II. Chemical Foundations

You should be familiar with the contents of this section before you go to case study.

Ionization of Water: Although water is generally considered to consist of only H₂O molecules, a small fraction of water molecules ionize to form H₃O⁺ and OH^–. The equilibrium constant for this ionization is 1.0 × 10^-14 at 25ºC. This equilibrium is expressed as:

K_w = [H⁺][OH^–] = 1.0 × 10^-14 (at 25°C)

Since the equilibrium constant for water is so important, it is represented as K_w rather than K_e. The expression for the ionization of water can be used to determine the K_e for any aqueous solution. If the concentration of hydronium ions (H₃O⁺) equals the concentration of hydroxide ions (OH^–), the solution is said to be neutral.

Acids: In aqueous solutions, if the concentration of the hydronium ion [H₃O⁺] is larger than the concentration of the hydroxide ion [OH^–], the solution is acidic. Strong acids, such as HCl, exist almost entirely as ions:

whereas weak acids are only partly ionized. The degree to which weak acids are ionized can be measured and expressed as the equilibrium constant (K_e). The equilibrium constants for weak acids vary considerably depending on the extent of the ionization. In an aqueous solution of a weak acid, HA, the equilibrium is expressed as

The equilibrium constant for the ionization of weak acids is expressed as K_a to indicate that it represents the ionization of a weak acid. K_a is referred to as the ion dissociation constant and is calculated from the following equation:

Hydrogen Ion Concentration Expressed as pH: Since in most cases the [H₃O⁺] is very small, it is more convenient to express it as a small whole number called the pH. This can be accomplished by taking the negative log to the base 10 of the H₃O⁺ concentration:

pH = -log[H₃O⁺]

For example, the pH of pure water is

pH = -log 10^-7 = 7

Refer to your calculator instructions or the appendix section of your chemistry book for a review of logarithms.

The pH range of aqueous solutions is 0.0 – 14.0. The pH is less than 7 for acidic solutions, is greater than 7 for basic solutions, and is 7 for neutral solutions.

Bases: Just as with acids, strong bases are completely dissociated in aqueous solutions. Only the alkali metals form strong bases. To determine the pH of bases, calculate the log[OH^–]; this is the pOH. Since pH + pOH = 14 (at 25ºC), the pH = 14 – pOH.

Indicators: Acid-base indicators are dyes that change color at specific pHs. Indicators are the method of choice for determining the concentration of an unknown acid solution by titrating a specific quantity of the acid with a base of known concentration. From the amount of base used to reach the equivalence point, the concentration of the acid can be determined. The indicator selected must change color when the equivalence point is reached. This color change is designated as the endpoint.

In order to tell the pH of a solution using an indicator, a color change must be observable. The range over which a color change is seen is determined by the acid dissociation reaction and the equilibrium constant of the indicator, which can be written as:

By rearranging this equation, it is shown that the concentration of H⁺ can determine the color by changing the ratio of the colored forms of the indicator being used. In previous experiments, you may have seen the color changes of phenolphthalein (pink to colorless) and eriochrome black T (blue to red) as acidity increased. In this experiment, we will be using bromocresol green, which changes from blue to yellow as acidity increases as shown below:

When [H⁺] = K_a (or pH = pK_a), there is an equal amount of acid and base forms of the indicator (equal yellow and blue). For this indicator, a greenish color would be expected at the equivalence point. From these arguments, it can be seen that an indicator is most sensitive for [H⁺] near the K_a of the indicator (or pH near pK_a).

Methods of pH Determination: There are a number of methods that can be used to measure pH. Two of the most common methods are the use of an indicator or a pH meter. Indicators are formed from weak, highly-colored acids that show a change in color going from the acid to the conjugate base form (see previous section).

The second method of pH determination that you will be using is electrochemical determination of pH using a pH meter. These instruments employ a glass/calomel pH electrode.

Buffers: Buffers are solutions with the capacity to resist changes in pH. Buffers are produced from a weak acid and a salt of its conjugate base. If we write a reaction of an acid with water as

the resulting acid dissociation constant is

Henderson-Hasselbach Equation: To solve for the hydrogen ion concentration, the equation can be rewritten as

At this point, it is convenient to take minus the log of both sides of this equation to yield

or

The last equation is the traditional expression used to describe the pH of a buffer solution. Buffers produced with equal amounts of a weak acid and conjugate base are the most resistant to pH changes. Keeping in mind that log(1) = 0, we can see that the most effective buffers have pH = pK_a. Thus, when choosing a buffer with a certain pH range, the acid dissociation constant (ionization constants) must almost match the desired [H⁺]. A table of the ionization constants of common acids can be found in the appendix section of most chemistry textbooks or online.