As we have seen,

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pHThe negative logarithm of the hydrogen ion concentration. is a logarithmic function of

pH = −log

pH is usually (but not always) between 0 and 14. Knowing the dependence of pH on

If pH If pH = 7, then the solution is neutral. If pH > 7, then the solution is basic.

This is known as the pH scaleThe range of values from 0 to 14 that describes the acidity or basicity of a solution.. You can use pH to make a quick determination whether a given aqueous solution is acidic, basic, or neutral.

Table of Contents

### Example 12

Label each solution as acidic, basic, or neutral based only on the stated pH.

milk of magnesia, pH = 10.5 pure water, pH = 7 wine, pH = 3.0

Solution

With a pH greater than 7, milk of magnesia is basic. (Milk of magnesia is largely Mg(OH)2.) Pure water, with a pH of 7, is neutral. With a pH of less than 7, wine is acidic.

*Test Yourself*

Identify each substance as acidic, basic, or neutral based only on the stated pH.

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human blood, pH = 7.4 household ammonia, pH = 11.0 cherries, pH = 3.6

*Answers*

basic basic acidic

Table 12.3 “Typical pH Values of Various Substances*” gives the typical pH values of some common substances. Note that several food items are on the list, and most of them are acidic.

Table 12.3 Typical pH Values of Various Substances*

Substance pH *Actual values may vary depending on conditions.stomach acid | 1.7 |

lemon juice | 2.2 |

vinegar | 2.9 |

soda | 3.0 |

wine | 3.5 |

coffee, black | 5.0 |

milk | 6.9 |

pure water | 7.0 |

blood | 7.4 |

seawater | 8.5 |

milk of magnesia | 10.5 |

ammonia solution | 12.5 |

1.0 M NaOH | 14.0 |

pH is a *logarithmic* scale. A solution that has a pH of 1.0 has 10 times the

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Using the definition of pH, it is also possible to calculate

You need to determine how to evaluate the above expression on your calculator. Ask your instructor if you have any questions. The other issue that concerns us here is significant figures. Because the number(s) before the decimal point in a logarithm relate to the power on 10, the number of digits *after* the decimal point is what determines the number of significant figures in the final answer:

### Example 13

What are

Solution

We need to evaluate the expression

Depending on the calculator you use, the method for solving this problem will vary. In some cases, the “−4.88” is entered and a “10x” key is pressed; for other calculators, the sequence of keystrokes is reversed. In any case, the correct numerical answer is as follows:

Because 4.88 has two digits after the decimal point,

*Test Yourself*

What are

*Answer*

There is an easier way to relate

pOH = −log

(In fact, p“anything” is defined as the negative logarithm of that anything.) This also implies that

A simple and useful relationship is that for any aqueous solution,

pH + pOH = 14

This relationship makes it simple to determine pH from pOH or pOH from pH and then calculate the resulting ion concentration.

### Example 14

The pH of a solution is 8.22. What are pOH,

Solution

Because the sum of pH and pOH equals 14, we have

8.22 + pOH = 14

Subtracting 8.22 from 14, we get

pOH = 5.78

Now we evaluate the following two expressions:

So

*Test Yourself*

The pOH of a solution is 12.04. What are pH,

*Answer*

pH = 1.96;

### Key Takeaways

pH is a logarithmic function of

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