Chapter 22, Problem 6STP

Interpretation Introduction

Interpretation:

The expression for acid dissociated constant for second ionization of succinic acid needs to be determined.

Concept introduction:

The general equilibrium reaction is represented as follows:

$A+B\rightleftharpoons AB$

The equilibrium constant of the reaction can be represented as follows:

$K_a=\frac{\left[AB\right]}{\left[A\right]\left[B\right]}$

Here, $K_a$ is acid dissociation constant.

Answer to Problem 6STP

Correct Answer: Option (b)

Explanation of Solution

Reason for correct option:

The formula of diprotic succinic acid is ${\text{H}}_{\text{2}}{\text{C}}_{\text{4}}{\text{H}}_{\text{4}}{\text{O}}_{\text{4}}$. There are two ionizable H atoms thus, reaction of first and second ionization is represented as follows:

${\text{H}}_{\text{2}}{\text{C}}_{\text{4}}{\text{H}}_{\text{4}}{\text{O}}_{\text{4}}+{\text{H}}_{\text{2}}\text{O}\rightleftharpoons {\text{H}}_{\text{3}}{\text{O}}^{+}+{\text{HC}}_{\text{4}}{\text{H}}_{\text{4}}{\text{O}}_{\text{4}}{}^{-}$

And,

${\text{HC}}_{\text{4}}{\text{H}}_{\text{4}}{\text{O}}_{\text{4}}{}^{-}+{\text{H}}_{\text{2}}\text{O}\rightleftharpoons {\text{H}}_{\text{3}}{\text{O}}^{+}+{\text{C}}_{\text{4}}{\text{H}}_{\text{4}}{\text{O}}_{\text{4}}{}^{2-}$

Thus, the expression for the second ionization constant of succinic acid is as follows:

$K_a=\frac{\left[{\text{H}}_{\text{3}}{\text{O}}^{+}\right]\left[{\text{C}}_{\text{4}}{\text{H}}_{\text{4}}{\text{O}}_{\text{4}}{}^{2-}\right]}{\left[{\text{HC}}_{\text{4}}{\text{H}}_{\text{4}}{\text{O}}_{\text{4}}{}^{-}\right]}$

Therefore, correct option is (b)

Conclusion

Reason for incorrect option:

The equilibrium constant expression for any reaction is written by taking ratio of concentration of product to reactant.

Option (a) represents equilibrium constant expression for first ionization reaction. In option (c) and (d), ratio of reactant to product is written for first and second ionization respectively thus, these are incorrect options.