The pH Scale and pH Calculation

Introduction

Presenter: Chad from Chad's Prep
Goals: Understand the pH scale and calculations related to it.
Context: Part of a new General Chemistry playlist, which covers high school, college science prep, MCAT, DAT, and OAT.
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Auto-Ionization of Water: Water molecules can split into hydrogen (H⁺) and hydroxide (OH⁻) ions.
- H₂O ↔ H⁺ + OH⁻
Hydronium Ion (H₃O⁺): More stable form of hydrogen ion in solution, formed by H⁺ joining with water molecules.
- 2H₂O ↔ H₃O⁺ + OH⁻

Definition: pH = -log[H⁺]
Equivalence: pH can also be calculated using [H₃O⁺]: pH = -log[H₃O⁺]
Auto-Ionization Constant (Kw): Kw = [H⁺][OH⁻] = 1x10⁻¹⁴ at 25°C
- For pure water: [H⁺] = [OH⁻] = 1x10⁻⁷ M
- pH and pOH Relationship: pH + pOH = 14

Logarithmic Nature: Each pH unit represents a 10x change in [H⁺] concentration
Range: pH is not bound between 0 and 14 (can go below 0 or above 14)
- Examples:
  - pH 6 vs. pH 7: pH 6 has 10x more [H⁺] than pH 7
  - pH 5 vs. pH 7: pH 5 has 100x more [H⁺] than pH 7

Given [H⁺] = 1x10⁻⁷ M
- pH = 7, pOH = 7, [OH⁻] = 1x10⁻⁷ M
Given pH 3
- pOH = 11, [H⁺] = 1x10⁻³ M, [OH⁻] = 1x10⁻¹¹ M
- Acidic Solution: pH < 7
Given [OH⁻] = 1x10⁻¹⁰ M
- pOH = 10, pH = 4, [H⁺] = 1x10⁻⁴ M
- Acidic Solution: pH < 7
Given pOH = 2
- pH = 12, [OH⁻] = 1x10⁻² M, [H⁺] = 1x10⁻¹² M
- Basic Solution: pH > 7
Given [H⁺] = 3.2x10⁻⁸ M
- Calculate pH ≈ 7.5, pOH ≈ 6.5, [OH⁻] ≈ 3.2x10⁻⁷ M
- Approximation and Logs: Use calculator for non-round numbers

Different Temperature (e.g., 37°C):
- New Kw: 1x10⁻¹³
- Recalculate: [H⁺] and [OH⁻] = 3.2x10⁻⁷ M
- New Neutral pH and pOH: 6.5 (since pH + pOH = 13)
- pH of 7 at 37°C: Basic solution, not neutral

Use a Calculator: Helps with accuracy for logarithmic and anti-logarithmic calculations
Practice Problems: General Chemistry Master Course available with 1200+ questions