Chapter 16, Problem 16.69QP

Interpretation Introduction

Interpretation:

The pH of a 0.045-M solution of a weak base is 9.88 at $\text{25}{}^{\text{o}}\text{C}$.  The ${\text{K}}_b$ of the given base has to be calculated

Concept Information:

Strong base and weak base:

Strong base dissociates into its constituent ions fully. It produces more of hydroxide ions while dissolved in water.  Weak bases partially dissociates into its constituent ions.

According to Bronsted-Lowry, strong base is a good proton acceptor whereas weak base is a poor proton acceptor

Since, the ionization of a weak base is incomplete; it is treated in the same way as the ionization of a weak acid.

The ionization of a weak base $\text{B}$ is given by the below equation.

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

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

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

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

$\text{pOH}$definition:

The $\text{pOH}$ of a solution is defined as the negative base-10 logarithm of the hydroxide ion ${\text{[OH}}^{\text{-}}\text{]}$ concentration. $\text{pOH}$ scale is analogous to pH scale.

$\text{pOH}\text{=}{\text{-log[OH}}^{\text{-}}\text{]}$

Relationship between $\text{pH}$ and $\text{pOH}$

$\text{pOH}$ is similar to $\text{pH}$.  The only difference is that in $\text{pOH}$ the concentration of hydroxide ion is used as a scale while in $\text{pH}$, the concentration of hydronium ion is used.

The relationship between the hydronium ion concentration and the hydroxide ion concentration is given by the equation,

$\text{pH}\text{+}\text{pOH}\text{=}\text{14,}\text{at}\text{25}{}^{\text{o}}\text{C}$

As $\text{pOH}$ and $\text{pH}$ are opposite scale, the total of both has to be equal to 14.

To Calculate: The ${\text{K}}_b$ of the given weak base