Hydrogen ion concentration decides the pH

1. The square brackets in $[H^{+}]$ stand for the concentration of hydrogen ions, measured in ${mol/dm}^3$.
2. The higher the $[H^{+}]$, the lower the pH and the more acidic the solution.
3. The lower the $[H^{+}]$, the higher the pH.
4. Pure water contains a tiny concentration of hydrogen ions, $1\times 10^{-7}{mol/dm}^3$, which gives it pH 7.
   1. For whole-number values the pH matches the power of ten, so $[H^{+}]=1\times 10^{-3}{mol/dm}^3$ gives pH 3.

Hydrogen ions in neutral, acidic and alkaline solutions

1. In a neutral solution at pH 7, the concentrations of hydrogen ions and hydroxide ions are equal.
2. An acidic solution has more hydrogen ions than hydroxide ions, so its pH is below 7.
3. An alkaline solution has fewer hydrogen ions than hydroxide ions, so its pH is above 7.
   1. Even at pH 12 some hydrogen ions are present, at $1\times 10^{-12}{mol/dm}^3$.
4. Adding acid raises the $[H^{+}]$ and lowers the pH, while adding alkali removes hydrogen ions and raises the pH.

Each tenfold concentration increase lowers pH by one

1. Multiplying $[H^{+}]$ by ten lowers the pH by one.
   1. Going from $1\times 10^{-4}$ to $1\times 10^{-3}{mol/dm}^3$ gives ten times more hydrogen ions, and the pH falls from 4 to 3.
2. Dividing $[H^{+}]$ by ten raises the pH by one.
   1. Diluting a strong acid tenfold with water divides its $[H^{+}]$ by ten, so pH 1 becomes pH 2.
3. A change of two pH units means a factor of $10\times 10=100$ in $[H^{+}]$, and three units means a factor of $1000$.

pH differences give the hydrogen ion concentration factor

1. Subtract the smaller pH from the larger one to find the number of steps.
2. Raise ten to that power to find the factor, so a difference of three gives $10^3=1000$.
3. The solution with the lower pH has the higher hydrogen ion concentration.
4. The same method works in reverse, so a solution with $1000$ times fewer hydrogen ions has a pH three units higher.