Derive the equation of ionization constants ${K_a}$ of weak acids $HX$.
Derive the equation of ionization constants ${K_a}$ of weak acids $HX$.
A weak acid $HX$ that is partially ionized in the aqueous solution. The equilibrium can be expressed by :
$\text { Equilibrium : } \text { Concentration M : } \mathrm{HX}_{\text {(aq) }}+\mathrm{H}_{2} \mathrm{O}_{(l)}+\mathrm{H}_{3} \mathrm{O}_{\text {(aq) }}^{+}+\mathrm{X}_{\text {(aq) }}^{-} $
$\text {Change in conce. : } -\mathrm{C} \alpha \ \ 0 \ \ \ 0 $
$ \text { Concentration at } (\mathrm{C}-\mathrm{C} \alpha) (0+\mathrm{C} \alpha) (0+\mathrm{C} \alpha) $
$ \text { Equili. in molarity : } =\mathrm{C}(1-\alpha) \mathrm{C} \alpha \mathrm{C} \alpha $
$ =\mathrm{C} \alpha =\mathrm{C} \alpha$
where, $\alpha=$ Extent upto which $\mathrm{HX}$ is ionized into ions.
Suppose, initial concentration of undissociated acid $\mathrm{HX}=\mathrm{C} \alpha \mathrm{M}$
$\therefore \quad$ Ionized $\mathrm{HX}=\mathrm{C} \alpha \mathrm{M}$
At equilibrium $[\mathrm{HX}]=(\mathrm{C}-\mathrm{C} \alpha)=\mathrm{C}(1-\alpha)$
$\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=\left[\mathrm{X}^{-}\right]=\mathrm{C} \alpha \mathrm{M}$
The equilibrium constant for the above discussed acid-dissociation equilibrium:
$\mathrm{K}=\frac{\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\left[\mathrm{X}^{-}\right]}{[\mathrm{HX}]\left[\mathrm{H}_{2} \mathrm{O}\right]} \quad \therefore \mathrm{K}\left[\mathrm{H}_{2} \mathrm{O}\right]=\frac{\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\left[\mathrm{X}^{-}\right]}{[\mathrm{HX}]}$
In $\left[\mathrm{H}_{2} \mathrm{O}\right]=$ constant $=\mathrm{K}^{\prime}$ So,
$\quad \mathrm{K}\left[\mathrm{H}_{2} \mathrm{O}\right]=\mathrm{K} \times \mathrm{K}^{\prime}$ new constant $\mathrm{K}_{a}$
where, $\mathrm{K}_{a}=$ Ionization constant of weak acid.
$\therefore \mathrm{K}_{a}=\frac{\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\left[\mathrm{X}^{-}\right]}{[\mathrm{HX}]}=\frac{\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]^{2}}{[\mathrm{HX}]} \ldots .($ Eq. $-{i})$
$\therefore \mathrm{K}_{a}=\frac{(\mathrm{C} \alpha)(\mathrm{C} \alpha)}{\mathrm{C}(1-\alpha)}=\frac{\mathrm{C} \alpha^{2}}{\left(1-\alpha^{2}\right)} \ldots . .( Eq.-ii )$
Above equation-$(ii)$ is used for calculation of ionization constant of weak acid $HX$.
Similar Questions
The ionization constant of $HF$, $HCOOH$ and $HCN$ at $298\, K$ are $6.8 \times 10^{-4}, 1.8 \times 10^{-4}$ and $4.8 \times 10^{-9}$ respectively. Calculate the ionization constants of the corresponding conjugate base.
The ionization constant of $HF$, $HCOOH$ and $HCN$ at $298\, K$ are $6.8 \times 10^{-4}, 1.8 \times 10^{-4}$ and $4.8 \times 10^{-9}$ respectively. Calculate the ionization constants of the corresponding conjugate base.
Dimethyl amine ${\left( {C{H_3}} \right)_2}NH$ is weak base and its ionization constant $ 5.4 \times {10^{ - 5}}$. Calculate $\left[ {O{H^ - }} \right],\left[ {{H_3}O} \right]$, $pOH$ and $pH$ of its $0.2$ $M$ solution at equilibrium.
Dimethyl amine ${\left( {C{H_3}} \right)_2}NH$ is weak base and its ionization constant $ 5.4 \times {10^{ - 5}}$. Calculate $\left[ {O{H^ - }} \right],\left[ {{H_3}O} \right]$, $pOH$ and $pH$ of its $0.2$ $M$ solution at equilibrium.
$K _{ a_1,}, K _{ a_2 }$ and $K _{ a_3}$ are the respective ionization constants for the following reactions $(a), (b),$ and $(c)$.
$(a)$ $H _{2} C _{2} O _{4} \rightleftharpoons H ^{+}+ HC _{2} O _{4}^{-}$
$(b)$ $HC _{2} O _{4}^{-} \rightleftharpoons H ^{+}+ HC _{2} O _{4}^{2-}$
$(c)$ $H _{2} C _{2} O _{4} \rightleftharpoons 2 H ^{+}+ C _{2} O _{4}^{2-}$
The relationship between $K_{a_{1}}, K_{ a _{2}}$ and $K_{ a _{3}}$ is given as
$K _{ a_1,}, K _{ a_2 }$ and $K _{ a_3}$ are the respective ionization constants for the following reactions $(a), (b),$ and $(c)$.
$(a)$ $H _{2} C _{2} O _{4} \rightleftharpoons H ^{+}+ HC _{2} O _{4}^{-}$
$(b)$ $HC _{2} O _{4}^{-} \rightleftharpoons H ^{+}+ HC _{2} O _{4}^{2-}$
$(c)$ $H _{2} C _{2} O _{4} \rightleftharpoons 2 H ^{+}+ C _{2} O _{4}^{2-}$
The relationship between $K_{a_{1}}, K_{ a _{2}}$ and $K_{ a _{3}}$ is given as
- [JEE MAIN 2022]
Calculate the degree of ionization of $0.05 \,M$ acetic acid if its $p K_{ a }$ value is $4.74$
How is the degree of dissociation affected when its solution also contains $(a)$ $0.01 \,M$ $(b)$ $0.1 \,M$ in $HCl$ ?
Calculate the degree of ionization of $0.05 \,M$ acetic acid if its $p K_{ a }$ value is $4.74$
How is the degree of dissociation affected when its solution also contains $(a)$ $0.01 \,M$ $(b)$ $0.1 \,M$ in $HCl$ ?
The solubility of a salt of weak acid $( A B )$ at $pH 3$ is $Y \times 10^{-3} mol L ^{-1}$. The value of $Y$ is
. . . . . (Given that the value of solubility product of $A B \left( K _{ sp }\right)=2 \times 10^{-10}$ and the value of ionization constant of $H B \left( K _{ a }\right)=1 \times 10^{-8}$ )
The solubility of a salt of weak acid $( A B )$ at $pH 3$ is $Y \times 10^{-3} mol L ^{-1}$. The value of $Y$ is
. . . . . (Given that the value of solubility product of $A B \left( K _{ sp }\right)=2 \times 10^{-10}$ and the value of ionization constant of $H B \left( K _{ a }\right)=1 \times 10^{-8}$ )
- [IIT 2018]