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Chapter 15
Acid-Base Equilibria

Shaun Williams, PhD

Common Ion Effect

Key Points about Buffered Solutions

Solving Problems with Buffered Solution

In order to go from original buffered solution pH to the modified pH with the addition of an acid or base you first assume the added acid or base totally reacts with the buffer then perform the equilibrium calculation with these new concentrations.

Buffering: How Does It Work?

Adding hydroxide ions replaced by the conjugate base from the original buffer system therefore the final pH of the system will be close to that of the original buffer.

Henderson-Hasselbalch Equation

$$ \mathrm{pH} = \mathrm{p}K_a + \log \frac{\conc{A^-}}{\conc{HA}} $$

Exercise

What is the \(\mathrm{pH}\) of a buffer solution that is \(0.45\,\mathrm{M}\) acetic acid (\(\chem{HC_2H_3O_2}\)) and \(0.85\,\mathrm{M}\) sodium acetate (\(\chem{NaC_2H_3O_2}\))? The \(K_a\) for acetic acid is \(1.8 \times 10^{–5}\).

\( \mathrm{pH} = 5.02 \)

Buffered Solution Characteristics

Buffering Capacity

Choosing a Buffer

Titration Curve

The \(\mathrm{pH}\) Curve for the Titration of \(50.0\,\mathrm{mL}\) of \(0.200\,\mathrm{M}\,\chem{HNO_3}\) with \(0.100\,\mathrm{M}\,\chem{NaOH}\)

The pH curve begins low (acidic) and then rises rapidly around the equivalence point (occuring at a pH of 7) and finally flattening out at a high pH as the base is added.

The \(\mathrm{pH}\) Curve for the Titration of \(100.0\,\mathrm{mL}\) of \(0.50\,\mathrm{M}\,\chem{NaOH}\) with \(1.0\,\mathrm{M}\,\chem{HCl}\)

The pH curve begins high (basic) and then falls rapidly around the equivalence point (occuring at a pH of 7) and finally flattening out at a low pH as the acid is added.

Weak Acid-Strong Base Titration

  1. A stoichiometry problem (reaction is assumed to run to completion) then determine concentration of acid remaining and conjugate base formed.
  2. An equilibrium problem (determine position of weak acid equilibrium and calculate \(\mathrm{pH}\).

Concept Check

Calculate the \(\mathrm{pH}\) of a solution made by mixing \(0.20\,\mathrm{mol}\,\chem{HC_2H_3O_2}\) (\(K_a=1.8 \times 10^{--5}\)) with \(0.030\,\mathrm{mol}\,\chem{NaOH}\) in \(1.0\,\mathrm{L}\) of aqueous solution.

\(\mathrm{pH}=3.99\)

Exercise

Calculate the \(\mathrm{pH}\) of a \(100.0\,\mathrm{mL}\) solution of \(0.100\,\mathrm{mol}\,\chem{HC_2H_3O_2}\), with \(K_a=1.8 \times 10^{--5}\).

\(\mathrm{pH}=2.87\)

The \(\mathrm{pH}\) Curve for the Titration of \(50.0\,\mathrm{mL}\) of \(0.100\,\mathrm{M}\,\chem{HC_2H_3O_2}\) with \(0.100\,\mathrm{M}\,\chem{NaOH}\)

The pH curve begins low, around 3, and then rises rapidly around the equivalence point (occuring at a pH of about 9) and finally flattening out at a high pH as the base is added.

The \(\mathrm{pH}\) Curves for the Titrations of \(50.0-\mathrm{mL}\) Samples of \(0.10\,\mathrm{M}\) Acids with Various \(K_a\) Values with \(0.10\,\mathrm{M}\,\chem{NaOH}\)

The pH curve always begins low and transition to a higher pH. As the acid gets weaker, the initial pH of the curve gets higher.

The \(\mathrm{pH}\) Curve for the Titration of \(100.0\,\mathrm{mL}\) of \(0.050\,\mathrm{M}\,\chem{NH_3}\) with \(0.10\,\mathrm{M}\,\chem{HCl}\)

The pH curve begins high (basic) and then falls rapidly around the equivalence point (occuring at a pH of about 5) and finally flattening out at a low pH as the acid is added.

Acid-Base Indicators

The Acid and Base Forms of the Indicator Phenolphthalein

In an acidic solution, phenolphthalein is clear. In a basic solution, phenolphthalein is pink.

In its acidic form, phenolphthalein has three hydroxide groups whose hydrogens get removed when phenolphthalein is in a basic solution.

The Methyl Orange Indicator is Yellow in Basic Solution and Redi in Acidic Solution

Methyl orange transitions from yellowish-orange in basic solutions to red in acidic solutions.

Useful \(\mathrm{pH}\) Ranges for Several Common Indicators

The ranges at which a variety of indicator undergo their color change.

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