Chapter 15, Problem 15.16QE

Interpretation Introduction

Interpretation:

$K_{\text{a}}$ for the conjugate acid of ${\text{NH}}_{\text{3}}$ has to be determined. Also, whether $K_{\text{a}}$ and $K_{\text{b}}$ for ${\text{NH}}_{\text{3}}$ and ${\text{NH}}_2{}^{-}$ can be calculated from $K_{\text{b}}$ of ${\text{NH}}_{\text{3}}$ and $K_{\text{w}}$ has to be determined.

Concept Introduction:

$K_{\text{a}}$ is defined as the acid dissociation constant in conjugate acid-base pairs. $K_{\text{b}}$ is defined as the base ionization constant in acid-base pairs. $K_{\text{w}}$ is the equilibrium constant for water. At $25°\text{C}$, $K_{\text{w}}$ is equal to $1.0\times {10}^{-14}$.

The expression for relation between $K_{\text{b}}$ and $K_{\text{a}}$ is as follows:

  $K_{\text{a}}\cdot K_{\text{b}}=K_{\text{w}}$        (1)

At $25°\text{C}$, $K_{\text{w}}$ is equal to $1.0\times {10}^{-14}$, the equation (1) will be modified as follows:

    $K_{\text{a}}\cdot K_{\text{b}}=1.0\times {10}^{-14}$        (2)