Chapter 9, Problem 9.44P

a)

Interpretation Introduction

Interpretation:

The pH and concentrations of $\text{HA}$ and ${\text{A}}^{\text{-}}$ in the solution has to be calculated.

Concept Introduction:

The concentrations of $\text{HA}$ and ${\text{A}}^{\text{-}}$ will not be equal to their formal concentrations for dilute solutions or at extreme $\text{pH}$ .

Consider the mixing of ${\text{F}}_{\text{HA}}$ moles of $\text{HA}$ and ${\text{F}}_{{\text{A}}^{\text{-}}}$ moles of the salt ${\text{Na}}^{\text{+}}{\text{A}}^{\text{-}}$. Then, the mass and charge balances can be given as,

Mass balance: ${\text{F}}_{\text{HA}}{\text{+F}}_{{\text{A}}^{\text{-}}}\text{=}\left[\text{HA}\right]\text{+}\left[{\text{A}}^{\text{-}}\right]$

Charge balance: $\left[{\text{Na}}^{\text{+}}\right]\text{+}\left[{\text{H}}^{\text{+}}\right]\text{=}\left[{\text{OH}}^{\text{-}}\right]\text{+}\left[{\text{A}}^{\text{-}}\right]$

The substitution $\left[{\text{Na}}^{\text{+}}\right]{\text{=F}}_{{\text{A}}^{\text{-}}}$ leads to the equation,

$\begin{array}{l}\left[\text{HA}\right]{\text{=F}}_{\text{HA}}\text{-}\left[{\text{H}}^{\text{+}}\right]\text{+}\left[{\text{OH}}^{\text{-}}\right]\\ \\ \left[{\text{A}}^{\text{-}}\right]{\text{=F}}_{{\text{A}}^{\text{-}}}\text{+}\left[{\text{H}}^{\text{+}}\right]\text{-}\left[{\text{OH}}^{\text{-}}\right]\end{array}$

Assumption has to be made that $\left[\text{HA}\right]\approx {\text{F}}_{\text{HA}}$ and $\left[{\text{A}}^{\text{-}}\right]\approx {\text{F}}_{{\text{A}}^{\text{-}}}$ and these values are used in Henderson-Hasselbalch equation.

Henderson-Hasselbalch equation:

Henderson- Hasselbalch equation is rearranged form of acid dissociation expression.

For acid:

Consider an acidic reaction:

$\text{HA}\stackrel{{\text{K}}_{\text{a}}}{\rightleftharpoons }{\text{H}}^{\text{+}}{\text{+A}}^{\text{-}}$

The Henderson- Hasselbalch equation for an acidic reaction can be given as,

${\text{pH=pK}}_{\text{a}}\text{+log}\frac{\left[{\text{A}}^{\text{-}}\right]}{\left[\text{HA}\right]}$

To calculate the pH and concentrations of $\text{HA}$ and ${\text{A}}^{\text{-}}$ in the solution

b)

Interpretation Introduction

Interpretation:

Excel goal seek has to be used to calculate the pH and concentrations of $\text{HA}$ and ${\text{A}}^{\text{-}}$ in the solution.

To calculate the pH and concentrations of $\text{HA}$ and ${\text{A}}^{\text{-}}$ in the solution using Excel goal seek