E. Chemical Systems and Equilibrium · Acid-Base and Solubility EquilibriaAcid-Base and Solubility Equilibria in Our Bodies, Environment and Industry
E1.2 E3.8 E2.1 A1.9 A2.1About 70 minutes
Learning goals- I can explain how the carbonic acid-hydrogen carbonate buffer keeps blood pH within a narrow range.
- I can describe how equilibria affect hemoglobin, tooth enamel and kidney stones.
- I can assess the impact of acid-base and solubility equilibria on lakes, oceans and the treatment of contaminated water.
- I can use calculations from this unit to support an argument about an environmental or technological issue.
Words to know
acidosis / alkalosis
Conditions in which blood pH falls below about 7.35 (acidosis) or rises above about 7.45 (alkalosis).
ocean acidification
The decrease in ocean pH caused by the ocean absorbing CO₂ from the atmosphere.
buffering capacity of a lake
The ability of a lake's water and surrounding rock and soil to neutralize added acid, mainly through carbonate and hydrogen carbonate ions.
hydroxyapatite
Ca₅(PO₄)₃OH, the slightly soluble mineral that makes up most of tooth enamel.
remediation
Cleaning up contaminated water or soil, for example by precipitating dissolved metal ions as insoluble solids.
Equilibrium is everywhere
Right now your blood is holding its pH between about 7.35 and 7.45 while your muscles make acid and your lungs breathe out CO₂. The ocean is absorbing about a quarter of the CO₂ that people release into the air each year. In Northern Ontario, many lakes near Sudbury that were damaged by acid rain have been recovering since smelter emissions were cut. All of these depend on the equilibria from this unit: Ka, buffers, Ksp and Le Châtelier's principle. In Equilibrium in Living Things, the Environment and Technology (unit Chemical Equilibrium) you explained several of these systems qualitatively with Le Châtelier's principle. This lesson adds the numbers from this unit (pH, buffer ratios and Ksp) and is about assessing their impact: using chemistry to explain real systems and to judge claims and decisions about them.
1. The blood buffer
The main buffer in blood plasma is the carbonic acid-hydrogen carbonate system:
CO₂(aq) + H₂O(l) ⇌ H₂CO₃(aq) ⇌ H⁺(aq) + HCO₃⁻(aq)
At body temperature, with dissolved CO₂ counted as the acid, the effective pKa is about 6.1. Normal blood has [HCO₃⁻] ≈ 24 mmol/L and dissolved CO₂ ≈ 1.2 mmol/L, a ratio of 20 : 1:
pH = 6.1 + log(24 ÷ 1.2) = 6.1 + log 20 = 7.4
That pH is more than one unit above pKa, so on paper this is a lopsided buffer. It works so well because the body controls both partners: the lungs remove CO₂ (within minutes) and the kidneys adjust HCO₃⁻ and excrete H⁺ (over hours to days). When exercise floods the blood with acid, the HCO₃⁻ absorbs it, and faster breathing removes the extra CO₂, shifting the equilibria to the left.
If breathing is too slow (for example during some lung diseases), CO₂ builds up, the equilibria shift right and pH falls (respiratory acidosis). Breathing too fast (hyperventilating) removes too much CO₂, and pH rises (respiratory alkalosis). Phosphate (H₂PO₄⁻/HPO₄²⁻) and proteins act as buffers too, especially inside cells.
The blood buffer is an open system. The lungs control the CO₂ end of the equilibrium and the kidneys control the HCO₃⁻ end.Worked exampleExample 1: When CO₂ builds up
A patient's breathing slows, and dissolved CO₂ in the blood rises from 1.2 to 1.8 mmol/L while [HCO₃⁻] stays at 24 mmol/L. Estimate the new blood pH (pKa = 6.1). Is the patient in acidosis?
- pH = pKa + log([HCO₃⁻] ÷ [CO₂]) = 6.1 + log(24 ÷ 1.8).
- 24 ÷ 1.8 = 13.3; log 13.3 = 1.12.
- pH = 6.1 + 1.12 = 7.22.
pH ≈ 7.2, below 7.35: respiratory acidosis. Respiratory therapists and physicians measure exactly these values ("blood gases") to diagnose breathing problems.
2. Hemoglobin, teeth and kidney stones
Hemoglobin (recap). You studied Hb + O₂ ⇌ HbO₂, altitude and carbon monoxide in Equilibrium in Living Things, the Environment and Technology. The acid-base link is new here: muscles produce CO₂ and H⁺, and a lower pH makes hemoglobin release O₂ more readily (the Bohr effect), so oxygen goes where it is needed most. The blood buffer above keeps that pH change small everywhere else.
Tooth enamel. As you saw in Chemical Equilibrium, enamel is mostly hydroxyapatite:
Ca₅(PO₄)₃OH(s) ⇌ 5 Ca²⁺(aq) + 3 PO₄³⁻(aq) + OH⁻(aq)
When bacteria in plaque ferment sugars, they make acids. H₃O⁺ removes OH⁻ and PO₄³⁻ (both are bases), so the equilibrium shifts right and enamel dissolves (demineralization). Saliva, a buffer containing HCO₃⁻ and phosphate, raises the pH again so minerals can re-deposit. Fluoride replaces OH⁻ to form fluorapatite, Ca₅(PO₄)₃F, which is less soluble in acid; F⁻ is a much weaker base than OH⁻.
Kidney stones. The most common kind is calcium oxalate (Ksp ≈ 2.3 × 10⁻⁹). When urine becomes concentrated (for example with too little water intake), the ion product of Ca²⁺ and oxalate can exceed Ksp, and crystals can form and grow. Drinking more water lowers both concentrations, and therefore Q.
3. Lakes, acid rain and the Canadian Shield
Burning fossil fuels and smelting sulfide ores release SO₂ and NOₓ, which form sulfuric and nitric acids in the atmosphere. Normal rain has a pH of about 5.6 (from dissolved CO₂); acid rain is lower.
What happens next depends on buffering capacity. Lakes in areas with limestone (CaCO₃) contain plenty of HCO₃⁻ and CO₃²⁻, which neutralize added acid. Many lakes on the Canadian Shield, which covers much of Northern Ontario, sit on granite and other rocks that dissolve very little, so they have little HCO₃⁻ and are easily acidified. As the pH of a lake falls, fish and other organisms are harmed, and aluminium leached from soil (its compounds are more soluble in acid) adds to the damage.
Around Sudbury, decades of smelter emissions acidified many lakes and damaged the surrounding land. In 1960 the Sudbury smelters were the largest single source of sulfur emissions in the world, and an estimated 7000 lakes in the region were damaged by acid. Since then, SO₂ and metal emissions have been cut by more than 90 % (through smelter controls such as acid plants and process changes), and many lakes have recovered chemically, with fish such as lake trout returning. Recovery is not complete: calcium loss from soils, climate change and other stresses slow it in some lakes. The Sudbury regreening program spread crushed limestone on acidic, barren soils so that plants could grow again: an acid-base reaction (CaCO₃ + 2 H₃O⁺ → Ca²⁺ + CO₂ + 3 H₂O) used on a landscape scale.
4. Ocean acidification
The ocean absorbs CO₂, which forms carbonic acid. The average pH of surface seawater has dropped from about 8.2 before industrialization to about 8.05 today (8.04 in 2024), often rounded to "about 8.1". That sounds small, but it is a logarithmic scale: [H₃O⁺] has risen by about 30%. In 2025, scientists assessing Earth's "planetary boundaries" reported that ocean acidification has moved past its proposed safe limit. The extra H⁺ combines with carbonate ions, lowering [CO₃²⁻]. Corals, oysters, mussels, pteropods and many plankton build shells and skeletons of CaCO₃, which becomes harder to build and easier to dissolve when [CO₃²⁻] falls.
How CO₂ from the air lowers ocean pH and removes the carbonate ions that shell-building organisms need. Each step is an equilibrium you have studied in this unit.5. Cleaning up water with Ksp
Acid mine drainage forms when sulfide minerals exposed by mining react with air and water, making acidic water rich in dissolved metal ions. A common treatment is to add lime (Ca(OH)₂ or CaO). Raising the pH neutralizes the acid and pushes Q above Ksp for metal hydroxides such as Fe(OH)₃ and Cu(OH)₂, so the metals precipitate and can be settled out as sludge. Treatment plants choose the pH carefully, because each metal hydroxide precipitates over a different pH range (and some, such as aluminium hydroxide, redissolve if the pH goes too high).
Other examples from industry and medicine:
- Water softening: hard water contains Ca²⁺ and Mg²⁺. Adding lime and sodium carbonate precipitates CaCO₃ and Mg(OH)₂.
- Medical imaging: BaSO₄ is so slightly soluble that a patient can drink a suspension of it before an X-ray; very little toxic Ba²⁺ dissolves.
- Swimming pools: operators keep pH near 7.2 to 7.8, using buffers and acids or bases, so that chlorine disinfects well and CaCO₃ scale does not form.
Careers that use this unit: respiratory therapist, nurse, physician, dentist and dental hygienist, pharmacist, water and wastewater treatment operator, environmental technologist, chemical engineer, mining engineer, oceanographer and food scientist.
Worked exampleExample 2: How much limestone for a lake?
A small Canadian Shield lake holds 1.0 × 10⁹ L of water at pH 4.5. Estimate the mass of CaCO₃ needed to raise it to pH 6.5, considering only the H₃O⁺ already in the water. CaCO₃ + 2 H₃O⁺ → Ca²⁺ + CO₂ + 3 H₂O.
- [H₃O⁺] at pH 4.5 = 3.16 × 10⁻⁵ mol/L; at pH 6.5 = 3.2 × 10⁻⁷ mol/L.
- H₃O⁺ to remove = 3.16 × 10⁻⁵ − 0.03 × 10⁻⁵ = 3.13 × 10⁻⁵ mol/L.
- Total moles = 3.13 × 10⁻⁵ × 1.0 × 10⁹ = 3.1 × 10⁴ mol of H₃O⁺.
- n(CaCO₃) = 3.1 × 10⁴ ÷ 2 = 1.57 × 10⁴ mol; mass = 1.57 × 10⁴ × 100.09 g = 1.6 × 10⁶ g.
About 1.6 tonnes of CaCO₃ as a minimum. In practice much more is needed, because acid keeps arriving in rain and runoff and acidic soils around the lake also consume it: liming treats the symptom, while cutting emissions treats the cause.
Worked exampleExample 3: Removing copper from mine water
Mine water is treated with lime until the pH is 8.0. What is the highest concentration of Cu²⁺ that can remain dissolved? (Ksp of Cu(OH)₂ = 2.2 × 10⁻²⁰; M(Cu) = 63.55 g/mol)
- At pH 8.0, pOH = 6.0, so [OH⁻] = 1.0 × 10⁻⁶ mol/L.
- At saturation, [Cu²⁺] = Ksp ÷ [OH⁻]² = 2.2 × 10⁻²⁰ ÷ (1.0 × 10⁻⁶)² = 2.2 × 10⁻⁸ mol/L.
- In mass: 2.2 × 10⁻⁸ × 63.55 = 1.4 × 10⁻⁶ g/L = 1.4 µg/L.
At most about 2.2 × 10⁻⁸ mol/L (1.4 µg/L) of copper stays dissolved. (Real values can be higher, because some Cu²⁺ forms soluble complexes; operators check with lab tests.)
Just for funBefore some X-rays, patients drink a chalky "barium milkshake" of BaSO₄. It doesn't win any taste awards, but thanks to a Ksp of about 1 × 10⁻¹⁰, almost none of the barium dissolves, so the drink is safe and the X-ray picture comes out sharp.
Hands-on activityBreath, buffers and shells: a kitchen model of ocean acidification
You need: red cabbage indicator, 2 clear glasses, a drinking straw for each person, baking soda, white vinegar, and a clean eggshell (or a piece of white chalk, which is often calcium carbonate or calcium sulfate; eggshell works better).
Grown-up note: supervise the indicator preparation (knife, hot water). When using the straw, blow out only, never sip, and use a fresh straw for each person.
- Glass A: ½ cup of water + 3 tablespoons of indicator. Glass B: the same, plus a small pinch of baking soda (it should turn bluish).
- Blow gently through a straw into glass A for 1 to 2 minutes. Watch the colour. Then do the same for glass B and compare.
- Explain: CO₂ from your breath forms carbonic acid in the water. Which glass is like a poorly buffered Canadian Shield lake, and which is like the ocean or a limestone lake?
- Put a piece of eggshell in a small glass of vinegar and watch it for a few minutes, then leave it overnight. Write the equation for the reaction. (Vinegar is far more acidic than seawater, so this exaggerates the effect: it shows the direction of the change, not its speed in the ocean.)
What to look for: glass A slowly shifts from purple toward pink-purple as CO₂ dissolves. Glass B stays bluish much longer, because HCO₃⁻ absorbs the acid (its buffering capacity). The eggshell fizzes: CaCO₃(s) + 2 CH₃COOH(aq) → Ca²⁺(aq) + 2 CH₃COO⁻(aq) + H₂O(l) + CO₂(g), and becomes thin and soft. Acid shifts the CaCO₃ dissolving equilibrium to the right by removing CO₃²⁻.
Your turn
1Write the equilibria that make up the blood's main buffer system.
CO₂(aq) + H₂O(l) ⇌ H₂CO₃(aq) ⇌ H⁺(aq) + HCO₃⁻(aq).
2During hard exercise, lactic acid enters the blood. Explain how the blood buffer and the lungs respond.
HCO₃⁻ reacts with the extra H⁺ to form H₂CO₃, which breaks down to CO₂ and water (the equilibria shift left). Breathing speeds up to remove the extra CO₂, so the pH changes very little.
3Find the blood pH if [HCO₃⁻] = 24 mmol/L and dissolved CO₂ = 0.80 mmol/L (pKa 6.1). What condition is this?
pH = 6.1 + log(24 ÷ 0.80) = 6.1 + log 30 = 6.1 + 1.48 = 7.58: above 7.45, so alkalosis (for example from hyperventilating).
4Explain, using Le Châtelier's principle, why acids produced by plaque bacteria damage tooth enamel.
Ca₅(PO₄)₃OH(s) ⇌ 5 Ca²⁺ + 3 PO₄³⁻ + OH⁻. Acid removes OH⁻ (forming water) and converts PO₄³⁻ to HPO₄²⁻. Removing products shifts the equilibrium right, so more enamel dissolves.
5Why are many lakes on the Canadian Shield more harmed by acid rain than lakes in limestone areas?
Limestone (CaCO₃) supplies CO₃²⁻ and HCO₃⁻ that neutralize added acid (high buffering capacity). The granite of the Canadian Shield dissolves very little, so those lakes have little buffering capacity, and their pH drops.
6Ocean surface pH fell from about 8.2 to about 8.1. By what factor did [H₃O⁺] increase?
10^(8.2 − 8.1) = 10⁰·¹ = 1.26, an increase of about 26%.
More practice: warm-up
1What is the normal pH range of human blood?
2Which organ removes CO₂ from the blood?
3What mineral is tooth enamel mostly made of?
Hydroxyapatite, Ca₅(PO₄)₃OH.
4Name one substance added to acidic lakes or soils to neutralize them.
Limestone (calcium carbonate), or lime.
5Why is BaSO₄ safe to drink for X-rays, even though Ba²⁺ is toxic?
Its Ksp is so small that very little Ba²⁺ dissolves.
More practice: on your own
1Explain the Bohr effect in terms of equilibrium, and why it is useful.
In active muscle, CO₂ and H⁺ levels are higher (lower pH). This lowers hemoglobin's affinity for O₂, so the equilibrium Hb + O₂ ⇌ HbO₂ shifts left and more O₂ is released where it is needed most.
2A home has a gas furnace. Use equilibrium ideas to explain why a carbon monoxide alarm is important.
CO binds to hemoglobin more than 200 times as strongly as O₂, so even a small amount of CO ties up hemoglobin and shifts the oxygen equilibrium away from HbO₂. The blood carries less oxygen, and because CO has no smell, an alarm is the only warning.
3Explain why fluoride makes enamel more resistant to acid.
Fluorapatite, Ca₅(PO₄)₃F, forms when F⁻ replaces OH⁻. F⁻ is a much weaker base than OH⁻ (HF has Ka 6.6 × 10⁻⁴), so acid does not remove it as easily, and the mineral is less soluble in acidic conditions.
4Mine water at pH 3 contains dissolved Fe³⁺. Use Ksp to explain why adding lime removes the iron.
Lime raises [OH⁻]. Because Fe(OH)₃ has an extremely small Ksp (2.8 × 10⁻³⁹), Q = [Fe³⁺][OH⁻]³ soon exceeds Ksp as the pH rises, so Fe(OH)₃ precipitates and can be settled out.
5A student claims that "a drop of 0.1 in ocean pH is too small to matter." Evaluate the claim using chemistry from this unit.
pH is logarithmic: a 0.1 drop means about 26% more H₃O⁺. The extra H⁺ converts CO₃²⁻ to HCO₃⁻, lowering [CO₃²⁻] and therefore the ion product for CaCO₃. Shell-building organisms need CO₃²⁻, so even this change makes building shells harder. The claim ignores the log scale and the carbonate equilibria.
Challenge
1Why does the blood buffer work so well even though its pKa (6.1) is more than one unit below blood pH (7.4)?
In a closed beaker, a 20 : 1 buffer would have little capacity against added base. But blood is an open system: the lungs can quickly change the CO₂ (acid) level and the kidneys can change the HCO₃⁻ level, so the body adjusts both partners and keeps the ratio near 20 : 1. Because the lungs remove the CO₂ formed, HCO₃⁻ can absorb a lot of acid.
2Use Ksp (2.3 × 10⁻⁹) to find the largest [C₂O₄²⁻] that can stay dissolved in a solution with [Ca²⁺] = 2.5 × 10⁻³ mol/L. Explain how drinking more water helps prevent calcium oxalate stones.
[C₂O₄²⁻] = 2.3 × 10⁻⁹ ÷ 2.5 × 10⁻³ = 9.2 × 10⁻⁷ mol/L. More water dilutes both ions; diluting each by half lowers Q by a factor of 4, which keeps Q below Ksp. (Real urine contains other substances that slow crystal growth, so stones are more complicated than this model.)
3Write a short argument (4 to 6 sentences) assessing whether liming is a good long-term solution for acidified lakes. Use at least two calculations or equilibria from this unit.
Model answer: Liming works chemically: CaCO₃ + 2 H₃O⁺ → Ca²⁺ + CO₂ + 3 H₂O neutralizes acid, and the HCO₃⁻ formed adds buffering capacity. Example 2 shows that even a small lake needs at least 1.6 t of CaCO₃ just to neutralize the acid already in it, and acid rain keeps adding more, so liming must be repeated. Because Canadian Shield rocks supply little natural carbonate, the lake cannot rebuild its own buffer. Liming therefore treats symptoms; the long-term solution is to cut SO₂ and NOₓ emissions, as the recovery of Sudbury-area lakes after emission cuts shows. Liming is still useful as a short-term measure to protect fish in sensitive lakes. (Look for correct chemistry, at least two pieces of quantitative or equilibrium evidence, and a clear judgment.)
Check your understandingQuiz
1. What happens to blood pH if a person hyperventilates (breathes too fast)?
2. Why are lakes in limestone regions less affected by acid rain?
3. How does fluoride protect teeth?
4. How does adding lime to acid mine drainage remove dissolved metals?
5. Ocean acidification makes it harder for oysters to build shells mainly because
6. A blood sample has [HCO₃⁻] = 24 mmol/L and dissolved CO₂ = 1.2 mmol/L (pKa 6.1). What is its pH?
For parents and teachersBig idea (E1.2): the equilibria in this unit control real systems. The CO₂/HCO₃⁻ buffer, managed by the lungs and kidneys, keeps blood pH near 7.4. Acid shifts the solubility equilibria of tooth enamel and shells. Buffering capacity decides how much acid rain harms a lake, and Ksp lets engineers remove toxic metals from water.
How to help: Discuss a current news story about acid rain recovery, ocean acidification or water treatment, and ask your teen to explain the chemistry behind it using one equation from this unit. The breath activity is safe and quick; make sure everyone blows out (never sips) and uses their own straw. The Challenge argument question is like an exam essay question; look for chemistry evidence and a clear judgment.
Common difficulties:
- Treating the blood buffer like a closed beaker and forgetting the lungs and kidneys.
- Underestimating small pH changes: 0.1 pH unit is about a 26% change in [H₃O⁺].
- Thinking liming cures acidification permanently; the acid source must also be reduced.
- Mixing up which ion is removed by acid (OH⁻, CO₃²⁻ and PO₄³⁻ are bases; Cl⁻ is not).