#### Learning Objective

- Convert between pH and pOH scales to solve acid-base equilibrium problems.

#### Key Points

- The p-scale is a negative logarithmic scale. It allows numbers with very small units of magnitude (for instance, the concentration of H
^{+}in solution) to be converted into more convenient numbers, often within the the range of -2 – 14. - The most common p-scales are the pH and pOH scales, which measure the concentration of hydrogen and hydroxide ions. According to the water ion product, pH+pOH =14 for all aqueous solutions.
- Because of the convenience of the p-scale, it is used to also denote the small dissociation constants of acids and bases, which are given by the notation pK
_{a}and pK_{b}.

#### Terms

- logarithmfor a number [latex]x[/latex] , the power to which a given base number must be raised in order to obtain x; written log
_{b}x.; for example, log_{2}16 = 4 because 2^{4}= 16 - dissociationthe process by which compounds split into smaller constituent molecules, usually reversibly

## pH and pOH

Recall the reaction for the autoionization of water:

[latex]H_2O\rightleftharpoons H^+(aq)+OH^-(aq)[/latex]

This reaction has a special equilibrium constant denoted K_{W}, and it can be written as follows:

[latex]K_W=[H^+][OH^-]=1.0\times 10^{-14}[/latex]

Because H+ and OH- dissociate in a one-to-one molar ratio,

[latex][H^+]=[OH^-]=\sqrt{1.0\times 10^{-14}}=1.0\times 10^{-7}[/latex]

If we take the negative logarithm of each concentration, we get:

[latex]pH=-log[H^+]=-log(1.0\times 10^{-7})=7.0[/latex]

[latex]pOH=-log[OH^-]=-log(1.0\times 10^{-7})=7.0[/latex]

Here we have the reason that neutral water has a pH of 7.0 -; this is the pH at which the concentrations of H^{+} and OH^{–} are exactly equal.

Lastly, we should take note of the following relationship:

[latex]pH+pOH=14[/latex]

This relationship will always apply to aqueous solutions. It is a quick and convenient way to find pH from pOH, hydrogen ion concentration from hydroxide ion concentration, and more.

## pK_{a} and pK_{b}

Generically, this p-notation can be used for other scales. In acid-base chemistry, the amount by which an acid or base dissociates to form H^{+} or OH^{– } ions in solution is often given in terms of their dissociation constants (K_{a} or K_{b}). However, because these values are often very small for weak acids and weak bases, the p-scale is used to simplify these numbers and make them more convenient to work with. Quite often we will see the notation pK_{a} or pK_{b}, which refers to the negative logarithms of K_{a} or K_{b}, respectively.