6.2 pH and pOH calculations

pH and pOH are crucial measures in acid-base chemistry. They help us quantify the acidity or basicity of solutions, which is essential for understanding chemical reactions and biological processes.

Calculating pH and pOH involves using logarithms and equilibrium constants. These calculations allow us to predict solution properties and determine the concentrations of hydrogen and hydroxide ions in various chemical systems.

pH and pOH: Definition and Relationship

Defining pH and pOH

• pH measures the acidity of a solution, defined as the negative logarithm of the hydrogen ion concentration: $pH = -log[H⁺]$
  • Lower pH values indicate higher acidity (pH < 7)
  • Examples: lemon juice (pH 2), vinegar (pH 3)
• pOH measures the basicity of a solution, defined as the negative logarithm of the hydroxide ion concentration: $pOH = -log[OH⁻]$
  • Lower pOH values indicate higher basicity (pOH < 7)
  • Examples: milk of magnesia (pOH 2), ammonia solution (pOH 3)

The pH and pOH Relationship

• The sum of pH and pOH for any aqueous solution at 25°C always equals 14: $pH + pOH = 14$
  • This relationship is derived from the autoionization of water: $K_w = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴$ at 25°C
• In neutral solutions at 25°C, $[H⁺] = [OH⁻] = 1.0 × 10⁻⁷ M$, resulting in a pH and pOH of 7
  • Examples: pure water, saline solution
• Acidic solutions have a higher concentration of H⁺ ions than OH⁻ ions
  • $[H⁺] > 1.0 × 10⁻⁷ M$ and $pH < 7$
• Basic solutions have a higher concentration of OH⁻ ions than H⁺ ions
  • $[OH⁻] > 1.0 × 10⁻⁷ M$ and $pOH < 7$

Calculating pH and pOH

Calculating pH and pOH for Strong Acids and Bases

• For strong acids and bases, pH and pOH can be calculated directly from the concentration of the acid or base, assuming complete dissociation
  • For a strong acid with concentration [HA], $pH = -log[HA]$
    • Example: 0.1 M HCl, pH = -log(0.1) = 1
  • For a strong base with concentration [MOH], $pOH = -log[MOH]$, and pH can be calculated using $pH + pOH = 14$
    • Example: 0.01 M NaOH, pOH = -log(0.01) = 2, pH = 14 - 2 = 12

Calculating pH and pOH for Weak Acids and Bases

• For weak acids and bases, pH and pOH calculations involve the acid dissociation constant (Ka) or base dissociation constant (Kb)
  • For a weak acid with concentration [HA] and dissociation constant Ka, the pH can be calculated using: $pH = -log(√(Ka × [HA]))$
    • Example: 0.1 M acetic acid (Ka = 1.8 × 10⁻⁵), pH = -log(√(1.8 × 10⁻⁵ × 0.1)) = 2.87
  • For a weak base with concentration [B] and dissociation constant Kb, the pOH can be calculated using: $pOH = -log(√(Kb × [B]))$, and pH can be determined using $pH + pOH = 14$
    • Example: 0.1 M ammonia (Kb = 1.8 × 10⁻⁵), pOH = -log(√(1.8 × 10⁻⁵ × 0.1)) = 2.87, pH = 14 - 2.87 = 11.13
• When calculating pH or pOH for polyprotic acids or bases, consider the stepwise dissociation constants (Ka1, Ka2, etc., or Kb1, Kb2, etc.) and focus on the dominant equilibrium

Converting between pH, pOH, [H⁺], and [OH⁻]

Converting from pH or pOH to [H⁺] or [OH⁻]

• To convert from pH to [H⁺], use the antilogarithm function: $[H⁺] = 10⁻ᵖᴴ$
  • Example: pH 4, [H⁺] = 10⁻⁴ = 1 × 10⁻⁴ M
• To convert from pOH to [OH⁻], use the antilogarithm function: $[OH⁻] = 10⁻ᵖᴼᴴ$
  • Example: pOH 3, [OH⁻] = 10⁻³ = 1 × 10⁻³ M

Converting from [H⁺] or [OH⁻] to pH or pOH

• To convert from [H⁺] to pH, use the logarithm function: $pH = -log[H⁺]$
  • Example: [H⁺] = 1 × 10⁻⁵ M, pH = -log(1 × 10⁻⁵) = 5
• To convert from [OH⁻] to pOH, use the logarithm function: $pOH = -log[OH⁻]$
  • Example: [OH⁻] = 1 × 10⁻² M, pOH = -log(1 × 10⁻²) = 2
• When given either [H⁺] or [OH⁻], the other concentration can be calculated using the water autoionization constant: $K_w = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴$ at 25°C
  • Example: [H⁺] = 1 × 10⁻⁵ M, [OH⁻] = Kw ÷ [H⁺] = (1.0 × 10⁻¹⁴) ÷ (1 × 10⁻⁵) = 1 × 10⁻⁹ M

Acidity and Basicity: pH vs pOH

Predicting Acidity and Basicity from pH

• Solutions with pH < 7 are acidic, while solutions with pH > 7 are basic
  • Example: orange juice (pH 3) is acidic, baking soda solution (pH 9) is basic
• A solution with pH = 7 is neutral at 25°C
  • Example: distilled water
• The further the pH is from 7, the more acidic the solution
  • Example: hydrochloric acid (pH 0) is more acidic than acetic acid (pH 3)

Predicting Acidity and Basicity from pOH

• Solutions with pOH < 7 are basic, while solutions with pOH > 7 are acidic
  • Example: seawater (pOH 6) is basic, tomato juice (pOH 9) is acidic
• A solution with pOH = 7 is neutral at 25°C
  • Example: pure water
• The further the pOH is from 7, the more basic the solution
  • Example: sodium hydroxide (pOH 0) is more basic than ammonia (pOH 3)
• Comparing two solutions, the one with the lower pH is more acidic, while the one with the lower pOH is more basic