Chapter 16, Problem 16.80QP

Interpretation Introduction

Interpretation:

From the given problem statement having three salts $\text{NaX}\text{(X=A,}\text{B}\text{or C)}$,

Which ( ${\text{X}}^{\text{-}}$) has the weakest conjugate acid has to be explained.

The three ${\text{X}}^{\text{-}}$ anions has to be arranged in the order of decreasing base strength

Concept Introduction:

Base  ionization constant $K_b$

The equilibrium expression for the ionization of weak base $\text{B}$ will be,

${\text{B}}_{\text{(aq)}}{\text{+H}}_{\text{2}}{\text{O}}_{\text{(l)}}\to {\text{HB}}^{\text{+}}{}_{\text{(aq)}}{\text{+OH}}^{\text{-}}{}_{\text{(aq)}}$

${\text{K}}_b=\frac{[{\text{HB}}^{\text{+}}][{\text{OH}}^{\text{-}}]}{[\text{B}]}$

Where $K_b$ is base ionization constant, $[{\text{OH}}^{-}\text{]}$ is concentration of hydroxide ion, $[{\text{HB}}^{\text{+}}\text{]}$ is concentration of conjugate acid, $[\text{B]}$ is concentration of the base

Relationship between $K_a$ and $K_b$

$K_a\times K_b=K_w$

Where,

$K_w$ is autoionization of water.

$\begin{array}{l}\text{The autoionization of water}:\\ K_w=[{\text{H}}^{\text{+}}\text{]}[{\text{OH}}^{\text{-}}]\\ =1.0\times {10}^{-14}\end{array}$

In general, there is a reciprocal relationship between the strength of an acid or base and the strength of its conjugate.

To Explain: 

Which ( ${\text{X}}^{\text{-}}$) has the weakest conjugate acid.

The three ${\text{X}}^{\text{-}}$ anions in the order of decreasing base strength