16. Ions and Equilibrium;
       Acids and Bases
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       The pH Scale

Concentrations involving such extreme powers of ten, extending over 14 orders of magnitude, are clumsy to handle. In the discussion of entropy in Chapter 13 we found it convenient to reduce a wide-ranging quantity, probability, to more manageable numbers by taking the logarithm

In chapter 14 we saw that standard free energies convey the same information as equilibrium constants, but in a more compact logarithmic form:

The value of logarithmic notation can be illustrated by the 10 X 10 X 10 stack of blocks at the right. The entire stack contains 1000 blocks. One face of the stack has 100 blocks, or 1/10 of the whole.

One edge contains 10 blocks, or 1/100 of the stack, and one corner block represents 1/1000 of the entire ensemble. The fractions represented by the full block, face, edge, and corner, can be represented by 1 (or 100), 10-1, 10-2 , and 10-3.

We also can represent these different orders of magnitude by picking out the negative exponents: 0, 1, 2, and 3. We can label these numbers pF values if we define pF as the negative logarithm to base ten of the fraction, F:

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