Chapter 16, Problem 16.96QP

Interpretation Introduction

Interpretation:

The ratio of the concentration of the Novocaine (a weak base) to that of its acid in the blood plasma (pH=7.40) of a patient has to be calculated

Concept Information:

Acid ionization constant ${\text{K}}_{\text{a}}$:

The equilibrium expression for the reaction ${\text{HA}}_{(aq)}\to {\text{H}}^{+}{}_{(aq)}+{\text{A}}^{\text{-}}{}_{(aq)}$ is given below.

  $K_a=\frac{[{\text{H}}^{\text{+}}{\text{][A}}^{\text{-}}\text{]}}{[\text{HA]}}$

Where $K_a$ is acid ionization constant, $[{\text{H}}^{\text{+}}\text{]}$  is concentration of hydrogen ion, $[{\text{A}}^{\text{-}}\text{]}$  is concentration of acid anion, $[\text{HA]}$ is concentration of the acid

Base  ionization constant $K_b$

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

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

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

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.

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

$\text{pH}$ definition:

The concentration of hydrogen ion is measured using $\text{pH}$ scale.  The acidity of aqueous solution is expressed by $\text{pH}$ scale.

The $\text{pH}$ of a solution is defined as the negative base-10 logarithm of the hydrogen or hydronium ion concentration.

  $\text{pH}\text{=}{\text{-log[H}}_{\text{3}}{\text{O}}^{\text{+}}\text{]}$

To Calculate: The ratio of the concentration of the Novocaine (a weak base) to that of it s acid in the blood plasma (pH=7.40) of a patient