Intermediate Algebra (11th edition)

Using pH in an Application

Wetlands are classified as bogs, fens, marshes,

and swamps,on the basis of pH values. A pH

value between 6.0 and 7.5, such as that of Sum-

merby Swamp in Michigan’s Hiawatha National

Forest, indicates that the wetland is a “rich fen.”

When the pH is between 3.0 and 6.0, the wet-

land is a “poor fen,” and if the pH falls to 3.0 or

less, it is a “bog.” (Source: Mohlenbrock,

R., “Summerby Swamp, Michigan,” Natural

History.)

Suppose that the hydronium ion concentration of a sample of water from a wet-

land is How would this wetland be classified?

Definition of pH

Product rule

Use a calculator to find log 6.3.

Distributive property

Add.

Since the pH is less than 3.0, the wetland is a bog. NOW TRY

pH L2.2

pH =-0.7993+ 3

pH =- 3 0.7993- 31124

pH =- 1 log 6.3+ log 10-^32

pH =-log 1 6.3* 10 -^32

6.3* 10 -^3.

EXAMPLE 2

SECTION 10.5 Common and Natural Logarithms 605

Acidic Neutral Alkaline

1147

FIGURE 14pH Scale

Finding Hydronium Ion Concentration

Find the hydronium ion concentration of drinking water with pH 6.5.

Let

Multiply by

Solve for by writing the equation in exponential form using base 10.

3 H 3 O+ 4 L3.2* 10 -^7 Use a calculator.

3 H 3 O+ 4 = 10 - 6.5

3 H 3 O+ 4

log 3 H 3 O+ 4 =-6.5 -1.

6.5=-log 3 H 3 O+ 4 pH=6.5.

pH =-log 3 H 3 O+ 4

EXAMPLE 3

The pHof a solution is defined as

where is the hydronium ion concentration in moles per liter. It is customary

to round pH values to the nearest tenth.

3 H 3 O+ 4

pHlog 3 H 3 O 4 ,

NOW TRY
EXERCISE 2
Water taken from a wetland
has a hydronium ion concen-
tration of

Find the pH value for the
water and classify the wetland
as a rich fen, a poor fen, or
a bog.

3.4* 10 -^5.

NOW TRY ANSWERS

2. 4.5; poor fen

NOW TRY
EXERCISE 3
Find the hydronium ion con-
centration of a solution with
pH 2.6.

3. 2.5* 10 -^3 NOW TRY