10.2 pH and pOH Scale

pH and pOH Scale

The pH and pOH scales give you a compact way to express how acidic or basic a solution is. Instead of dealing with tiny hydrogen or hydroxide ion concentrations (like 0.000001 M), you convert them into simple numbers on a 0–14 scale. Understanding these scales is essential for acid-base chemistry, from predicting reaction behavior to interpreting biological systems.

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The Basics of pH and pOH Scales

pH measures the concentration of hydrogen ions ($H^+$) in a solution:

$pH = -\log[H^+]$

pOH measures the concentration of hydroxide ions ($OH^-$) in a solution:

$pOH = -\log[OH^-]$

Both scales range from 0 to 14 under standard conditions (25°C):

• A value of 7 is neutral (pure water).
• Below 7 means acidic (more $H^+$ ions).
• Above 7 means basic (more $OH^-$ ions).

One thing that trips people up: pH and pOH work in opposite directions. A low pH means high acidity, but a low pOH means high basicity. They're mirror images of each other.

Also note that the pH scale is logarithmic. Each whole number change represents a tenfold change in ion concentration. A solution with pH 3 is ten times more acidic than one with pH 4, and a hundred times more acidic than pH 5.

Calculating pH and pOH

Here's the step-by-step process:

1. To find pH from $[H^+]$: Take the negative log of the hydrogen ion concentration. $pH = -\log[H^+]$

2. To find pOH from $[OH^-]$: Take the negative log of the hydroxide ion concentration. $pOH = -\log[OH^-]$

3. To find $[H^+]$ from pH: Reverse the log operation. $[H^+] = 10^{-pH}$

4. To find $[OH^-]$ from pOH: Same idea. $[OH^-] = 10^{-pOH}$

Practice Problem

If lemon juice has a hydrogen ion concentration of $[H^+] = 1 \times 10^{-3}$ M, what is its pH?

Solution:

$pH = -\log[H^+]$

$pH = -\log(1 \times 10^{-3})$

$pH = 3$

That places lemon juice solidly in the acidic range, which makes sense if you've ever tasted it.

Understanding Relationships: Water Ion Product

Pure water undergoes self-ionization, meaning a small number of water molecules split into $H^+$ and $OH^-$ ions. This equilibrium is described by the ion product constant of water ($K_w$):

$K_w = [H^+][OH^-] = 1.0 \times 10^{-14} \text{ at 25°C}$

This constant links pH and pOH together. If you take the negative log of both sides, you get:

$pH + pOH = 14 \text{ (at 25°C)}$

This relationship is extremely useful. If you know one value, you can always find the other. For example, if a solution has a pH of 4, its pOH is $14 - 4 = 10$.

Keep in mind that $K_w$ changes with temperature. The value $1.0 \times 10^{-14}$ and the "adds to 14" rule only hold at 25°C. At higher temperatures, $K_w$ increases, so pH + pOH will be slightly different.

Advanced Applications

Buffers are solutions that resist changes in pH when small amounts of acid or base are added. Your blood, for example, uses a bicarbonate buffer system ($H_2CO_3 / HCO_3^-$) to maintain a pH near 7.4. Even slight deviations from this range can be dangerous, which is why buffer chemistry matters in biology.

Titrations are a lab technique for determining an unknown concentration of an acid or base. You slowly add a solution of known concentration (the titrant) to the unknown solution until the reaction reaches the equivalence point, where moles of acid equal moles of base. An indicator dye changes color at or near this point to signal that you've arrived.

Practice Problem

You titrate NaOH (a strong base) into 10 mL of HCl (a strong acid). It takes 20 mL of 0.5 M NaOH to reach the equivalence point. What is the molarity of the HCl?

Solution:

At the equivalence point, moles of acid equal moles of base:

$M_{HCl} \times V_{HCl} = M_{NaOH} \times V_{NaOH}$

$M_{HCl} \times 10 \text{ mL} = 0.5 \text{ M} \times 20 \text{ mL}$

$M_{HCl} = \frac{0.5 \times 20}{10} = 1.0 \text{ M}$

Note: You need at least one known molarity to solve for the other. That's the whole point of a titration.