Chapter 16, Problem 105QP

Interpretation Introduction

Interpretation:

The pH of the solution that contains the salt ${\text{C}}_2{\text{H}}_5{\text{NH}}_3\text{I}$ is to be determined.

Concept introduction:

Salt is a strong electrolyte that dissociates completely when added to water.

When a salt contains a cation that comes from a weak acid, the cation recombines with water to produce a weak base and hydronium ions, and forms an acidic solution. The anion that comes from a strong acid does not recombine and is present in the solution as a free ion without having any effect on the pH of the solution.

The reaction of the salt which takes place is:

${\text{BH}}^{+}\left(aq\right)+{\text{H}}_2\text{O}\left(l\right)\rightleftharpoons \text{B}\left(aq\right)+{\text{H}}_3{\text{O}}^{+}\left(aq\right)$

Here, ${\text{BH}}^{\text{+}}$ comes from the weak base $\text{B}$ and ${\text{A}}^{-}$ comes from strong acid $\text{HA}$. The pH of this solution is determined by the $\left[{\text{H}}_3{\text{O}}^{+}\right]$.

The relationship between $K_{\text{b}}$, $K_{\text{a}}$, and $K_{\text{w}}$ gives the quantitative basis of the reciprocal relationship between the strength of an acid and its conjugate base or vice-versa.

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

$K_{\text{a}}$ is the measure of dissociation of an acid and is known as acid-ionization constant, which is specific at a particular temperature.

$K_{\text{a}}=\frac{\left[{\text{H}}_3{\text{O}}^{+}\right]\left[\text{B}\right]}{\left[{\text{BH}}^{+}\right]}$ …… (2)

The formula to calculate pH is:

$\text{pH}=-\log \left[{\text{H}}_3{\text{O}}^{+}\right]$ …… (3)