echoesof.science · Ages 15–16
The chemistry of tooth decay
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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).
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.
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.
Experiment: Does fluoride toothpaste protect an eggshell from acid?
- 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?
| Piece | Treatment | m₁ (g) | m₂ (g) | Mass loss (%) |
|---|---|---|---|---|
| 1 | Predict: which group will lose the larger percentage of mass? | |||
| 2 | Predict: which group will lose the larger percentage of mass? | |||
| 3 | Predict: which group will lose the larger percentage of mass? | |||
| 4 | Predict: which group will lose the larger percentage of mass? | |||
| 5 | Predict: which group will lose the larger percentage of mass? | |||
| 6 | Predict: which group will lose the larger percentage of mass? |
Questions
Write the dissolving equilibrium for hydroxyapatite and use Le Châtelier's principle to explain why a fall in pH increases demineralisation.
Calculate how many times more acidic (in [H₃O⁺]) vinegar at pH 2.4 is than a drink at pH 5.4.
A shell piece goes from m₁ = 1.84 g to m₂ = 1.52 g. Calculate the percentage mass loss. If the balance reads to ±0.01 g, is the uncertainty in the mass loss important?
Give two reasons why an eggshell is only a limited model of tooth enamel.
Sources for every fact on this sheet: echoesof.science/school/teeth/sources/