pH

The definition of pH is straightforward: pH describes the concentration (or activity) of positively charged hydrogen ions (H⁺) in a solution. Underlying this definition is a set concepts that can be challenging to understand. The challenge comes from needing to appreciate:

• The concentrations represented by specific pH values
• The relationship between H⁺ ion concentration and pH values
• The range of concentrations covered by the pH scale
• The dramatic effect changes in pH have on the chemical properties of a solution.

Take water. Water surrounds us. It covers 70% of the surface of the earth and comprises well over half the mass of our own bodies. Given it’s ubiquity, it is easy to forget that water is a chemical. A water molecule has two hydrogen atoms covalently bonded to a single oxygen atom. Water’s chemical formula is H₂O.

The vast majority of hydrogen and oxygen molecules in a volume of water are bonded together as water. However, in any container of water, a small proportion of molecules are present as H⁺ and hydroxide (OH^-) ions. These ions are present because some water molecules are constantly splitting into H⁺ and OH^- ions while some of the H⁺ and OH^- ions present are combining back into water. The two processes occur at the same rate so the amount of each type of molecule remains constant as long as nothing is added or removed from the solution.

Concentrations represented by specific pH values
To demonstrate the connection between pH and ion concentration, consider the following:

• A liter of pure water contains about 55.5 moles of water molecules.
• Since there are 6.022x10²³ molecules per mole, a liter of water contains over 3x10²⁵ individual molecules.
• In pure water, about 1 of every 555 million molecules are in the form of H⁺ and OH^- ions. This is roughly 6x10¹⁶molecules per liter, or (6x10¹⁶/6.022x10²³) 1x10^-7 moles per liter (M).

A concentration of 1x10^-7 M seems small but it represents a huge number of individual molecules.

The presence of H⁺ and OH^- ions is what gives solutions with different pH’s their chemical characteristics. The ratio of H⁺ to OH^- ions present in a solution varies in a predictable way. This allows the concentration of one ion to be calculated if the concentration of the other is known.

Link between pH and H⁺ ion concentration
Since hydrogen ion concentration is an important property of many solutions and 1x10^-7 is cumbersome to write, scientists use pH as an easy, shorthand way of reporting the H⁺ ion concentration. To demonstrate this, contrast the following two statements:

A. The H⁺ concentration of water-based solutions can range from 1 to 1x10-14 M. A value of 1x10-7 M is considered neutral. Any H⁺ concentration lower than 1x10-7 M is basic, any concentration greater than 1x10^-7 is acidic. The further the H⁺ concentration is from 1x10^-7 M, the more basic or acidic the solution is.

B. The pH water-based solution can range from 1 to 14. A value of 7 is considered neutral. Any pH greater than 7 is basic, any pH less than 7 is acidic. The further the pH is from 7, the more basic or acidic the solution is.

These are equivalent statements. pH is simply a shorthand notation used to report cumbersome concentration values. It is easy to write, allowing a one or two digit number to provide concentration information across 14 orders of magnitude (between 1 and 0.00000000000001). In mathematical terms, pH equals the negative log of the H⁺ concentration:

pH = -log[H⁺]

Range of concentrations covered by pH
The pH scale is logarithmic. This means a solution with a pH of 9 is 10 time more basic than one with a pH of 8. And, a solution with a pH of 10 is 100 times (10x10) more basic than a solution with a pH of 8.

Effect of pH on chemical properties of a solution
H⁺ and OH^- are very reactive. The relative concentration of these ions that give acidic and basic solutions their properties. An acidic solution is one that contains an excess of hydrogen ions and a basic solution has an excess of hydroxide solutions. pH uses a log scale because the concentration of H⁺ and OH^- range over many orders of magnitude even for common items such as vinegar, coffee, milk, ammonia and bleach.

The illustration below explores the numerical relationship between a solutions hydrogen and hydroxide ion concentrations and the pH values used to report these concentrations. A video demonstration of the animation can be found at the bottom of the post.

Video demonstration: