Question

One of the main functions of saliva is to buffer against acid from food and plaque, which contributes significantly to the formation of cavities. While there are several buffers in saliva, carbonic acid (H2CO3) has the highest concentration and has the greatest effect on pH.

(a) While the salivary concentration of carbonic acid stays at a fairly constant 1.3 mM, the level of bicarbonate (HCO3-) can vary with the rate that saliva flows from salivary glands. For low flow rates, the bicarbonate concentration is around 2 mM; for medium flow rates, it is 30 mM; and for high flow rates, around 60 mM. The pKa of carbonic acid at body temperature is 6.1. Assuming that the pH of Saliva is determined primarily by carbonic acid and bicarbonate, determine the pH of saliva for each of the three flow rates. The normal pH of saliva is about 6.3.

(b) The most prevalent bacterium in the mouth, streptococcus mutans, breaks down sugar and releases lactic acid (pKa = 3.86). If S. mutans has produced 10^-8 moles of lactic acid since your last swallow, what is the pH of your saliva? What would the pH be without the bicarbonate buffer? Assume that your mouth contains about 1 mL of saliva and that your saliva is flowing at a low rate.

(c) You take a drink of orange juice, and after you swallow, 0.5 mL remains in your mouth. What is the pH of your saliva if your mouth contains 1 mL of pure saliva, and if you model orange juice as 1.0 mM citric acid (pKa = 3.13; assume only one dissociation).

(d) Why do some toothpastes contain baking soda (sodium bicarbonate)?

Answer 1

(a) H₂CO₃ HCO₃^- + H⁺

Henderson–Hasselbalch equation

pH = pKa + log (A^-]/[HA]

pKa of carbonic acid at body temperature is 6.1

salivary concentration of carbonic acid stays at a fairly constant 1.3 mM

For low flow rates, the bicarbonate concentration is around 2 mM

pH = 6.1 + log [2 x 10^-3]/[1.3 x 10^-3]

pH = 6.1 + 0.187

pH = 6.287

for medium flow rates, it is 30 mM

pH = 6.1 + log [30 x 10^-3]/[1.3 x 10^-3]

pH = 6.1 + 1.36

pH = 7.46

high flow rates, around 60 mM

pH = 6.1 + log [60 x 10^-3]/[1.3 x 10^-3]

pH= 6.1 + 1.66

pH= 7.76

(b) lactic acid (pKa = 3.86)

C₃H₆O₃ C₃H₅O₃^- + H⁺

Ka = [C₃H₅O₃^-] [H⁺]/[C₃H₆O₃] = 10^-3.86 = 1.38 x 10^-4

Lactic acid produced = 10^-8 moles in 1 mL of saliva concentration is 10^-5M

at equilibrium if x M H⁺ is formed simultaneously x M C₃H₅O₃^- is also formed

1.38 x 10^-4 = x²/(10^-5-x) since x is small

1.38 x 10^-4 x 10^-5 = x²

x= [H⁺]= 3.71 x 10^-5

pH = -log [H+]

pH = -log (3.71 x 10^-5)

pH = 4.43 This is would be the pH of the saliva in the absence of Saliva with the lactic acid formed

In the presence of saliva the Base concentration is 2 mM at low flow rate this reacts with the lactic acid to get reduced 2 x 10-3 - 1 x10-5 = 1.99mM

pH in saliva will be

pH = 6.1 + log [1.99 x 10^-3]/[1.3 x 10^-3]

pH = 6.1 + 0.185

pH = 6.285

c) citric acid (pKa = 3.13)

C₆H₈O₇ C₆H₇O₇^- + H⁺

Ka = [C₆H₇O₇^-] [H⁺]/[C₆H₈O₇] = 10^-3.13 = 7.41 x 10^-4

1mM citric acid

at equilibrium if x M H⁺ is formed simultaneously x M C₆H₇O₇^- is also formed

7.41 x 10^-4 = x²/(1 x 10^-3-x) since x is small

7.41 x 10^-4 x 10^-3 = x²

x = [H⁺] = 8.61 x 10^-4

In the presence of saliva the Base concentration is 2 mM at low flow rate this reacts with the citric acid to get reduced 2 x 10^-3 - 8.61 x 10^-4 = 1.14mM

pH in saliva will be

pH = 6.1 + log [1.14 x 10^-3]/[1.3 x 10^-3]

pH = 6.1 - 0.057

pH = 6.04

d) Your enamel is made of calcium phosphate. This is sensitive to acid as it would dissolve in contact with it. One of the main functions of saliva is to buffer against acid from food and plaque, which contributes significantly to the formation of cavities. Toothpaste contains weak bases to neutralise the acids or sugar acids formed from our food so that it does not attache our teeth and enamel.