Acid-Base Chemistry in Tooth Decay

Learning Objectives

This Exemplar will teach the following concepts from the ACS Examinations Institute General Chemistry ACCM:

• V. A. 1. b. Predicting the reactivity of chemicals is a key skill that ultimately involves the ability to write a balanced chemical equation.

• VIII. C. 2. a. Dissolving of solids in water provides an example of equilibrium systems, for which quantitative understanding via Ksp can be derived.

• VIII. E. 1. a. The ability to predict the direction a reaction will progress for a given perturbation is a key concept.

• VIII. G. 1. a. Acid-base chemistry, particularly in water, forms an important example of equilibrium systems. Conceptual and quantitative understanding of this form of equilibrium system is important.

As a child, you probably heard your parents warn you not to eat too much candy about a million times. And when you asked why, they said it was because it would supposedly lead to cavities. Despite how annoying you may find this statement to be, it is rooted in the truth! Today, we will explore the fascinating chemistry behind tooth decay – you will get to see food and acid-base chemistry in action!

What are our teeth made of?

The outside of your tooth is called the enamel, composed of mostly calcium and phosphate ions. These ions combine to form hydroxyapatite (Ca₅(PO₄)₃) crystals, which form the hard enamel. Underneath the enamel is a softer (but still hard!) tissue called dentin, composed of fewer minerals than enamel.¹ Dentin is the more susceptible tissue to cavities. Lastly, the innermost layer of the tooth is known as the pulp, which consists of blood vessels, nerves, and connective tissue.²

Figure 1. A basic diagram showing the three key layers of the tooth: enamel, dentin, and pulp.
Source: American Dental Association.²

How does tooth decay actually happen?

Plaque, made of bacteria, sticks to your teeth. As the bacteria live and grow, they produce lactic acid, lowering the pH of your teeth. This acidic environment is what causes your teeth to demineralize or decay. Eating sugary foods contributes to tooth decay because the bacteria feed on the sugar and thus produce more lactic acid. Similarly, consuming acidic drinks such as soda and fruit juice will directly lower the pH of your teeth, advancing the decay process. In fact, most beverages available on the market have a pH lower than 4!³

Figure 2. Many of our favorite drinks are quite acidic. To name a few: apple juice (pH = 3.3), Coca-Cola (pH = 2.5), and lemonade (pH = 2.0, ouch!).
Source: Lincoln Park Smiles.⁴

The example problem below provides more detail on the chemical basis for this manner of decay. Try it out!

Example 1: Acid-Base Equilibrium in Tooth Decay

Problem

The outer covering of our teeth is called enamel, and it is composed mostly of hydroxyapatite (Ca₁₀(PO₄)₆(OH)₂). Equation i describes the solubility of hydroxyapatite.⁵

(i) Ca₁₀(PO₄)₆(OH)_{2 (s)} ⇌ 10Ca²⁺ _(aq) + 6PO₄^3– _(aq) + 2OH^– _(aq)

Given this equilibrium equation, explain why acidic drinks like soda might contribute to greater tooth decay.

Solution

Drinking more acidic beverages translates to reacting hydroxyapatite with acid (H⁺). PO₄^3– and OH^– both act as bases, meaning that they are neutralized by the acid. First, we write out equations representing the neutralization reaction of each base.¹

(ii) PO₄^3– _(aq) + H₃O⁺ _(aq) → HPO₄^2– _(aq) + H₂O _(l)

(iii) OH^– _(aq) + H₃O⁺ _(aq) → 2H₂O _(l)

These neutralization reactions decrease the concentration of PO₄^3– and OH^– on the products side of Equation i. Essentially, as more and more PO₄^3– and OH^– are consumed in neutralization reactions with H₃O⁺, the less PO₄^3– and OH^– there is available in the system. We can then apply Le Chatelier’s principle to predict how this change would affect the system: according to the principle, when the equilibrium is disturbed, the system shifts the equilibrium to counteract that change. In our case, the equilibrium would shift to the right to compensate for the decrease in PO₄^3– and OH^–. The forward reaction is favored, and more hydroxyapatite is broken down. In the end, the addition of more acid leads to more dissociation of enamel. This weakens our teeth overall, making them more vulnerable to cavities.

How can we combat tooth decay?

There are a number of preventative measures we can take to fight tooth decay. Just like your dentist recommends, consistent brushing and flossing help rid your teeth of plaque, which will reduce the amount of lactic acid produced. Fluoride, commonly found in toothpaste, mouthwash, and even the water we drink, helps strengthen the enamel layer. Specifically, the fluoride ions form fluorapatite (Ca₅(PO₄)₃F), a compound that is less soluble than hydroxyapatite.⁶ See the example problem below to learn just how strong fluorapatite is!

Example 2: Solubility of Fluorapatite

Problem

If the K_sp of fluorapatite is 1.0 x 10^-60 at 25°C,⁷ what is its solubility in water at 25°C?

Solution

First, let’s write the equation for the solubility of fluorapatite:

Ca₅(PO₄)₃F _(s) ⇌ 5Ca²⁺ _(aq) + 3PO₄^3– _(aq) + F^– _(aq)

Using this equation, we can write out the solubility product (K_sp). Remember, we do not include any liquids or solids in our equilibrium constants:

K_sp = [Ca²⁺]⁵ • [PO₄^3–]³ • [F^–]

Next, we can set up an “ICE” table to show the dissociation of fluorapatite into its ions.

	Ca5(PO4)3F	⇌	5Ca2^+	3PO4^3^–	F^–
Initial	-		0	0	0
Change	-		+5x	+3x	+x
Equilibrium	-		5x	3x	x

Substituting the equilibrium concentrations into the K_sp expression, we have:

K_sp = (5x)⁵ • (3x)³ • (x) = 84375x⁹

Since we are given the value of K_sp (1.0 x 10^-60), we can set this expression equal to that value and solve for x.

1.0 x 10^-60 = 84375x⁹

x = 6.1 x 10^-8

So, the molar solubility of fluorapatite is 6.1 x 10^-8 M. To convert this to solubility in terms of g/L, we can multiply molar solubility by the molar mass of fluorapatite (504.3 g/mol).

\[\frac{6.11 \times {10^{-8}} mol}{1L} \times \dfrac{504.3 g}{1 mol} = 3.1 \times {10^{-5}} \frac{g}{L} \nonumber\]

We got it! The solubility of fluorapatite in water at 25°C is 3.1 x 10^-5 g/L. Now we can see why fluorapatite is so resistant to being broken down, and why we should incorporate fluoride into our dental hygiene!

Finally, just as your parents said, reducing your overall sugar intake will decrease the amount of sugar available for bacteria to feed on and grow. The next time you find yourself sipping on a soda or sinking your teeth in a candy bar, just remember – floss, brush, and rinse!

References

1. Solubility and pH. ChemPages Netorials. https://www2.chem.wisc.edu/deptfiles...alts/salt4.htm (accessed 2022-11-10).

2. American Dental Association. Parts of the Tooth. https://www.youtube.com/watch?v=-cR0mZ4XGkk (accessed 2022-11-10).

3. Reddy, A.; Norris, D. F.; Momeni, S. S.; Waldo, B.; Ruby, J. D. The PH of Beverages Available to the American Consumer. J Am Dent Assoc 2016, 147 (4), 255–263. https://doi.org/10.1016/j.adaj.2015.10.019.

4. Lincoln Park Smiles. The Dangers of Acidity in Beverages. https://www.lincolnparksmiles.com/th...-in-beverages/ (accessed 2022-11-10).

5. Dawes, C. What Is the Critical PH and Why Does a Tooth Dissolve in Acid? J Can Dent Assoc 2003, 69 (11), 722–724.

6. Fluoride’s Mechanism of Action. dentalcare.com. https://www.dentalcare.com/en-us/ce-...nism-of-action (accessed 2022-11-10).

7. Wei, C.; Zhu, Y.; Yang, F. Dissolution and Solubility of Hydroxylapatite and Fluorapatite at 25°C at Different PH. Res J Chem Environ 2003, 17 (11).

Further Reading

1. Stopping tooth decay before it starts — without killing bacteria. American Chemical Society. https://www.acs.org/content/acs/en/p...-bacteria.html (accessed 2022-11-10).

2. Ophardt, C. Virtual Chembook. http://chemistry.elmhurst.edu/vchemb...oothdecay.html (accessed 2022-11-10).

3. Uva, E. Chem 13 News Magazine. https://uwaterloo.ca/chem13-news-mag...ces-and-habits (accessed 2022-11-10).