The pH of a solution describes its acidity and is the negative logarithm (log) of its hydrogen ion concentration. The term pH is used because the hydrogen ion concentration in solutions of weak acids and in many other fluids is frequently much less than 1. Therefore, when the concentration is expressed exponentially, it contains a negative exponent. Many people find numbers with negative exponents to be confusing, and they answer with some hesitation such questions as: Is 1.8 X 10-4 larger or smaller than 3.6 X 10-5? (To answer the question, state both numbers with the same exponent of 10. This restatement changes 3.6 X 10-5 to 0.36 X 10-4, a value that is clearly less than 1.8 X 10-4.) To avoid confusion when dealing with small numbers, dissociation constants and ion concentrations are stated not in exponential form, but as the negative logarithms of the actual values. The letter p has been chosen to mean "negative logarithm of." Thus, pH means the negative log of the hydrogen ion concentration, and pOH means the negative log of the hydroxide ion concentration:

pH = -log pOH = -log


A. Calculation of pH On most hand-held calculators we can calculate pH with the push of a button. To calculate the pH of a solution with a hydrogen ion concentration of 0.0003 M, enter .003 on your calculator. Find and press the Log button to find the log of 0.003. The number now on the display of your calculator is - 2.52.

log(3.0 X 10-3) = - 2.52

To find the negative of - 2.52, press the +/- button on your calculator. The number on the display of your calculator is 2.52.

- ( - 2.52) = 2.52

The pH is the negative log of the hydrogen ion concentration; thus, for = 3.0 X 10-3, pH = 2.52.


a. Calculate the pH of a solution with a hydrogen ion concentration of 0.00040 M.

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b. Calculate the hydrogen ion concnetration of a solution of pH 8.52.


a. State in exponential form:

= 0.00040 M = 4.0x10-4 M

Determine the log of using Table 12.6 or your calculator:

pH = -log(4.0x10-4) = -(log 4.0 + log 10-4)

= -<0.602 +(-4)> = -0.602 + 4 = 3.40

b. This calculation is performed by reversing the steps in part a.

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pH = -log = 8.52 = 9 - 0.48

log = -9 + 0.48

= (antilog 0.48)x10-9 M

= 3.0x10-9 M

B. The Interpretation of pH Values When the hydrogen ion concentration is stated in exponential notation, the smaller the exponent, the greater the acidity of the solution. Consequently, with pH values, the lower the pH, the more acidic the solution.In 0.1 M HCl = 1 X 10-1 MpH = 1In 0.0001 M HCl = 1 X 10-4 MpH = 4 Figure 12.2 shows the pH of several familiar fluids. Many of these values are the midpoint of a range. Human blood plasma normally varies only between pH 7.35 and pH 7.45. Human gastric fluid is much more acidic; its normal range is between pH 1.0 and pH 2.0.
FIGURE 12.2 pH and hydrogen ion concentration.