Acids and Bases

People noticed the pattern long before they could explain it. In 1680 Robert Boyle reported that acid solutions dissolve many substances, change the colors of certain natural dyes, and lose these traits after meeting alkali (base) solutions.^[1] That last trait, acids and bases canceling each other, is called neutralization.

Arrhenius: what they make in water

In 1884 Svante Arrhenius defined an acid as a compound that dissolves in water to give hydrogen ions, and a base as one that gives hydroxide ions, OH⁻.^[1] Hydrochloric acid and sodium hydroxide fit well:

HCl(aq) → H⁺(aq) + Cl⁻(aq)    NaOH(aq) → Na⁺(aq) + OH⁻(aq)

Brønsted–Lowry: who passes the proton

A bare H⁺ is just a proton, and in water it never floats around alone: it sticks to a water molecule to make the hydronium ion, H₃O⁺.^[1] In 1923 Johannes Brønsted and Thomas Lowry proposed a broader idea based on the transfer of protons.^[1] A Brønsted–Lowry acid donates a proton; a Brønsted–Lowry base accepts one.^[1] Ammonia has no OH⁻ to give, yet it is a base because it takes a proton from water:

NH₃ + H₂O ⇌ NH₄⁺ + OH⁻

Conjugate pairs. When an acid gives up its proton, what is left is its conjugate base; when a base gains a proton it becomes its conjugate acid.^[1] Above, NH₃/NH₄⁺ is one pair and H₂O/OH⁻ is the other. Water acted as an acid here, but with HCl it acts as a base. A substance that can do both is called amphiprotic.^[1]

Worked example: find the conjugate pairs in HF + H₂O ⇌ H₃O⁺ + F⁻

1. HF loses a proton and becomes F⁻: HF is the acid, F⁻ its conjugate base.
2. H₂O gains a proton and becomes H₃O⁺: H₂O is the base, H₃O⁺ its conjugate acid.
3. Each pair differs by exactly one H⁺.

Strength is about how completely an acid ionizes in water. If ionization is essentially complete, the acid is strong; if relatively little ionization happens, it is weak.^[3] Hydrochloric, nitric and perchloric acids are strong. Acetic acid, the acid in vinegar, is weak: most of its molecules stay whole, which is why its ionization is written with a double arrow, ⇌.^[3][6]

Concentration is a different question: how much acid is dissolved in each liter. A weak acid can be concentrated and a strong acid can be dilute. Compare the four beakers:

HA stands for an un-ionized acetic acid molecule and A⁻ for acetate. Water molecules are not drawn. The weak-acid fraction is exaggerated so you can see it: in 0.100 M acetic acid only about 1% of molecules are ionized.

Worked check: about 1% ionized?

For 0.100 M acetic acid, [H₃O⁺] ≈ √(K_a × C) = √(1.74 × 10⁻⁵ × 0.100) = 1.3 × 10⁻³ M, using K_a = 10^−4.76.^[7] That is 1.3 × 10⁻³ ÷ 0.100 = 1.3% of the molecules.

Even pure water makes a few ions by passing protons between its own molecules: at 25 °C about two in every billion water molecules are ionized.^[1]

H₂O + H₂O ⇌ H₃O⁺ + OH⁻    K_w = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25 °C

The value of K_w grows with temperature, so the numbers on this page are for 25 °C.^[1] In pure water [H₃O⁺] = [OH⁻] = 1.0 × 10⁻⁷ M. A solution is acidic if [H₃O⁺] > [OH⁻], neutral if they are equal and basic if [H₃O⁺] < [OH⁻].^[2]

Numbers like 0.0000001 are clumsy, so chemists use logarithms:

pH = −log[H₃O⁺]    pOH = −log[OH⁻]    pH + pOH = 14.00 (25 °C)

Because pH is a logarithm, each step of 1 is a factor of 10: water at pH 5 is ten times more acidic than water at pH 6, and pH 4 is a hundred times more acidic than pH 6.^[10] pH goes down as acidity goes up. A sig-fig rule: the number of decimal places in a pH equals the number of significant figures in the concentration, so pH 3.00 means [H₃O⁺] = 1.0 × 10⁻³ M.

Worked example: pH of 0.0010 M HCl

1. HCl is strong, so [H₃O⁺] = 0.0010 M = 1.0 × 10⁻³ M.
2. pH = −log(1.0 × 10⁻³) = 3.00
3. pOH = 14.00 − 3.00 = 11.00, so [OH⁻] = 1.0 × 10⁻¹¹ M.

Worked example: [H₃O⁺] in blood at pH 7.40

[H₃O⁺] = 10^−7.40 = 4.0 × 10⁻⁸ M. That is less than 1.0 × 10⁻⁷ M, so blood is slightly basic.

Typical values at 25 °C, from the sources listed. Treat these as ballpark figures. If you test your own kitchen, a dark roast and a light roast won't give the same reading, and neither will two bottles of bleach from different shelves.

An acid–base indicator is a dye, itself a weak acid or weak base, whose color depends on pH.^[5]

• Litmus: paper turns red in acid and blue in base.^[16]
• Phenolphthalein: colorless below about pH 8.3, red or pink above it.^[5] That makes it the classic indicator for titrating an acid with NaOH.
• Universal indicator: a mixture of dyes that runs through a rainbow, roughly red in strong acid, through yellow and green near neutral, to blue and violet in strong base.^[2] pH paper works the same way.

For finer readings chemists use a pH meter: a research-grade meter can resolve 0.001 pH units.^[2]

When an acid meets a base, H₃O⁺ and OH⁻ combine to make water. With a strong acid and a strong base the other product is a salt:

HCl(aq) + NaOH(aq) → NaCl(aq) + H₂O(l)    net: H₃O⁺ + OH⁻ → 2H₂O

A titration uses this to measure an unknown. Base of known concentration drips from a burette into the acid until the moles of OH⁻ added equal the moles of acid you started with. That is the equivalence point. An indicator that changes color right there marks the end point.^[5]

• Strong acid + strong base: the equivalence point is at pH 7.00, because Na⁺ and Cl⁻ don't react with water.^[5]
• Weak acid + strong base: the equivalence point is above 7, because the acetate ion left behind is a weak base. Halfway there, at the half-equivalence point, [HA] = [A⁻] and pH = pK_a.^[5]

The figure shows both curves for 25.00 mL of 0.100 M acid titrated with 0.100 M NaOH:

Worked example: strong acid at 0, 12.50, 25.00 and 37.50 mL

Start: 25.00 mL × 0.100 M = 2.500 mmol HCl.

1. 0 mL: [H₃O⁺] = 0.100 M, pH = 1.00.
2. 12.50 mL: 1.250 mmol OH⁻ added; 1.250 mmol H₃O⁺ left in 37.50 mL → 0.0333 M, pH = 1.48.
3. 25.00 mL: equivalence, only NaCl and water: pH = 7.00.
4. 37.50 mL: 1.250 mmol extra OH⁻ in 62.50 mL → 0.0200 M, pOH = 1.70, pH = 12.30.

These match the OpenStax worked example.^[5]

Worked example: acetic acid (pK_a 4.76) at 0, 12.50 and 25.00 mL

1. 0 mL: [H₃O⁺] ≈ √(K_aC) = √(1.74 × 10⁻⁵ × 0.100) = 1.32 × 10⁻³ M, pH = 2.88.
2. 12.50 mL: half the acid is now acetate, so pH = pK_a + log(1) = 4.76 (Henderson–Hasselbalch).
3. 25.00 mL: 2.500 mmol acetate in 50.00 mL = 0.0500 M. K_b = K_w/K_a = 5.75 × 10⁻¹⁰; [OH⁻] ≈ √(K_bC) = 5.36 × 10⁻⁶ M; pOH = 5.27; pH = 8.73.

OpenStax uses K_a = 1.8 × 10⁻⁵ (pK_a 4.74) and gets 4.74 and 8.72; this page uses PubChem's pK_a of 4.76, so its numbers are 0.01–0.02 higher.^[5][6][7]

A buffer is a mixture of a weak acid and its conjugate base. It soaks up small amounts of added acid or base, so its pH barely changes. The flat middle of the acetic acid curve is buffer behavior. Your blood is buffered mainly by carbonic acid, H₂CO₃, and bicarbonate, HCO₃⁻,^[4] which keeps it at a normal pH of about 7.35 to 7.45.^[11]

H₃O⁺ + HCO₃⁻ → H₂CO₃ + H₂O    OH⁻ + H₂CO₃ → HCO₃⁻ + H₂O

Ocean acidification. The ocean takes up carbon dioxide from the air, and dissolved CO₂ forms carbonic acid. NOAA reports that the pH of surface ocean water has fallen by 0.1 units over the period of rising carbon dioxide, which, because the scale is logarithmic, means about a 30 percent increase in acidity. The ocean's average pH is now around 8.1, still basic.^[12]

Check the math: why does 0.1 pH unit mean about 30%?

10^0.1 = 1.26, so [H₃O⁺] is about 1.26 times larger, a rise of about 26%, which NOAA rounds to approximately 30%. Either way, a small pH change is a large change in concentration.

• Wear goggles whenever acids or bases are out, even dilute ones. Strong bases like NaOH are as dangerous to eyes as strong acids.
• Never taste or smell a sample to test it. Use an indicator or a pH meter.
• Never mix bleach with acids or ammonia. These mixtures can release dangerous amounts of chlorine or chloramine gas.^[15]
• If something splashes on you, rinse with lots of water and tell your teacher straight away.