# 21.9: The pH Scale

Grapefruit juice has a pH of somewhere between 2.9 and 3.3, depending on the specific product. Excessive exposure to this juice can cause erosion of tooth enamel and can lead to tooth damage. The acids in grapefruit juice are carbon-based, with citric acid being one of the major constituents. This compound has three ionizable hydrogens on each molecule which contribute to the relatively low pH of the juice. Another component of grapefruit juice is malic acid, containing two ionizable hydrogens per molecule.

## The pH Scale

Expressing the acidity of a solution by using the molarity of the hydrogen ion is cumbersome because the quantities are generally very small. Danish scientist Søren Sørensen (1868 - 1939) proposed an easier system for indicating the concentration of $$\ce{H^+}$$ called the pH scale. The letters pH stand for the power of the hydrogen ion. The pH of a solution is the negative logarithm of the hydrogen-ion concentration.

$\text{pH} = -\text{log} \: \left[ \ce{H^+} \right]$

In pure water or a neutral solution the $$\left[ \ce{H^+} \right] = 1.0 \times 10^{-7} \: \text{M}$$. Substituting into the pH expression:

$\text{pH} = -\text{log} \left[ 1.0 \times 10^{-7} \right] = -\left( -7.00 \right) = 7.00$

The pH of pure water or any neutral solution is thus 7.00. For recording purposes, the numbers to the right of the decimal point in the pH value are the significant figures. Since $$1.0 \times 10^{-7}$$ has two significant figures, the pH can be reported as 7.00.

A logarithmic scale condenses the range of acidity to numbers that are easy to use. Consider a solution with $$\left[ \ce{H^+} \right] = 1.0 \times 10^{-4} \: \text{M}$$. That is a hydrogen-ion concentration that is 1000 times higher than the concentration in pure water. The pH of such a solution is 4.00, a difference of just 3 pH units. Notice that when the $$\left[ \ce{H^+} \right]$$ is written in scientific notation and the coefficient is 1, the pH is simply the exponent with the sign changed. The pH of a solution with $$\left[ \ce{H^+} \right] = 1 \times 10^{-2} \: \text{M}$$ is 2 and the pH of a solution with $$\left[ \ce{H^+} \right] = 1 \times 10^{-10} \: \text{M}$$ is 10.

As we saw earlier, a solution with $$\left[ \ce{H^+} \right]$$ higher than $$1.0 \times 10^{-7}$$ is acidic, while a solution with $$\left[ \ce{H^+} \right]$$ lower than $$1.0 \times 10^{-7}$$ is basic. Consequently, solutions whose pH is less than 7 are acidic, while those with a pH higher than 7 are basic. Figure $$\PageIndex{1}$$ illustrates this relationship, along with some examples of various solutions.

## Summary

• The concept of pH is defined.
• pH values for several common materials are listed.

## Contributors

• CK-12 Foundation by Sharon Bewick, Richard Parsons, Therese Forsythe, Shonna Robinson, and Jean Dupon.