Question

Succinic acid dissociates in two steps:

Short answer

Base dissociation constant for given reaction is,

$$\begin{gathered} {\mathrm{K}}_{\mathrm{b}1}=4.3\mathrm{x}{10}^9 \\ {\mathrm{K}}_{\mathrm{b}2}=1.6\mathrm{x}{10}^{-10} \end{gathered}$$

Step-by-step solution

formula for acid and base dissociation constant

Consider a weak-acid equilibrium reaction${\mathrm{HA}}^{{\mathrm{K}}_3}{\mathrm{H}}^{+}+{\mathrm{A}}^{\mathbf{-}}$

The acid dissociation constant ${\mathbf{K}}_{\mathbf{a}}$can be given as,

${\mathbf{K}}_{\mathbf{a}}\mathbf{=}\frac{\left[H^{+}\right]\left[A^{-1}\right]}{\left[\mathrm{HA}\right]}$

Consider a reaction of weak base,

role="math" localid="1663382177574" $\mathrm{B}+{\mathrm{H}}_2{\mathrm{O}}^{{\mathrm{K}}_{\mathrm{O}}}{\mathrm{BH}}^{+}+{\mathrm{OH}}^{-}$

The value of ${\mathbf{K}}_{\mathbf{b}}$can be calculated as,

${\mathbf{K}}_{\mathbf{b}}\mathbf{=}\frac{\left[{\mathrm{BH}}^{+}\right]\left[\mathrm{OH}\right]}{\left[B\right]}$

Where ${\mathrm{K}}_{\mathrm{b}}$is called as base dissociation constant.

The value of ${\mathbf{K}}_{\mathbf{w}}$is calculated by the formula,

${\mathbf{K}}_{\mathbf{w}}\mathbf{=}{\mathbf{K}}_{\mathbf{a}}\mathbf{}\mathbf{x}\mathbf{}{\mathbf{K}}_{\mathbf{b}}$

Step 2: calculate Base dissociation constant 

Acid dissociation constant for given reaction is,

$$\begin{gathered} {\mathrm{K}}_{\mathrm{a}1}=6.2\times {10}^{-5} \\ {\mathrm{K}}_{\mathrm{a}2}=2.3\times {10}^{-6} \end{gathered}$$

To calculate: Base dissociation constant $\left({\mathrm{K}}_{\mathrm{b}}\right)$for first step

${\mathrm{K}}_{\mathrm{w}}={\mathrm{K}}_{\mathrm{a}}\times {\mathrm{K}}_{\mathrm{b}}$

Where,

$\left({\mathrm{K}}_{\mathrm{b}}\right)$is base dissociation constant.

$\left({\mathrm{K}}_{\mathrm{w}}\right)$is ionic product of water$(1.00\times {10}^{14})$

$\left({\mathrm{K}}_a\right)$is acid dissociation constant

${\mathrm{K}}_{\mathrm{b}1}=\frac{{\mathrm{K}}_{\mathrm{w}}}{{\mathrm{K}}_{\mathrm{a}2}}$

$$\begin{gathered} \frac{1.0\times {10}^{-14}}{2.3\times {10}^6} \\ {\mathrm{K}}_{\mathrm{b}1}=4.3\times {10}^9 \end{gathered}$$

To calculate: Base dissociation constant$\left({\mathrm{K}}_{\mathrm{b}}\right)$for second step

${\mathrm{K}}_{\mathrm{b}2}=\frac{{\mathrm{K}}_{\mathrm{w}}}{{\mathrm{K}}_{\mathrm{a}1}}$