H⁺ + OH^–

Solutions with a pH lower than 7 are acidic; those with a pH more than 7 are basic. A solution of a strong acid, such as hydrochloric acid, has a pH of 0; a solution of a strong base (alkali), such as sodium hydroxide, has a pH of 14. (Note: Molar concentration of acids is used to identify the amount of hydrogen ions in the solution. Therefore a 0.1 M [molar] solution contains 1 × 10 ^{– 1} hydrogen ions.)

High or low pHs denature proteins, cause enzymes to not function and may even cause death. The stability of many drugs in solution depends upon maintaining the pH within a given range.

pH is defined as the negative log of the hydrogen ion concentration, written

pH = – log [H⁺]

pOH is defined as the negative log of the hydroxyl ion concentration, written

pH = – log [OH^–]

The dissociation constant indicates the extent of dissociation of the acid or base (K_a or K_b). The negative log of K_a or K_b can be taken to yield pK_a and pK_b, expressed as

pK_a = – log pK_a

or

pK_b = – logK_b

For water, the dissociation constant is pK_w. Since water is neutral (pH = 7), and there are equal amounts of hydrogen ion and hydroxyl ions, then

pK_w = pH + pOH = 14

Furthermore, because pH is a logarithmic relationship, a one unit change is equivalent to a tenfold difference in hydrogen ion concentration.

The pH in the human body varies widely from the pH of 1 for stomach contents up to over 8 for pancreatic secretions. The pH of blood is slightly basic (pH of about 7.4); urine is slightly acidic, having a pH of 6; and cerebrospinal fluid is close to neutral at 7.3.

The most common disorder in acid-base homeostasis is acidosis, where the pH drops below 7.35.

Practice Problems

1. Indicate whether the following pH values correspond to acid or basic solutions:

a. pH = 5.6

b. pH = 8.7

c. pH = 10.3

d. pH = 3.3

e. pH = 2.8

f. pH = 7.8

g. pH = 2.5

h. pH = 12.5

i. pH = 4.4

j. pH = 10.9

Answer

Indicate acid (A) or base (B)

a. A

b. B

c. B

d. A

e. A

f. B to neutral

g. A

h. B

i. A

j. B

2. The pH of an intravenous saline is 6.8. Calculate the hydrogen ion concentration of this solution.

Answer

pH = – log [H⁺]
6.8 = – log [H⁺]
– 6.8 = log [H⁺]
Antilog – 6.8 = [H⁺]
1.6 × l0 ^{– 7} = [H⁺]

3. What is the pH of a preparation if the hydrogen ion concentration is 1 × 10 ^{– 8}?

Answer

[H⁺] = 1 × 10 ^{– 8}
pH = – log [H⁺]
pH = – log [l × 10 ^{– 8}]
pH = 8

4. Calculate the pH of a solution where the hydrogen ion concentration is 0.1 M.

Answer

[H⁺] = 0.1 M
[H+] = 1 × 10 ^{– 1}
pH = – log [H⁺]
pH = – log [l × l0 ^{– 1}]
pH = l

5. Calculate the pH of a solution where the hydrogen ion concentration is 0.01 M.

Answer

[H⁺] = 0.01 M
[H+] = 1 × 10 ^{– 2}
pH = – log [H⁺]
pH = – log [l × 10 ^{– 2}]
pH = 2

6. Instant coffee has a pH of 5.7. What is the hydrogen ion concentration?

Answer

pH = 5.7 [H⁺] = ?
pH = – log [H⁺]
5.7 = – log [H⁺]
– 5.7 = log [H⁺]
Antilog – 5.7 = [H⁺]
2 × 10 ^{– 6} = [H⁺]

7. What is the pOH value of a solution whose pH is 7.3?

Answer

pH = 7.3
pH + pOH = pK_w = 14
7.3 + pOH = 14
pOH = 6.7

8. An intramuscular drug is manufactured to have a pH between 6.8 and 7.8. What is the hydrogen ion concentration of this range?

Answer

pH = 6.8 to 7.8
pH = – log [H⁺]
6.8 to 7.8 = – log [H⁺]
– 6.8 to – 7.8 = log [H⁺]
Antilog – 6.8 to – 7.8 = [H⁺]
1.6 × l0 ^{– 7} to 1.6 × l0 ^{– 8}