pH Scale
The pH scale measures how acidic or basic a solution is on a scale from 0 to 14, where 7 is neutral, below 7 is acidic, and above 7 is basic.
Formula
\text{pH} = -\log_{10}[\text{H}^+]
Definition
The pH scale is a number line, typically running from $0$ to $14$, that measures how acidic or basic a solution is based on its concentration of hydrogen ions: $7$ is neutral, lower numbers are acids, and higher numbers are bases, and because the scale is logarithmic each step of one pH unit represents a tenfold change in hydrogen ion concentration. Formally, $\text{pH} = -\log_{10}[H^+]$ (strictly, hydrogen ion activity), and in water it connects to pOH through the ion product $K_w = [H^+][OH^-] = 1.0 \times 10^{-14}$ at $25^\circ\text{C}$, so $\text{pH} + \text{pOH} = 14$; neutral pH is exactly $7$ only at $25^\circ\text{C}$, since $K_w$ rises with temperature, and the scale is not truly bounded, as very concentrated strong acids can reach negative pH and very concentrated strong bases can exceed $14$.
Example
Pure water sits at pH $7$, lemon juice around $2$, milk around $6.5$, baking soda water around $8$, and bleach around $12.5$, so a solution at pH $3$ has $10$ times more hydrogen ions than one at pH $4$ and $1{,}000$ times more than one at pH $6$, which is why human blood must be held tightly between $7.35$ and $7.45$. A $0.0050\text{ M}$ solution of $HCl$ has $\text{pH} = -\log(0.0050) = 2.30$, while $0.020\text{ M}$ $NaOH$ gives $\text{pOH} = 1.70$ and $\text{pH} = 12.30$, and a buffer of acetic acid and acetate holds pH near its $\text{p}K_a$ of $4.76$ following the Henderson-Hasselbalch equation, $\text{pH} = \text{p}K_a + \log([A^-]/[HA])$.
Key Insight
Acid rain at pH $4$ is not just a little more acidic than clean rain at pH $5.6$; it carries about $40$ times the hydrogen ion concentration, enough to kill fish and dissolve limestone statues, since the lower pH number always means a stronger acid even though it looks like a smaller number. Sorensen introduced pH in 1909 to simplify brewing chemistry, and the logarithm is really the whole point of the scale, since hydrogen ion concentrations span more than fourteen orders of magnitude and no ordinary linear scale could fit both stomach acid and drain cleaner on the same axis.