Chapter 17.1, Problem 1P

Interpretation Introduction

Interpretation: To explain the $\text{p}{K}_{\text{a}}$ value of hydrogen bonded to the ${\text{sp}}^{\text{3}}$ carbon of propene is greater than that of the any of the carbon acids listed in table 17.1 but is less than the $\text{p}{K}_{\text{a}}$ of an alkane.

Concept introduction: An equilibrium constant $\left(K\right)$ is the ratio of the concentration of products and reactants raised to appropriate stoichiometric coefficient at equilibrium.

The reaction of an acid HA with water is written as,

$\text{HA}\left(\text{aq}\right)+{\text{H}}_{\text{2}}\text{O}\left(\text{l}\right)\rightleftharpoons {\text{H}}_{\text{3}}{\text{O}}^{+}\left(\text{aq}\right)+{\text{A}}^{-}\left(\text{aq}\right)$

The relative strength of an acid and base in water can be also expressed quantitatively with an equilibrium constant as follows:

$K_{\text{a}}=\frac{\left[{\text{H}}_{\text{3}}{\text{O}}^{+}\right]\left[{\text{A}}^{-}\right]}{\left[\text{HA}\right]}$

An equilibrium constant $\left(K\right)$ with subscript $\text{a}$ indicates that it is an equilibrium constant of an acid in water.

The relation between $K_{\text{a}}$ and $\text{p}{K}_{\text{a}}$ is expressed as,

$\text{p}{K}_{\text{a}}=-\log \left(K_{\text{a}}\right)$

Stronger the acid higher the value of $K_{\text{a}}$ and smaller the value of $\text{p}{K}_{\text{a}}$.