Acid‑Base Equilibria and Buffer Systems

Understanding the Ionic Product of Water (Kw)

The ionic product of water, denoted as Kw, is a fundamental constant in aqueous chemistry. At 25 °C, Kw is defined by the relationship:

• [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ mol² L⁻²

It is crucial to remember that Kw is the product of the hydrogen‑ion concentration [H⁺] and the hydroxide‑ion concentration [OH⁻], not their sum. This distinction explains why adding a strong acid or base does not change the value of Kw; the constant is temperature‑dependent, not concentration‑dependent.

Because water is neutral, the concentrations of the two ions are equal, each being 1.0 × 10⁻⁷ mol L⁻¹. However, this equality holds only for pure water; any acid or base will shift the individual concentrations while keeping their product at the constant Kw value.

Linking pH and pOH: The 14‑Point Scale

In aqueous solutions at 25 °C, the sum of pH and pOH always equals 14:

• pH + pOH = 14

Thus, if a solution has a pH of 4.2, the pOH is calculated as:

• pOH = 14 – 4.2 = 9.8

This relationship provides a quick way to move between the two scales and reinforces the idea that the product of [H⁺] and [OH⁻] remains constant.

Why Kw Remains Unchanged When Adding Strong Acids or Bases

Kw is a constant for a given temperature because it reflects the equilibrium position of the auto‑ionization of water:

H₂O ⇌ H⁺ + OH⁻

Adding a strong acid increases [H⁺] while decreasing [OH⁻] proportionally, and vice‑versa for a strong base. The product [H⁺][OH⁻] therefore stays at the same value, 1.0 × 10⁻¹⁴ mol² L⁻². Think of Kw as a thermostat setting that does not shift when you open a window; the temperature (product) stays the same, even though the individual contributions (ion concentrations) change.

Buffer Systems: The Henderson‑Hasselbalch Equation

What Is a Buffer?

A buffer is a solution that resists drastic pH changes when small amounts of acid or base are added. It typically consists of a weak acid (HA) and its conjugate base (A⁻) in comparable concentrations.

Calculating Buffer pH

The pH of a buffer can be estimated using the Henderson‑Hasselbalch equation:

• pH = pKa + log([A⁻]/[HA])

For a solution containing 0.10 M acetic acid (Ka = 1.8 × 10⁻⁵) and 0.10 M sodium acetate, the ratio [A⁻]/[HA] equals 1. Therefore:

• pKa = –log(1.8 × 10⁻⁵) ≈ 4.74
• pH = 4.74 + log(1) = 4.74

This demonstrates why a buffer with equal concentrations of acid and conjugate base has a pH equal to its pKa.

Effect of Adding Strong Base to a Buffer

When a small amount of strong base is introduced to a HA/A⁻ buffer, the base reacts primarily with the weak acid:

HA + OH⁻ → A⁻ + H₂O

Consequently, the concentration of the conjugate base [A⁻] increases, while [HA] decreases. However, because the base also reacts with water, a portion of the added OH⁻ converts water to H⁺, which then combines with A⁻ to form more HA. The net effect is an increase in [HA] as A⁻ accepts H⁺ from water, stabilizing the pH.

Choosing the Right Indicator for Titrations

Indicator Basics

Indicators are weak acids or bases that change color at a specific pH range. Selecting an indicator that changes color near the equivalence point of a titration ensures a clear visual endpoint.

Case Study: Methyl Orange vs. Phenolphthalein

Methyl orange transitions between red and yellow around pH 3‑4, making it suitable for strong acid–strong base titrations where the equivalence point is acidic. However, for the titration of a weak acid with a strong base, the equivalence point typically lies in the basic region (pH 8‑10). Using methyl orange would give a misleading endpoint because its color change occurs far below the actual equivalence point.

Phenolphthalein, on the other hand, changes from colorless to pink between pH 8 and 10, perfectly matching the steep rise observed in such titration curves. This alignment provides an accurate visual cue for the endpoint.

Practical Tip

Always examine the titration curve before selecting an indicator. If the steep pH increase occurs between pH 8 and 10, phenolphthalein is the optimal choice.

Why Strong Acid–Strong Base Mixtures Are Not Buffers

A true buffer requires a weak acid–conjugate base pair (or weak base–conjugate acid pair) that can reversibly absorb added H⁺ or OH⁻. Strong acids and strong bases dissociate completely in water, leaving no weak component to provide this reversible capacity.

Because both the acid and the base are fully ionized, the solution lacks the necessary equilibrium that would moderate pH changes. Consequently, any addition of acid or base leads to a direct and large shift in pH, confirming that strong acid–strong base mixtures cannot function as buffers.

Key Takeaways for Acid‑Base Equilibria and Buffer Systems

• Kw is a temperature‑dependent constant: [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ mol² L⁻² at 25 °C.
• pH and pOH relationship: pH + pOH = 14 (at 25 °C).
• Buffer pH calculation: Use the Henderson‑Hasselbalch equation, pH = pKa + log([A⁻]/[HA]).
• Effect of added strong base: In a HA/A⁻ buffer, the conjugate base converts to the weak acid, increasing [HA] and stabilizing pH.
• Indicator selection: Match the indicator’s transition range to the equivalence point pH; phenolphthalein for basic endpoints, methyl orange for acidic ones.
• Buffers require weak acid/base pairs: Strong acid–strong base mixtures lack the reversible equilibrium needed for buffering.

By mastering these concepts, you will be equipped to solve a wide range of problems involving acid‑base equilibria, calculate buffer capacities, and choose appropriate indicators for titrations.