Reactivity 3.1.4 – The pH Scale and Hydrogen Ion Concentration

What is pH?

• The term pH refers to the “power of hydrogen” and is a scale used to quantify the acidity or alkalinity of an aqueous solution.
• It measures the concentration of hydrogen ions \( [\text{H}^+] \), or more accurately hydronium ions \( [\text{H}_3\text{O}^+] \), in solution.
• The pH scale provides a logarithmic expression of acidity, which means each pH unit change corresponds to a 10-fold change in \( [\text{H}^+] \).

Mathematical Relationship:

• The formula for pH is:
  \( \text{pH} = -\log_{10}[\text{H}^+] \)
• This can be rearranged to find the hydrogen ion concentration:
  \( [\text{H}^+] = 10^{-\text{pH}} \)
• These equations are used to convert between the acidity of a solution (measured as pH) and the molar concentration of hydrogen ions \( [\text{H}^+] \).

Understanding the Logarithmic Scale:

• The pH scale is logarithmic, not linear.
• This means a change of 1 unit in pH reflects a tenfold difference in hydrogen ion concentration:

For example:

pH 3 has ten times more \( \text{H}^+ \) ions than pH 4 and a solution with pH 2 has 100 times more \( \text{H}^+ \) than a solution with pH 4.

Typical pH Scale Range:

• pH = 7: Neutral (e.g., pure water at 25°C)
• pH < 7: Acidic solution (higher \( [\text{H}^+] \))
• pH > 7: Basic or alkaline solution (lower \( [\text{H}^+] \))
• The scale usually ranges from 0 to 14, but values can go below 0 or above 14 in very concentrated solutions.

pH and Hydrogen Ion Concentration Table

Note: This table assumes 25°C and aqueous solutions. The actual pH may vary with concentration and temperature.

pH of Acids

• Strong Acids: pH range ≈ 0–3
  • Examples: HCl, HNO₃, H₂SO₄ (in high concentrations)
  • These fully dissociate in water, releasing a high concentration of H⁺ ions.
• Moderate Acids: pH range ≈ 3–5
  • Examples: CH₃COOH (ethanoic acid), H₂CO₃
  • These partially dissociate, producing fewer H⁺ ions than strong acids.
• Weak Acids: pH range ≈ 5–6.9
  • Examples: Organic acids, like citric acid or carbonic acid in low concentrations
  • Only a small proportion of acid molecules release H⁺ ions.

pH of Bases

• Weak Bases: pH range ≈ 7.1–9
  • Examples: NH₃ (ammonia), CH₃NH₂ (methylamine)
  • They only slightly accept H⁺ ions from water, giving a mildly basic solution.
• Moderate Bases: pH range ≈ 9–11
  • Examples: NaHCO₃ (sodium bicarbonate), basic amino acids
  • These generate more OH⁻ ions but are still partially dissociative or weakly ionic.
• Strong Bases: pH range ≈ 11–14
  • Examples: NaOH, KOH, Ca(OH)₂
  • These fully dissociate in water, producing a high concentration of OH⁻ ions.

Representing Hydrogen Ions in Solution:

• In aqueous solution, hydrogen ions \( \text{H}^+ \) associate with water molecules to form hydronium ions \( \text{H}_3\text{O}^+ \).
• For simplicity, IB conventions allow both \( [\text{H}^+] \) and \( [\text{H}_3\text{O}^+] \) to represent acidity.

Calculations Involving pH and [H⁺]

• Calculating pH from [H⁺]: Use the negative logarithm (base 10) of the concentration.
• Calculating [H⁺] from pH: Use the inverse logarithm (10 to the power of –pH).
• Always include correct units for concentration: mol·dm⁻³.
• Round pH values to 2 decimal places, unless instructed otherwise.

Understanding Precision in pH Measurement:

There are two main ways to determine the pH of a solution:

1. Universal Indicator:

• • A mixture of dyes that change color depending on pH.
  • Gives only an approximate value by comparing to a color chart.
  • Color is compared against a reference chart ranging from red (strong acid) to purple (strong base).
  • pH is inferred to the nearest whole number or 0.5 units.
  • Useful for qualitative or classroom observations.

2. pH Meter / pH Probe:

• • A precise and sensitive instrument using a glass electrode sensitive to \( \text{H}^+ \) concentration and voltmeter.
  • Gives a quantitative digital reading to 2 decimal places.
  • More reliable, especially in titrations and lab experiments.
  • Preferred method in titrations, research, and analytical chemistry.

Important Notes for IB Chemistry:

• The relationship between pH and \( [\text{H}^+] \) is temperature dependent (assumes 25°C unless stated otherwise).
• pH is only defined for aqueous systems — not in gaseous or nonpolar solvents.
• Always express \( [\text{H}^+] \) in mol·dm⁻³ and pH values to 2 decimal places unless otherwise specified.
• Always check if a question requires estimation (indicator) or precise calculation (pH meter).
• Ensure your calculator is in base-10 log mode when solving for pH.
• pH changes significantly even with small concentration shifts — remember it’s logarithmic!