The pH Scale

The concentration of H⁺ ion in solution is a pretty small number that can, nonetheless, vary over a considerable range.

• To conveniently represent the magnitude and range of concentration that the H⁺ ion can have in aqueous solutions, the term pH is used
• pH is defined as the negative logarithm (base 10) of the H⁺ ion concentration

What is the pH of a neutral solution at 25°?

• Under this condition, the concentration of hydrogen ion is 1.0 x 10^-7M
• pH = -log(1.0 x 10^-7) = -(-7.0) = 7.0

• An acidic solution is one where we have an increase in [H⁺]
• If a neutral solution has a [H⁺] of 1 x 10^-7M, then an acidic solution must have a [H⁺] that is greater than 1 x 10^-7M
• For example, a solution with a [H⁺] = 1 x 10^-6M will be acidic. What will be the pH of this solution?
• pH = -log(1.0 x 10^-6) = -(-6.0) = 6.0
• Because of the negative sign in the log term of the definition of pH, acidic solutions (i.e. those with increasing concentrations of H⁺ ions) will have increasingly lower values of pH (i.e. pH 1.0 is a potent acid and this pH is used to help digest your food in your stomach).

• A basic solution is one in which the [OH^-] is greater than 1 x 10^-7M
• For example, a solution has a [OH^-] = 1.0 x 10^-5M (this is greater than 1 x 10^-7M, and so this solution is basic)

• Basic solutions will have increasingly higher values of pH (i.e. pH 12 would be a potent base)

The nature of the pH scale, based upon the -log[H⁺], is that a 10 x fold change in [H⁺] results in a single unit change in the pH value.

• A pH 7.0 solution has a [H⁺] of 1 x 10^-7M. If we increase the concentration 10 x fold (to 1 x 10^-6M) the pH decreases by 1 unit (to pH 6.0)
• A pH 4.0 solution has a [H⁺] of 1 x 10^-4M. If we decrease the concentration 10 x fold (to 1 x 10^-5M) the pH increases by 1 unit (to pH 5.0)

Although the concentration of [H⁺] may seem very low indeed, even small changes can have a big impact on chemical reactions that include [H⁺] as a component in their reaction

• For reactions that are first order in [H⁺] doubling the concentration (even though the starting concentration is a very small amount) can double the reaction rate
• Blood is approximately pH 7.4. If the pH of blood varies by as much as 0.5 pH units outside this value, illness and death may result

By convention, the negative log of a quantity is labeled p(quantity)

• For example, we could reference the quantity of OH^- ions directly:

pOH = -log [OH^-]

• From the definition of K_w:

K_w = [H⁺][OH^-] = 1 x 10^-14

-log(K_w) = (-log([H⁺]) - log([OH^-]) = 14

Measuring pH

• pH meters; detect changes in voltage in response to changes in pH
• Indicator dyes; change colors at different pH's.
• Bromthymol Blue - changes color from yellow (pH 6) to blue (pH 7.4) - physiologically useful indicator
• Phenolphthalein - changes color from colorless (pH 8) to pink (pH 9) - often used to determine the endpoint in an acid/base titration