The Foundations of Chemistry

Note that we use pH rather than pH 3 O. At the time the pH concept was developed, H 3 O

was represented as H
. Various “p” terms are used. In general a lowercase “p” before a
symbol means “negative logarithm of the symbol.” Thus, pH is the negative logarithm of
the H 3 O
concentration, pOHis the negative logarithm of the OHconcentration, and
pKrefers to the negative logarithm of an equilibrium constant. It is convenient to describe
the autoionization of water in terms of pKw.

pKwlog Kw

EXAMPLE 18-3 Calculation of pH

Calculate the pH of a solution in which the H 3 O
concentration is 0.050 mol/L.

Plan

We are given the value for [H 3 O
]; so we take the negative logarithm of this value.

Solution

[H 3 O
]0.050 M5.0 10 ^2 M

pHlog [H 3 O
]log [5.0 10 ^2 ] 1.30

This answer contains only twosignificant figures. The “1” in 1.30 is nota significant figure; it
comes from the power of ten.

You should now work Exercise 22.

EXAMPLE 18-4 Calculation of H 3 O
Concentration from pH

The pH of a solution is 3.301. What is the concentration of H 3 O
in this solution?

Plan

By definition, pHlog [H 3 O
]. We are given the pH, so we solve for [H 3 O
].

When dealing with pH, we always use

the base-10 (common) logarithm, not

the base-e(natural) logarithm. This is

because pH is definedusing base-10

logarithms.

In a pH value, only the digits after the

decimal point are significant figures.

18-3 The pH and pOH Scales 757

pH Range for a Few Common Substances

Substance pH Range

Gastric contents (human) 1.6–3.0

Soft drinks 2.0–4.0

Lemons 2.2–2.4

Vinegar 2.4–3.4

Tomatoes 4.0–4.4

Beer 4.0–5.0

Urine (human) 4.8–8.4

Milk (cow’s) 6.3–6.6

Saliva (human) 6.5–7.5

Blood plasma (human) 7.3–7.5

Egg white 7.6–8.0

Milk of magnesia 10.5

Household ammonia 11–12

More acidic

More basic

The pH of some common

substances is shown by a universal

indicator. Refer to Figure 18-2 to

interpret the indicator colors.