14.2 pH and pOH

pH and pOH are key measures of acidity and basicity in solutions. They help us understand how acidic or basic a substance is, which is crucial for many chemical reactions and biological processes.

These concepts are based on the concentration of hydrogen and hydroxide ions in solution. Knowing how to calculate and interpret pH and pOH values is essential for predicting chemical behavior and solving real-world problems.

pH and pOH

Acidic, basic, and neutral solutions

• pH measures the acidity or basicity of an aqueous solution on a scale from 0 to 14
  • Neutral solutions have a pH of 7 (pure water at 25°C)
  • Acidic solutions have pH values below 7 due to a higher concentration of hydronium ions ($H_3O^+$) compared to hydroxide ions ($OH^-$)
    • Examples of acidic solutions: lemon juice (pH 2), vinegar (pH 3), and black coffee (pH 5)
  • Basic solutions have pH values above 7 due to a higher concentration of hydroxide ions ($OH^-$) compared to hydronium ions ($H_3O^+$)
    • Examples of basic solutions: baking soda (pH 8.3), milk of magnesia (pH 10.5), and bleach (pH 12.6)

Conversion of ion concentrations and pH

• pH is the negative logarithm of the hydronium ion concentration, expressed as $pH = -\log[H_3O^+]$
  • Hydronium ion concentration can be calculated from pH using $[H_3O^+] = 10^{-pH}$
    • Example: If pH = 4, then $[H_3O^+] = 10^{-4} M$
• pOH is the negative logarithm of the hydroxide ion concentration, expressed as $pOH = -\log[OH^-]$
  • Hydroxide ion concentration can be calculated from pOH using $[OH^-] = 10^{-pOH}$
    • Example: If pOH = 3, then $[OH^-] = 10^{-3} M$
• The acid dissociation constant (Ka) is related to pH and can be used to calculate the pH of weak acid solutions

Relationship between pH and pOH

• The sum of pH and pOH is always equal to 14 at 25°C, expressed as $pH + pOH = 14$
  • If given pH, pOH can be calculated by subtracting pH from 14, expressed as $pOH = 14 - pH$
    • Example: If pH = 5.5, then $pOH = 14 - 5.5 = 8.5$
  • If given pOH, pH can be calculated by subtracting pOH from 14, expressed as $pH = 14 - pOH$
    • Example: If pOH = 2.7, then $pH = 14 - 2.7 = 11.3$
• Knowing the relationship between pH and pOH allows for interconversion between hydronium and hydroxide ion concentrations using the ion product of water ($K_w$)
  1. If $[H_3O^+]$ is known, $[OH^-]$ can be calculated using $K_w = [H_3O^+][OH^-] = 1.0 \times 10^{-14}$ at 25°C
     • $[OH^-] = \frac{K_w}{[H_3O^+]}$
     • Example: If $[H_3O^+] = 1.0 \times 10^{-6} M$, then $[OH^-] = \frac{1.0 \times 10^{-14}}{1.0 \times 10^{-6}} = 1.0 \times 10^{-8} M$
  2. If $[OH^-]$ is known, $[H_3O^+]$ can be calculated using $K_w$
     • $[H_3O^+] = \frac{K_w}{[OH^-]}$
     • Example: If $[OH^-] = 1.0 \times 10^{-3} M$, then $[H_3O^+] = \frac{1.0 \times 10^{-14}}{1.0 \times 10^{-3}} = 1.0 \times 10^{-11} M$

Advanced pH Concepts

• Conjugate acid-base pairs play a crucial role in understanding acid-base reactions and equilibria
• Buffer solutions help maintain a relatively constant pH when small amounts of acid or base are added
• The Henderson-Hasselbalch equation relates the pH of a buffer solution to the concentrations of its components
• Titration is a technique used to determine the concentration of an acid or base by neutralizing it with a standard solution of known concentration