Acid-Base Chemistry

date2026-07-24tags:chem:

Acid-base chemistry makes chemistry quantitative. pH measures hydrogen ion activity directly, quickly, and cheaply with a glass electrode[fn::A glass electrode measures a membrane potential across a thin glass membrane. This membrane responds to H⁺ activity. The Nernst equation (see Electrochemistry) converts this potential to a pH reading.]. A Pourbaix diagram plots potential versus pH. This diagram is the central artifact of the corrosion wiki (see Corrosion). The diagram takes pH as one of its two axes. Acid-base chemistry explains this axis.

The Autoionization of Water and the Definition of pH

Pure water is not inert. A small fraction of water molecules undergo autoionization:

: H₂O ⇌ H⁺ + OH⁻

The equilibrium constant for this reaction is $K_w$. Scientists call this the "water dissociation constant" or the "ion product of water":

: K_w = [H⁺][OH⁻]

At 25 °C (298.15 K), $K_w = 1.0 \times 10^{-14}$ (mol/L)²[fn::The true value is closer to $1.008 \times 10^{-14}$ at 25 °C. Values use $1.0 \times 10^{-14}$ for convenience. This value is sufficient for most practical work.]. Pure water produces one H⁺ ion and one OH⁻ ion for each autoionization event:

: [H⁺]² = K_w = 1.0 × 10⁻¹⁴ : [H⁺] = 1.0 × 10⁻⁷ mol/L

The pH is the negative base-10 logarithm of the hydrogen ion activity[fn::A pH value measures activity, not concentration. Low ionic strength solutions have nearly equal activity and concentration. High ionic strength solutions have different activity. Use the formal definition $\text{pH} = -\log a_{H^+}$ for high ionic strength solutions. See *When It Breaks.]:

: pH = −log₁₀[H⁺]

Pure water has pH = 7.00:

: pH = −log₁₀(1.0 × 10⁻⁷) = 7.00

This result explains the "pH 7 is neutral" rule. But this rule applies only at 25 °C. $K_w$ depends on temperature. Autoionization absorbs heat ($\Delta H \approx +55.8$ kJ/mol). The value of $K_w$ increases with temperature. At 100 °C, $K_w \approx 5.13 \times 10^{-13}$. This gives a neutral pH of about 6.13. The "7 is neutral" rule is a temperature-specific convenience, not a universal truth[fn::Scientists often overlook the temperature dependence of $K_w$. This dependence explains why high-temperature Pourbaix diagrams (for nuclear or geothermal applications) need recomputation. See Electrochemical Thermodynamics.].

The log scale

A logarithmic scale compresses values. A pH change of 1 unit equals a tenfold change in $[H^+]$. A pH 2 solution has $10^5$ times the hydrogen ion concentration of a pH 7 solution. This compression makes the scale useful. The scale tames a concentration range of fifteen orders of magnitude. The scale fits on a single diagram axis. This compression also makes the scale dangerous. "pH 6 is slightly acidic" understates the facts. A pH 6 solution has ten times the $[H^+]$ of neutral water.

Brønsted-Lowry Theory

Brønsted and Lowry proposed this definition independently in 1923. The Brønsted-Lowry definition describes acid-base chemistry with proton transfer:

An acid donates a proton (HA → H⁺ + A⁻).
A base accepts a proton (B + H⁺ → BH⁺).

Every acid has a conjugate base. Scientists call this the species remaining after deprotonation. Every base has a conjugate acid. The reaction HA + B → A⁻ + BH⁺ is the generic acid-base equilibrium. This definition is more general than the Arrhenius definition. The Arrhenius definition requires OH⁻ as the base. The Brønsted-Lowry definition admits other bases. Ammonia (NH₃) accepts a proton to become NH₄⁺. Carbonate (CO₃²⁻) accepts a proton to become HCO₃⁻.

Acid strength uses the acid dissociation constant:

: K_a = [H⁺][A⁻] / [HA]

The value $\text{p}K_a = -\log K_a$ quantifies acid strength. A strong acid has a large $K_a$. It has a small $\text{p}K_a$. A weak acid has a small $K_a$. It has a large $\text{p}K_a$.

Lewis Theory

Lewis proposed this definition in 1923. The Lewis definition is even broader. A Lewis acid accepts an electron pair. It is also called an electrophile. A Lewis base donates an electron pair. It is also called a nucleophile. Reactions without proton transfer count as acid-base reactions under this definition. BF₃ + :NH₃ → F₃B←NH₃ is an acid-base reaction.

The Lewis definition generalizes Brønsted-Lowry theory. Every Brønsted acid is a Lewis acid. A proton (H⁺) accepts an electron pair from the base. Not every Lewis acid is a Brønsted acid. The Lewis frame is necessary for metal-ion hydrolysis, complexation, and non-aqueous solvent chemistry. Use the Brønsted-Lowry frame for pH, buffers, and Pourbaix diagrams. pH measures proton activity.

Strong vs Weak Acids and Bases

A strong acid dissociates completely in water. Its $K_a$ is much greater than 1. The equilibrium lies far to the right. The common strong acids are HCl, HBr, HI, HNO₃, HClO₄, and the first proton of H₂SO₄[fn::"Strong" is a practical classification. It means dissociated to about 99% at typical concentrations. Some acids have $\text{p}K_a$ near 0. Trichloroacetic acid has $\text{p}K_a \approx 0.7$. Its classification depends on concentration.].

A weak acid dissociates only partially. Its $K_a$ is less than 1. Significant amounts of HA and A⁻ coexist at equilibrium. Acetic acid ($\text{p}K_a = 4.76$) is the standard example. Weak acids and their conjugate bases can buffer. Strong acids lack this property. They have no conjugate base remaining in solution.

Strong bases dissociate completely to OH⁻. Example: NaOH, KOH, and other alkali hydroxides. Weak bases accept protons only partially. Their behavior uses $K_b$:

: K_b = [BH⁺][OH⁻] / [B]

An example weak base is NH₃. For any conjugate acid-base pair:

: $K_a \times K_b = K_w$

So $\text{p}K_a + \text{p}K_b = \text{p}K_w = 14$ (at 25 °C). This relationship links acid and base strength to water autoionization.

Polyprotic Acids

Polyprotic acids have more than one dissociable proton. Examples: H₂SO₄, H₂CO₃, H₃PO₄. Each dissociation step has its own $K_a$:

: H₃PO₄ ⇌ H⁺ + H₂PO₄⁻ (Ka1 = 7.5 × 10⁻³, pKa1 = 2.12) : H₂PO₄⁻ ⇌ H⁺ + HPO₄²⁻ (Ka2 = 6.2 × 10⁻⁸, pKa2 = 7.21) : HPO₄²⁻ ⇌ H⁺ + PO₄³⁻ (Ka3 = 4.8 × 10⁻¹³, pKa3 = 12.32)

Treat each step independently when successive $\text{p}K_a$ values are well separated (ΔpK_a > ~3). The first proton dissociates fully before the second begins. Treat overlapping steps differently when ΔpK_a < ~2. Intermediate species coexist in non-trivial proportions[fn::Malonic acid (HOOC-CH₂-COOH) has pKa1 = 2.83 and pKa2 = 5.69. Its ΔpKa ≈ 2.9. This value is borderline. Citric acid has pKa values of 3.13, 4.76, 6.40. All values are within ~3 units. Its titration curve shows three poorly-resolved steps.]. Polyprotic acids provide multiple buffer regions. Each region centers on one $\text{p}K_a$.

Buffer Solutions and the Henderson-Hasselbalch Equation

A buffer resists pH change upon addition of small amounts of acid or base. A buffer consists of a weak acid and its conjugate base (or a weak base and its conjugate acid) in comparable concentrations.

Derivation

Start from the acid dissociation equilibrium:

: HA ⇌ H⁺ + A⁻ : K_a = [H⁺][A⁻] / [HA]

Rearrange for $[H^+]$:

: [H⁺] = K_a × [HA] / [A⁻]

Take $-\log_{10}$ of both sides:

: −log[H⁺] = −log K_a − log([HA] / [A⁻]) : pH = pK_a + log([A⁻] / [HA])

This is the Henderson-Hasselbalch equation. It is the equilibrium expression rearranged and logarithmically compressed[fn::Some critics call "just algebra," which is true. But the equation makes the buffering relationship clear. When [A⁻] = [HA], pH = pKa exactly. This is the point of maximum buffer capacity.].

Worked example: acetate buffer at pH 4.76

Consider a buffer with 0.10 M acetic acid (CH₃COOH, $\text{p}K_a = 4.76$) and 0.10 M sodium acetate (CH₃COONa). Sodium acetate provides CH₃COO⁻. By Henderson-Hasselbalch:

: pH = 4.76 + log(0.10 / 0.10) = 4.76 + log(1) = 4.76

The buffer is at its $\text{p}K_a$. This is the point of maximum buffering capacity[fn::Buffer capacity is $\beta = dC_b/d(\text{pH})$. It measures the amount of strong base (or acid) needed to produce a unit pH change. It is maximal at pH = pKa. It falls off on either side, becoming negligible more than ~1.5 pH units from pKa. The full expression is $\beta = 2.303 \cdot C_{total} \cdot K_a[H^+] / (K_a + [H^+])^2$.].

Add 0.010 mol/L of strong acid (HCl). The added H⁺ converts A⁻ to HA:

: [A⁻] = 0.10 − 0.010 = 0.090 M : [HA] = 0.10 + 0.010 = 0.110 M : pH = 4.76 + log(0.090 / 0.110) = 4.76 − 0.087 ≈ 4.67

The pH dropped by only about 0.09 units. For comparison, adding 0.010 M HCl to pure water (pH 7) gives pH 2. This is a change of 5 units. "Buffering" means the weak base soaks up added protons. The logarithm compresses the effect.

Hydrolysis of Salts

Salts of weak acids or weak bases are not pH-neutral in water. The conjugate base of a weak acid (e.g., CH₃COO⁻ from sodium acetate) hydrolyzes:

: A⁻ + H₂O ⇌ HA + OH⁻

This reaction produces OH⁻. It makes the solution basic. The equilibrium constant is $K_h = K_w / K_a$. The pH is approximately:

: pH ≈ ½(pK_w + pK_a + log C)

Use this formula for a solution of concentration $C$ of the salt of a weak acid[fn::Derive from the hydrolysis equilibrium $K_h = [HA][OH^-]/[A^-] = K_w/K_a$. Combine with charge and mass balance. The result assumes $C \gg [OH^-]$. This assumption is good when $C \cdot K_h \ll K_w$.]. The analogous result for the salt of a weak base (e.g., NH₄Cl) gives an acidic solution.

A Na₂CO₃ solution is distinctly basic. Sodium carbonate is the salt of a weak acid. The carbonate ion ($\text{p}K_b \approx 3.67$) hydrolyzes to produce OH⁻. Salt hydrolysis explains why many natural solutions depart from neutrality. This mechanism is relevant to the pH axis of Pourbaix diagrams in natural waters.

A 0.10 M sodium acetate solution ($\text{p}K_a = 4.76$, so $\text{p}K_b = 14 - 4.76 = 9.24$):

: K_h = K_w / K_a = 10⁻¹⁴ / 10⁻⁴·⁷⁶ = 10⁻⁹·²⁴ ≈ 5.75 × 10⁻¹⁰ : [OH⁻] = √(K_h × C) = √(5.75 × 10⁻¹⁰ × 0.10) ≈ 7.58 × 10⁻⁶ : pOH = 5.12, pH = 14 − 5.12 = 8.88

A 0.10 M solution of a "neutral salt" is mildly basic. This is the rule, not the exception, for salts other than strong acid plus strong base pairs.

Connection to Pourbaix Diagrams

A Pourbaix diagram (E-pH diagram) is the main artifact of acid-base chemistry in the corrosion wiki. The diagram plots the thermodynamically stable species of a metal. It shows stability as a function of electrochemical potential (E, vertical axis) and pH (horizontal axis). The pH axis measures hydrogen ion activity. The boundaries between regions are acid-base equilibria, redox equilibria, or both.

A Pourbaix diagram has three types of boundary lines:

1. Horizontal lines show pure redox reactions. These reactions involve no H⁺. The potential depends on the ratio of oxidized to reduced species. It does not depend on pH. 2. Vertical lines show pure acid-base reactions. These reactions involve no electrons. The boundary depends on pH. It does not depend on E. The Fe²⁺/Fe(OH)₂ boundary uses a precipitation equilibrium. Its position depends on $[H^+]$. 3. Diagonal lines show reactions with both H⁺ and e⁻. The slope is $-0.0591 \, (n_{H^+}/n_e)$ V/pH at 25 °C. Scientists derive this from the Nernst equation (see Electrochemistry).

The pH axis determines which species is thermodynamically stable. For iron at low pH and low potential, Fe²⁺(aq) is stable. Iron dissolves (active corrosion). At high pH, Fe₂O₃ or Fe₃O₄ are stable. These passivating oxides suppress corrosion. The Corrosion note treats pH as a control variable. Adjusting pH shifts the system across a boundary. This changes the stable phase and the corrosion behavior.

The Pourbaix diagram inherits the entire acid-base framework. "pH 4" on the diagram uses the $[H^+]$ activity defined here. The buffer chemistry that sets local pH in a crevice or pit is the Henderson-Hasselbalch chemistry of this note. The temperature dependence of the Pourbaix pH scale is the temperature dependence of $K_w$. There is no separate "Pourbaix pH." It is the same quantity.

When It Breaks

Several assumptions fail in limiting cases:

Negative pH: The pH scale has no lower bound. A 2 M HCl solution has a hydrogen ion activity around 1.5--2. Its pH is about −0.3. Concentrated acids reach pH ≈ −1.1. The "0 to 14" range is a convenience of dilute aqueous chemistry[fn::Negative pH is physically real. Concentrated acid has $a_{H^+} > 1$. The value $-\log(a_{H^+})$ is less than 0. People confuse "the pH range 0--14" with "the definition of pH."].
Henderson-Hasselbalch at high ionic strength: The equation uses concentrations. The rigorous definition uses activities. Ionic strengths above ~0.1 M cause significant activity coefficient deviation. The Debye-Hückel limiting law holds only below ~0.01 M. The Henderson-Hasselbalch prediction can be off by 0.3--0.5 units or more[fn::Real buffer recipes in physiological contexts (e.g., PBS, ionic strength ~0.15 M) are empirically adjusted. The Davies equation extends Debye-Hückel to ~0.5 M. Specific ion effects dominate above that.]. Seawater (ionic strength ~0.7 M) requires explicit activity corrections.
Overlapping pKa in polyprotic acids: A full equilibrium calculation is necessary when successive $\text{p}K_a$ values are within ~2 units. The Henderson-Hasselbalch treatment assumes one dominant equilibrium. Multiple species coexist when pKa values overlap. Use numerical speciation instead[fn::Software like PHREEQC, Visual MINTEQ, or CHEAQS solves the full set of mass-action and mass-balance equations. Pourbaix diagram computation at high ionic strength also requires speciation codes.].
Temperature dependence of Kw: "pH 7 is neutral" holds only at 25 °C. At 0 °C, $K_w \approx 0.12 \times 10^{-14}$. The neutral pH is about 7.47. At 100 °C, $K_w \approx 5.13 \times 10^{-13}$. The neutral pH is about 6.14. Pourbaix diagrams at 25 °C do not apply at other temperatures. Both the pH scale and the potential scale shift[fn::High-temperature Pourbaix diagrams are an active research area for nuclear and geothermal systems. The water stability lines also move with temperature. They compress or expand the water-stable region of the diagram.].
Non-aqueous solvents: The framework uses water-specific values. $K_w$, pH 7, and the pKa scale apply to water only. Other solvents have different autoionization products, neutral points, and acid strengths. The pH concept generalizes to other solvents, but the numbers are not comparable across solvents.

Meta-Observation

Acid-base chemistry is the point where chemistry becomes computable from first principles. Give a $\text{p}K_a$ and concentrations. You can predict a pH. Give a pH and a potential. You can read a Pourbaix diagram. You can predict whether a metal corrodes. This capability is rare for chemistry. Most chemical predictions need expensive computation or empirical correlation. Acid-base equilibrium needs only algebra and a table of $\text{p}K_a$ values[fn::The underlying physics is not simple. The proton and hydrogen bond structure are quantum-mechanical questions. But the phenomenology is algebraic. This makes it useful.].

A glass electrode makes pH measurable in real time. It is the most consequential sensor in chemistry. It makes the Pourbaix diagram an operational tool. You can measure E and pH simultaneously. You can plot the point. You can know the stable phase on the map. The acid-base note is the foundation of corrosion-wiki quantitative content. Every Pourbaix diagram pH axis originates here.