l}}^{\text{ - }}}$ (chloride ion) is its weak conjugate base. Similarly ${\text{C}}{{\text{H}}_{\text{3}}}{\text{COOH}}$ is weak acid and its strong base is ${\text{C}}{{\text{H}}_{\text{3}}}{\text{CO}}{{\text{O}}^{\text{ - }}}$ (acetate ion).It should be noted that the larger the ${{\text{K}}_{\text{a}}}$ ,the stronger is the acid(${\text{p}}{{\text{K}}_{\text{a}}}$). Similarly the larger the ${{\text{K}}_{\text{b}}}$ , the stronger is the base (${\text{p}}{{\text{K}}_{\text{b}}}$) .