One of the main functions of saliva is to buffer against acid from food and plaq

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)?

Explanation / Answer

(a) H2CO3 <==> H+ + HCO3-

Ka1 = [HCO3-][H+]/[H2CO3]

with,

[H2CO3] = 1.3 mM = 0.0013 M

For low flow rates, [HCO3-] = 2 mM = 0.002 M

we get,

4.5 x 10^-7 = (0.002)[H+]/0.0013

[H+] = 2.925 x 10^-7 M

pH = -log[H+] = 6.53

For medium flow rates [HCO3-] = 30 mM = 0.03 M

4.5 x 10^-7 = (0.03)[H+]/0.0013

[H+] = 1.95 x 10^-8 M

pH = -log[H+] = 6.71

For high flow rates, [HCO3-] = 60 mM = 0.06 M

we get,

4.5 x 10^-7 = (0.06)[H+]/0.0013

[H+] = 9.75 x 10^-8 M

pH = -log[H+] = 7.01

(b) pKa = 3.86 = -logKa

Ka = 1.38 x 10^-4

lactic acid = 10^-8 moles

[lactic acid] = 10^-8/0.001 = 1 x 10^-5 M

let x amount of alctic acid has dissociated then,

Ka = 1.38 x 10^-4 = x^2/1 x 10^-5

x = [H+] = 3.71 x 10^-5 M

pH = 4.43

(c) moles of citric acid in 0.5 ml = 0.001 x 0.0005 = 5 x 10^-7 moles

molarity of citric acid in mouth = 5 x 10^-7/0.0015 = 3.33 x 10^-4 M

pKa = 3.13

Ka = 7.41 x 10^-4

let x amount of citric acid dissociated then,

7.41 x 10^-4 = x^2/3.33 x 10^-4

x = [H+] = 4.97 x 10^-4 M

pH = -log[H+] = 3.30

(d) Baking soda is added to improve the quality of toothpaste to strengthen the teeth and also helps to prevent dental cavitites.

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