Acids and Bases — Laboratorium

The pH scale from 0 to 14

drag the marker · ← → by 0.01 · Shift by 0.1

7.00neutral

pOH: 7.00
[H₃O⁺] mol/L: 1.0·10⁻⁷
[OH⁻] mol/L: 1.0·10⁻⁷
Universal indicator: green

The pH values are typical — a particular cola, coffee or soap may differ a little. pH + pOH = 14 holds at 25 °C.

Magnifier: how many ions?

The cube is sized so it always holds 100 H₃O⁺ ions. Each step up in pH needs 10 times the volume — so the edge grows about 2.15 times.

Logarithms — a scale of powers of ten

pH = −log [H₃O⁺] [H₃O⁺] in mol/L

pH 3 means [H₃O⁺] = 10⁻³ mol/L, and pH 4 means 10⁻⁴ mol/L. One step on the scale is a tenfold difference, two steps — a hundredfold. That's why lemon juice (pH ≈ 2) is about 1000 times more acidic than coffee (pH ≈ 5), not just “a bit more”.

[H₃O⁺]·[OH⁻] = K_w = 1.0·10⁻¹⁴ at 25 °C

pH + pOH = 14

In all water, autoionization takes place: 2 H₂O ⇄ H₃O⁺ + OH⁻. When H₃O⁺ ions increase, OH⁻ ions decrease — their product stays constant. In pure water both are at 10⁻⁷ mol/L, hence pH 7.

Dissociation: strong vs. weak acid

H₃O⁺Cl⁻CH₃COO⁻CH₃COOH moleculewater molecules not shown

Concentration of both acids0.1 mol/L

HCl + H₂O → H₃O⁺ + Cl⁻ (completely)
CH₃COOH + H₂O ⇄ H₃O⁺ + CH₃COO⁻ (equilibrium, K_a = 1.8·10⁻⁵)

pH of hydrochloric acid: 1.00
pH of acetic acid: 2.88
Degree of dissociation, HCl: ≈ 100%
Degree of dissociation, CH₃COOH: 1.3%

We draw 30 acid molecules each. In acetic acid, molecules keep breaking apart and rejoining — the number of ions fluctuates around an average (dynamic equilibrium). Dilution increases the degree of dissociation of a weak acid.

pH calculator

Substance

Concentration0.1 mol/L

pH 1.00

strong acid — dissociates completely

Titration settings

Acid in the flask + base in the burette

Indicator in the flask

Unknown acid concentration Show the theoretical curve

Burette and flask

drag the stopcock

Burette stopcockclosed

Titration curve

Added: 0.00 mL
pH in the flask: 1.00
Warming ΔT: +0.00 °C
Equivalence pt.: 25.00 mL

Open the stopcock and watch the color in the flask. Before the end point, switch to single drops.

How do you calculate the concentration?

In a 1 : 1 neutralization (HCl + NaOH, CH₃COOH + NaOH, HCl + NH₃), at the equivalence point the moles of base equal the moles of acid:

c_a·V_a = c_b·V_b ⇒ c_a = c_b·V_bV_a

The calculation will appear here once you record the end point.

For H₂SO₄ + NaOH the ratio is 1 : 2 (H₂SO₄ + 2 NaOH → Na₂SO₄ + 2 H₂O), so c_a = c_b·V_b / (2·V_a).

Neutralization gives off heat

H₃O⁺ + OH⁻ → 2 H₂O ΔH ≈ −56 to −57 kJ/mol

A strong acid reacting with a strong base in dilute solution releases about 56–57 kJ of heat for every mole of water formed, whether it's HCl with NaOH or HNO₃ with KOH — because it's always the same reaction between ions. With a weak acid or a weak base the value is slightly different (for NH₃ about −52 kJ/mol), because part of the energy goes into dissociation.

In a flask with 25 mL of a 0.1 mol/L solution, the temperature rises by only about 0.7 °C. Concentrated solutions, however, can get very hot — which is why in the lab they are diluted carefully: always pour acid into water, never the other way round.

Water vs. buffers

Open system: breathing removes excess CO₂ (blood buffer)

Beaker (100 mL at start)	Start pH	pH now
Distilled water	7.00	7.00
Acetate bufferCH₃COOH / CH₃COONa, 0.1 mol/L each	4.74	4.74
Blood bufferCO₂ / HCO₃⁻ (1.2 / 24 mmol/L)	7.40	7.40

Add acid or base — it goes into all three beakers at once.

pH vs. amount of acid or base added

Dashed lines — the theoretical course for the chosen reagent concentration; dots — your additions. The flat part of the curve is where the buffer works.

The Henderson–Hasselbalch equation

pH = pK_a + log [A⁻][HA]

Ratio [A⁻] : [HA]1 : 1

HA = CH₃COOH · A⁻ = CH₃COO⁻

pH 4.74

The buffer that keeps us alive

The pH of arterial blood stays within a narrow range of 7.35–7.45. The most important blood buffer is the CO₂ (carbonic acid) / HCO₃⁻ (bicarbonate ion) pair: CO₂ + H₂O ⇄ H₂CO₃ ⇄ H⁺ + HCO₃⁻. With [HCO₃⁻] ≈ 24 mmol/L and dissolved CO₂ ≈ 1.2 mmol/L the ratio is 20 : 1, and pH = 6.1 + log 20 ≈ 7.4.

This buffer is exceptionally effective because it is open: within minutes the lungs remove excess CO₂, and over hours and days the kidneys excrete H⁺ ions and recover HCO₃⁻. Fast, deep breathing (hyperventilation) removes too much CO₂ and blood pH rises — that's respiratory alkalosis; breathing too shallowly causes acidosis.

Blood →Lungs →Kidneys →Liver →

Simplified model: only one buffer at a time, 25 °C for water and the acetate buffer, pK_a = 6.1 for the CO₂/HCO₃⁻ pair at 37 °C. Real blood also has protein buffers (including hemoglobin) and phosphate buffers.

Acid rain

Rain pH4.3

2 SO₂ + O₂ → 2 SO₃; SO₃ + H₂O → H₂SO₄
CaCO₃ + H₂SO₄ → CaSO₄ + H₂O + CO₂↑

Clean rain has a pH of about 5.6 because of dissolved CO₂. Sulfur and nitrogen oxides from burning coal and fuels make it more acidic. In the 1980s, air pollution and acid rain badly damaged forests in Poland, including in the Jizera and Karkonosze Mountains. Since 1990, Poland's SO₂ emissions have dropped many times over — thanks to flue-gas desulfurization and changes in industry.

Ocean acidification

Year1850 · pH ≈ 8.20

CO₂ + H₂O ⇄ H₂CO₃ ⇄ H⁺ + HCO₃⁻
H⁺ + CO₃²⁻ → HCO₃⁻

The oceans absorb about a quarter of the CO₂ we emit. Their surface pH has fallen since preindustrial times from about 8.2 to about 8.1 — that's about 25–30% more H⁺ ions. Carbonate ions, which clams, snails and corals use to build shells and skeletons, are becoming scarcer. The slider values are illustrative.

Heartburn and antacids

pH ≈ 1.5

Mg(OH)₂ + 2 HCl → MgCl₂ + 2 H₂O
CaCO₃ + 2 HCl → CaCl₂ + H₂O + CO₂↑

Stomach juice contains hydrochloric acid (pH about 1.5–3.5). When it backs up into the esophagus, it burns — that's heartburn. Tablets with magnesium or aluminum hydroxide or calcium carbonate partly neutralize it. Frequent heartburn is a sign to talk to a doctor.

Baking soda and vinegar volcano

NaHCO₃ + CH₃COOH → CH₃COONa + H₂O + CO₂↑

Baking soda (basic) and vinegar (acidic) neutralize each other, and the carbon dioxide released makes the mixture foam. A drop of dish soap gives thicker foam. It's safe — but do it on a tray.

Descaling a kettle

CaCO₃ + 2 H⁺ → Ca²⁺ + H₂O + CO₂↑

Hard water contains calcium and bicarbonate ions; when it boils, calcium carbonate precipitates out — limescale. Citric acid or vinegar dissolves it with fizzing (CO₂). After descaling, rinse the kettle well.

Soap and saponification

fat + 3 NaOH → glycerol + 3 RCOONa (soap)

Soap forms when fat is boiled with a base — that's saponification. A soap molecule has a water-loving “head” and a long fat-loving “tail”. The tails dip into a drop of grime, the heads face the water — and the drop (a micelle) can be rinsed away. Soap solution is slightly basic (pH about 9–10).

Hydrangeas: blue or pink?

Soil pH5.0

In garden hydrangeas, the color depends on the soil: in acidic soil (pH below about 5.5) the plant readily takes up aluminum ions, which combine with the anthocyanin in the petals to give a blue color. In neutral and basic soil, aluminum is hard to get, and the flowers are pink. White-flowered varieties don't change color.

Tooth enamel and sweet drinks

plaque pH ≈ 6.8

Enamel is made mostly of hydroxyapatite, which starts to dissolve below about pH 5.5. Bacteria in dental plaque turn sugars into acids, and the pH drops for tens of minutes; acidic drinks also attack directly. Saliva gradually restores the pH, and fluoride makes enamel more resistant. Time on the graph is sped up.

Three definitions of an acid

1887Arrhenius: in water an acid releases H⁺ ions (in practice H₃O⁺), and a base releases OH⁻ ions.
1923Brønsted and Lowry: an acid donates a proton, a base accepts it. Ammonia NH₃ is a base even though it has no OH groups.
1923Lewis: an acid accepts an electron pair, a base donates it — e.g. BF₃ is a Lewis acid and NH₃ a base.

Each newer definition covers more compounds; at school, the first two are used most often.

Molecules and reactions →Periodic table →Electrochemistry →

How does it work?

An acid donates a proton, a base accepts it

In water, an acid hands an H⁺ ion (a proton) to a water molecule — forming the hydronium ion H₃O⁺. A base does the opposite: it takes a proton from water and leaves an OH⁻ ion. The breakup of a substance into ions in water is called electrolytic dissociation. Strong acids (HCl, HNO₃, H₂SO₄ in its first step) and strong bases (NaOH, KOH) dissociate practically completely; weak ones (acetic acid, ammonia) only to a small extent.

pH = −log [H₃O⁺] pOH = −log [OH⁻]

K_w = [H₃O⁺]·[OH⁻] = 1.0·10⁻¹⁴ ⇒ pH + pOH = 14 at 25 °C

Dissociation constant of a weak acid

K_a = [H₃O⁺]·[A⁻][HA] [H₃O⁺] = −K_a + √(K_a² + 4·K_a·c)2

The smaller the constant K_a (the larger pK_a = −log K_a), the weaker the acid. For acetic acid K_a = 1.8·10⁻⁵, so in a 0.1 mol/L solution only about 1 in 75 molecules is dissociated, and the pH is about 2.9 instead of 1.

Neutralization and titration

H₃O⁺ + OH⁻ → 2 H₂O c_a·V_a = c_b·V_b for a 1 : 1 reaction

At the equivalence point the base has exactly neutralized the acid. The pH at this point is 7 only for a strong acid + strong base pair; the salt of a weak acid (CH₃COONa) makes the solution basic, and the salt of a weak base (NH₄Cl) makes it acidic. That's why the indicator is chosen so that it changes color within the pH jump.

Buffers

pH = pK_a + log [A⁻][HA]

A buffer is a mixture of a weak acid and its salt (or a weak base and its salt). Added acid uses up A⁻, added base uses up HA — the concentration ratio barely changes, so the pH hardly moves. A buffer works best within pK_a ± 1, until its capacity runs out.

Simplifications: we use concentrations instead of activities (in concentrated solutions the real pH differs a little), assume 25 °C and K_w = 10⁻¹⁴, and the indicator colors are approximate — real shades depend on indicator concentration and lighting.

Acids and basesa colorful pH scale

The pH scale from 0 to 14

Magnifier: how many ions?

Logarithms — a scale of powers of ten

Dissociation: strong vs. weak acid

pH calculator

Rack of indicator test tubes

Indicator colors across the pH scale

Try at home: a cabbage indicator

Titration settings

Burette and flask

Titration curve

How do you calculate the concentration?

Neutralization gives off heat

Water vs. buffers

pH vs. amount of acid or base added

The Henderson–Hasselbalch equation

The buffer that keeps us alive

Acid rain

Ocean acidification

Heartburn and antacids

Baking soda and vinegar volcano

Descaling a kettle

Soap and saponification

Hydrangeas: blue or pink?

Tooth enamel and sweet drinks

Three definitions of an acid

How does it work?

An acid donates a proton, a base accepts it

Dissociation constant of a weak acid

Neutralization and titration

Buffers

Challenges

Did you know…?

Safety

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