The chemistry of tooth decay
Hydroxyapatite, pH and the critical pH, Le Châtelier's principle, fluoroapatite and parts per million. With a quantitative eggshell investigation.
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Enamel contains calcium hydroxyapatite, Ca10(PO4)6(OH)2. In water it sets up an equilibrium: Ca10(PO4)6(OH)2(s) ⇄ 10 Ca2+(aq) + 6 PO43−(aq) + 2 OH−(aq).[7]
Acidity is measured with pH = −log[H3O+]. At 25 °C a neutral solution has pH 7 and acids have pH below 7. Because the scale is logarithmic, one pH unit is a factor of 10 in [H3O+]; vinegar is about pH 2.4.[8]
Acid removes OH− ions and lowers the phosphate concentration. By Le Châtelier's principle the equilibrium shifts to the right and more hydroxyapatite dissolves: this is demineralisation.[7]
The critical pH is the pH at which saliva is just saturated with an enamel mineral; below it, enamel tends to dissolve. It is about 5.5, but it is not a fixed value and varies between people.[7]
The acid comes from bacteria in plaque that use sugars. Enamel loses minerals during each attack and regains them from saliva and fluoride afterwards; frequent snacks mean more attacks, and repeated attacks lead to a cavity.[2][3]
Fluoride combines with the outer enamel. Fluoroapatite is less soluble in acid than hydroxyapatite and lowers the critical pH, making teeth tougher; fluoride also slows the bacteria.[7][6][10]
Toothpaste strength is given in parts per million (ppm) of fluoride. The NHS advises 1,350–1,500 ppm for ages 7 and over. 1,450 ppm means 1,450 mg of fluoride per kg of toothpaste, which is 1.45 mg per gram.[1]
Try it: Does fluoride toothpaste protect an eggshell from acid?
You need
- Eggshell pieces from cleaned, dried eggshells (about 2 cm × 2 cm, 6–10 pieces)
- Fluoride toothpaste (check the ppm on the tube)
- White vinegar (about 4–5% acetic acid)
- Beakers or labelled cups
- Top-pan balance (0.01 g)
- Tweezers, paper towels, timer
- Safety glasses
Safety
Wear safety glasses: vinegar irritates eyes. Wash hands after handling eggshell (raw egg can carry bacteria); use shells that were washed and dried, or boiled. Do not taste anything. Wipe up spills. Check for egg allergies.
What to do
- Dry the shell pieces and weigh each one (m₁). Record the balance resolution as part of your uncertainty.
- Coat half the pieces in a thin layer of fluoride toothpaste and leave them for a fixed time (for example 30 min or overnight); leave the other half untreated as controls. Rinse all pieces gently and dry them.
- Put each piece into the same volume of vinegar for the same time (for example 30 min). Note when bubbles appear.
- Remove, rinse, dry fully (for example overnight) and reweigh (m₂). Calculate the percentage mass loss = (m₁ − m₂) / m₁ × 100.
- Find the mean and range for each group. Do the ranges overlap? Is the difference larger than your uncertainty? Evaluate the model: in what ways is an eggshell not like enamel?
What happens, and why?
Carbonates react with acids to give a salt, carbon dioxide and water (CaCO₃ + 2HCl → CaCl₂ + CO₂ + H₂O; acetic acid reacts in the same way), so the shell loses mass as CO₂ bubbles away and calcium ions go into solution. In a similar classroom test, a fluoride-treated egg reacted little or not at all. Fluoride displaces OH groups at the surface and makes it less reactive. But an eggshell is calcium carbonate, not hydroxyapatite, so the test models the idea, not real teeth.[9][10][11]
Play: Losing or gaining mineral?
Does each event push the enamel towards losing mineral (demineralisation) or towards keeping and regaining it (remineralisation)?
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Quiz
Other ages: Ages 6–7 · Ages 10–11