## pOH and Other p Scales

#### 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 pKa and pKb.

#### Terms

• logarithmfor a number $x$ , the power to which a given base number must be raised in order to obtain x; written logbx.; for example, log216 = 4 because 24 = 16
• dissociationthe process by which compounds split into smaller constituent molecules, usually reversibly

## pH and pOH

Recall the reaction for the autoionization of water:

$H_2O\rightleftharpoons H^+(aq)+OH^-(aq)$

This reaction has a special equilibrium constant denoted KW, and it can be written as follows:

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

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

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

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

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

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

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:

$pH+pOH=14$

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.

## pKa and pKb

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 (Ka or Kb). 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 pKa or pKb, which refers to the negative logarithms of Ka or Kb, respectively.