Acid-Base Titration and pH: Concepts, Calculations, and Applications

Chapter 15. Acid-Base Titration and pH

Section 1. Aqueous Solutions and the Concept of pH

This section introduces the fundamental concepts of acids, bases, and the pH scale, focusing on the behavior of hydronium and hydroxide ions in aqueous solutions.

• Self-Ionization of Water: Water molecules can transfer protons, producing hydronium ions (H3O+) and hydroxide ions (OH−).

• Ionization Constant of Water (Kw): The equilibrium constant for water ionization is given by: $K_w = [H_3O^+][OH^-]$ At 25°C, $K_w = 1.0 \times 10^{-14}$.

• Temperature Dependence: The value of $K_w$ increases as temperature increases.

• Neutral, Acidic, and Basic Solutions:

  • Neutral: $[H_3O^+] = [OH^-] = 1.0 \times 10^{-7}$ M

  • Acidic: $[H_3O^+] > [OH^-]$

  • Basic: $[OH^-] > [H_3O^+]$

• Strong Acids and Bases: These substances are considered completely ionized in aqueous solutions. For example, a 1.0 × 10−2 M NaOH solution has [OH−] = 1.0 × 10−2 M, and [H3O+] can be calculated using $K_w$.

• Calculating Ion Concentrations: If either [H3O+] or [OH−] is known, the other can be found using $K_w$.

Some Strong Acids and Some Weak Acids

This table compares the strengths of various acids and their conjugate bases, showing their dissociation constants ($K_a$).

Concentrations and Kw

This table summarizes the relationship between the concentrations of hydronium and hydroxide ions in various solutions, as well as the value of $K_w$.

The pH Scale

The pH scale is a logarithmic measure of the hydronium ion concentration in a solution. It is defined as:

• pH Definition: $pH = -\log [H_3O^+]$

• pOH Definition: $pOH = -\log [OH^-]$

• Relationship: $pH + pOH = 14.0$ at 25°C

pH Values of Common Materials

Everyday substances have characteristic pH values, ranging from highly acidic (battery acid) to highly basic (drain cleaner).

Relationship of [H3O+], [OH−], and pH

The following tables summarize the relationships among hydronium ion concentration, hydroxide ion concentration, and pH for various solutions.

Calculating pH and [H3O+]

pH and [H3O+] can be interconverted using logarithmic and antilogarithmic functions:

• Calculating pH from [H3O+]: $pH = -\log [H_3O^+]$

• Calculating [H3O+] from pH: $[H_3O^+] = 10^{-pH}$

Section 2. Determining pH and Titrations

Indicators and pH Meters

Indicators and pH meters are used to determine the pH of solutions. Indicators are weak acids or bases that change color depending on the pH, while pH meters provide precise measurements by detecting voltage changes.

• Transition Interval: The pH range over which an indicator changes color.

• Indicator Selection: Indicators are chosen based on the expected pH at the equivalence point of a titration.

Titration and Equivalence Point

Titration is a laboratory technique used to determine the concentration of an unknown solution by reacting it with a solution of known concentration. The equivalence point is reached when the reactants are present in stoichiometrically equivalent amounts.

• End Point: The point at which the indicator changes color, signaling the completion of the reaction.

• Indicator Choice: For strong acid/strong base titrations, indicators that change color near pH 7 are used. For strong acid/weak base titrations, indicators with a lower transition pH are used. For weak acid/strong base titrations, indicators with a higher transition pH are used.

Molarity and Titration Calculations

The concentration (molarity) of an unknown acid or base can be determined by titration using a standard solution. The steps are as follows:

1. Write the balanced equation for the neutralization reaction.

2. Determine the moles of acid or base from the known solution used during the titration.

3. Calculate the moles of solute in the unknown solution.

4. Determine the molarity of the unknown solution using the formula: $M = \frac{\text{moles of solute}}{\text{volume of solution in liters}}$

Key Terms:

• Standard Solution: A solution of known concentration used in titrations.

• Primary Standard: A highly purified compound used to check the concentration of the standard solution.