Getting Started
Even in a glass of the purest water, a dynamic chemical process is constantly occurring at the molecular level. Water is not merely a collection of inert H₂O molecules; it actively participates in a reversible reaction with itself, producing a small but crucial concentration of ions. Understanding this self-ionization is the foundation for quantifying acidity and basicity in any aqueous system.
What You Should Be able to Do
After completing this section, you will be able to:
Define and calculate pH and pOH using their logarithmic formulas.
Write the equilibrium expression for the autoionization of water and use the ion-product constant, Kw, to find the concentration of hydronium or hydroxide ions.
Describe the conditions for a neutral solution in terms of ion concentrations and pH at 25°C.
Explain how and why the pH of a neutral water solution changes with temperature.
Key Concepts & Analysis
This topic is best understood through the lens of Dynamics & Change, focusing on the reversible, temperature-sensitive equilibrium that governs the properties of water.
Baseline Condition: The Dynamic Equilibrium of Water at 25°C
In any sample of liquid water, a small fraction of molecules will react with each other in a process called autoionization. In this reaction, one water molecule acts as an acid (donating a proton) and another acts as a base (accepting the proton):
2 H₂O(l) ⇌ H₃O⁺(aq) + OH⁻(aq)
This is a dynamic equilibrium: the forward and reverse reactions occur at the same rate, so the concentrations of the hydronium ion (H₃O⁺) and the hydroxide ion (OH⁻) remain constant. The hydronium ion, H₃O⁺, is often represented by the shorthand H⁺ for simplicity.
The equilibrium constant for this reaction is called the ion-product constant for water, Kw. The expression is:
Kw = [H₃O⁺][OH⁻]
At a standard temperature of 25°C, extensive measurements show that Kw = 1.0 x 10⁻¹⁴. In pure, neutral water, the 1:1 stoichiometry of the reaction means that the concentrations of the ions must be equal:
[H₃O⁺] = [OH⁻]
Therefore, at 25°C in neutral water:
[H₃O⁺] = [OH⁻] = √(1.0 x 10⁻¹⁴) = 1.0 x 10⁻⁷ M
The Process or Stress: Quantifying Acidity and Temperature Changes
The concentrations of H₃O⁺ and OH⁻ are often very small, making them inconvenient to work with. To simplify this, we use a logarithmic scale called the p-scale, where "p" stands for "power of" and mathematically means "negative base-10 logarithm of".
pH is defined as: pH = -log[H₃O⁺]
pOH is defined as: pOH = -log[OH⁻]
Applying this to neutral water at 25°C:
pH = -log(1.0 x 10⁻⁷) = 7.00
pOH = -log(1.0 x 10⁻⁷) = 7.00
A useful relationship can be derived by taking the negative logarithm of the Kw expression:
-log(Kw) = -log([H₃O⁺][OH⁻])
-log(Kw) = -log[H₃O⁺] + (-log[OH⁻])
pKw = pH + pOH
At 25°C, pKw = -log(1.0 x 10⁻¹⁴) = 14.00. Thus, at this temperature, 14.00 = pH + pOH.
The autoionization of water is an endothermic process (it absorbs heat). If we apply a stress, such as increasing the temperature, Le Châtelier's principle predicts the equilibrium will shift to the right to consume the added heat.
The Resulting Change: Shifting Neutrality
When the temperature of water increases, the forward reaction (autoionization) is favored. This results in an increase in the equilibrium concentrations of both [H₃O⁺] and [OH⁻].
Effect on Kw: Since both ion concentrations increase, the value of Kw increases. For example, at 50°C, Kw is approximately 5.5 x 10⁻¹⁴.
Effect on Neutral pH: The definition of a neutral solution is one where [H₃O⁺] = [OH⁻]. This definition is true at any temperature. However, the pH value associated with neutrality changes.
Let's calculate the pH of neutral water at 50°C:
Kw = [H₃O⁺][OH⁻] = 5.5 x 10⁻¹⁴
Since [H₃O⁺] = [OH⁻], then [H₃O⁺]² = 5.5 x 10⁻¹⁴
[H₃O⁺] = √(5.5 x 10⁻¹⁴) ≈ 2.3 x 10⁻⁷ M
pH = -log(2.3 x 10⁻⁷) ≈ 6.64
At 50°C, the pH of pure, neutral water is 6.64. The water is still neutral because the concentrations of hydronium and hydroxide ions are equal, but the pH is less than 7.
| Condition | Relationship | Value at 25°C | Value at > 25°C |
|---|---|---|---|
| Kw | [H₃O⁺][OH⁻] | 1.0 x 10⁻¹⁴ | Increases (> 1.0 x 10⁻¹⁴) |
| Neutrality | [H₃O⁺] = [OH⁻] | 1.0 x 10⁻⁷ M | Increases (> 1.0 x 10⁻⁷ M) |
| Neutral pH | -log[H₃O⁺] | 7.00 | Decreases (< 7.00) |
| pKw | pH + pOH | 14.00 | Decreases (< 14.00) |
Key Models & Representations
The relationships between the four key quantities—[H₃O⁺], [OH⁻], pH, and pOH—can be visualized as a calculation flowchart. Knowing any one of these values allows you to calculate the other three at a given temperature (most commonly 25°C).
Calculation Flowchart for Aqueous Solutions at 25°C
[H₃O⁺] <----------------------> [OH⁻]
| (Use Kw = [H₃O⁺][OH⁻]) ^
| |
(Use pH = -log[H₃O⁺]) (Use pOH = -log[OH⁻])
| |
v |
pH <----------------------> pOH
(Use pH + pOH = 14.00)
Key Terms, Quantities, & Concepts
Autoionization of Water: The process in which water molecules react with one another to form hydronium (H₃O⁺) and hydroxide (OH⁻) ions.
Hydronium Ion (H₃O⁺): A water molecule with an extra proton. It is the species responsible for acidic properties in aqueous solutions and is often abbreviated as H⁺.
Hydroxide Ion (OH⁻): The species responsible for basic properties in aqueous solutions, formed when a water molecule loses a proton.
Ion-Product Constant for Water (Kw): The equilibrium constant for the autoionization of water. At 25°C, Kw = 1.0 x 10⁻¹⁴.
pH: A logarithmic measure of the hydronium ion concentration, defined as pH = -log[H₃O⁺].
pOH: A logarithmic measure of the hydroxide ion concentration, defined as pOH = -log[OH⁻].
Neutral Solution: An aqueous solution in which the concentration of hydronium ions equals the concentration of hydroxide ions ([H₃O⁺] = [OH⁻]).
Skill Snapshots
Causation
Cause: The chemical nature of water allows it to act as both a proton donor and acceptor. Effect: Water undergoes autoionization, creating H₃O⁺ and OH⁻ ions in any aqueous solution.
Cause: The autoionization of water is an endothermic process. Effect: Increasing the temperature increases the value of Kw.
Cause: The pH scale is logarithmic. Effect: A decrease of one pH unit (e.g., from 4 to 3) corresponds to a tenfold increase in the [H₃O⁺].
Comparison
pH vs. pOH: pH is a measure of the acidity ([H₃O⁺]) of a solution, while pOH is a measure of the basicity ([OH⁻]). They are inversely related; as one goes up, the other goes down.
Neutrality at 25°C vs. 50°C: A neutral solution at 25°C has a pH of 7.00, whereas a neutral solution at 50°C has a pH of 6.64.
[H₃O⁺] vs. [OH⁻] in a Neutral Solution: In any neutral solution, regardless of temperature, the concentration of hydronium ions is exactly equal to the concentration of hydroxide ions.
Change and Continuity Over Condition
Baseline: At 25°C, pure water is neutral with [H₃O⁺] = 1.0 x 10⁻⁷ M and a pH of 7.00.
Change 1: When water is heated to 60°C, the autoionization equilibrium shifts to the right, increasing the concentrations of both H₃O⁺ and OH⁻.
Change 2: Because [H₃O⁺] is now greater than 1.0 x 10⁻⁷ M, the pH of neutral water at 60°C drops to a value below 7.00.
Continuity: Despite the changes in Kw and pH with temperature, the fundamental definition of neutrality—that [H₃O⁺] must equal [OH⁻]—remains constant.
Common Misconceptions & Clarifications
Misconception: A solution with a pH of 7 is always neutral.
Clarification: Neutrality is defined by the condition [H₃O⁺] = [OH⁻]. This equality only corresponds to a pH of 7.00 at 25°C. At higher temperatures, the pH of a neutral solution is less than 7.
Misconception: Pure water contains only H₂O molecules.
Clarification: Pure water is a dynamic equilibrium. While the vast majority of particles are H₂O molecules, it always contains small, equal concentrations of H₃O⁺ and OH⁻ ions due to autoionization.
Misconception: A solution with pH = 6 is slightly acidic, so hot water (e.g., pH = 6.64) must be slightly acidic.
Clarification: Acidity and basicity are defined by the relative concentrations of H₃O⁺ and OH⁻. A solution is acidic only if [H₃O⁺] > [OH⁻]. In hot water, even though the pH is below 7, the concentrations are still equal, so the water is neutral.
One-Paragraph Summary
The self-ionization of water is a fundamental equilibrium process that establishes the basis for acidity and basicity in aqueous solutions. This reversible reaction, 2 H₂O(l) ⇌ H₃O⁺(aq) + OH⁻(aq), is governed by the ion-product constant, Kw, which has a value of 1.0 x 10⁻¹⁴ at 25°C. To manage the small ion concentrations, we use the logarithmic pH and pOH scales, where pH + pOH = 14 at 25°C. A neutral solution is defined by the equality [H₃O⁺] = [OH⁻], which corresponds to a pH of 7 only at 25°C. Because autoionization is endothermic, increasing the temperature increases Kw and lowers the pH of neutral water, demonstrating that the concept of neutrality is dependent on temperature.