BACKGROUND
One of the most important properties of an aqueous solution is its concentration of hydrogen or more accurately, hydronium ion. The H+ or H3O+ ion has a great effect on the solubility of many inorganic and organic substances, on the nature of complex metallic cations formed in solution, on the rates of many chemical reactions and plays a major role in buffer systems, especially those of living organisms. It is important that we know how to measure the concentration of hydronium ion and understand its effects on solution properties.

For convenience, the strength of the hydronium ion is frequently expressed as the power of H3O+ or the pH of the solution rather than as a molarity or a normality. The pH of a solution is defined by the relationship

Equation 1

here the logarithm is taken to the base 10. If the hydrogen ion concentration is 1 x 10-4 M, then the pH of the solution is 4.0. A solution having a hydrogen ion concentration of 5 x 10-2 has a pH of 1.3 (use your calculator to verify this); in a solution whose pH is 4.3, the molar concentration of the hydrogen ion is 5 x 10-5 (again, use your calculator to verify this). Basic solutions also can be described in terms of pH.

In aqueous solutions at 25 oC, the following auto-ionization of water equilibrium is at play:

2H2O(l)  H3O+(aq) + OH-(aq)

and thus the equilibrium constant is defined as

Equation 2

And at 25 0C = 1 x 10-14

In distilled water, the hydronium ion concentration is equal to the hydroxide ion concentration. Application of Equation 2 leads to the result that the hydronium ion concentration is 1 x 10-7 M. The pH of distilled water is, therefore, 7.0. Solutions in which the hydronium ion concentration exceeds the hydroxide ion concentration are said to be acidic and will have a pH less than 7. If the hydronium ion concentration is less than the hydroxide ion concentration, the solution is basic and has a pH greater than 7. A solution with a pH of 10.0 will have a [H3O+] of 1 x 10-10 M and a [OH-] of 1 x 10-4 M.

The pH of a solution can be measured experimentally in various ways. For example, one can use a chemical called an indicator, which is sensitive to pH. These substances have colors that change over a relatively short pH range (generally about 2 pH units) and can, when properly chosen, be used to make a rough determination of the pH of a solution. Two very common indicators are litmus, usually used in the form of litmus paper, and phenolphthalein solution, the most common indicator in acid-base titrations. Litmus changes from red to blue as the pH of a solution changes from about 6 to about 8. Phenolphthalein changes from colorless to pink as the pH changes from 8 to 10. A given indicator is useful for determining the pH only in the region in which it changes color. Indicators are available for measurement of pH in all the important ranges of acidity and basicity. Universal indicators, which contain a mixture of several indicators and show color changes over a wide pH range, also are in common use.

Another method for finding pH involves the use of an instrument known as a pH meter. With this device the pH is determined from a measurement of the potential which develops between two particular electrodes when they are in the solution being investigated. This potential varies with the pH and is used to activate a meter, which is calibrated so as to read pH directly. A pH meter can furnish a much more precise measurement of pH than is possible with indicators.

Many substances when dissolved in water will form solutions in which the pH is not 7. If the pH of the solution is less than 7, the dissolved substance behaved as an acid, but if the pH is greater than 7, it is a base. Some acids, like HCl and HNO3, ionize completely in solution. In an aqueous 1 M HCl solution, the hydronium ion concentration is 1 M, and there are essentially no HCl molecules in the solution. An acid which behaves in this way is said to be a strong acid. Similarly, there are some bases, like NaOH, which dissociate completely in solution. In 0.5 M NaOH, the hydroxide ion concentration is 0.5 M, and there are practically no NaOH molecules present. NaOH is an examples of a strong base.

Many substances, in addition to the strong acids, will produce acidic solutions. These substances are called weak acids because they do not dissociate completely in solution. In fact, many often dissociate around 5% or less. We can write the general formula of a weak mono-protic acid as HA. In water, this acid will ionize to a small extent according to the reversible reaction:

HA(aq) + H2O  H3O+ + A-

Using the law of mass action, the equilibrium constant is defined as

Equation 3

The condition imposed by Equation (3) will be obeyed in any solution in which some HA molecules are present. The equilibrium constant for this reaction, Ka, is known as the acid dissociation constant for the weak mono-protic acid HA, and it will have a constant value at any given temperature.

A common way to arrange initial concentrations and differentiate them from equilibrium concentrations is to arrange them in the form of an ICE table (ICE stands for Initial, Change, Equilibrium). Consequently, mathematical relationships between important quantities can more easily be recognized, e.g. relationships between K, % ionization, pH, pOH, and solubility. For example, the ICE corresponding to 1.5 M solution of HA would be

HA(aq) + H2O  H3O+ + A-
I 1.5 M —- 0 0
C -x —- x x
E 1.5 – x —- x x

And the corresponding relationships are thus derived from the definitions of K, % ionization, pH, pOH, and solubility through their relationship to x. For example, using the definitions of K, % ionization and pH we see that they are related to the algebraic parameter, x, found in the above ICE table as follows

;

And pH = – log [H3O+] = – log x

The weak acid represented by HA may be an organic acid, like acetic acid, HC2H3O2; a hydrated metallic cation, like Cu(H2O)42+; the ammonium ion, NH4+; or an inorganic molecule or anion, like H2CO3 or HSO4-. The reactions for these species are

HC2H3O2(aq) + H2O  H3O+ + C2H3O2-

Cu(H2O)42+ + H2O  H3O+ + Cu(H2O)3OH+

NH4+ + H2O  H3O+ + NH3(aq)

H2CO3(aq) + H2O  H3O+ + HCO3-

HSO4- + H2O  H3O+ + SO42-

Clearly, there are many substances, including many salts, which form acidic solutions. The extent of the dissociation reaction usually is small, with perhaps five percent or less of the acid-forming species undergoing ionization. In 0.1 M HC2H3O2, the [H3O+] is about 0.001 M, the [C2H3O2-] also is about 0.001 M, and, since so little of the acid dissociates, the [HC2H3O2] is approximately 0.1 M. The pH of this solution is about 3.0. This is strikingly different for strong acids, for example, 0.1 M HCl solutions, where there are essentially no HCl molecules and complete 100% ionization into 0.1 M H3O+ and Cl- ions resulting in a pH = -log [0.1] = 1.0.

There are many substances besides NaOH which form basic solutions. Many of which can be recognized as conjugate bases and are related to weak acids. In fact, this relationship is a great way to help identify weak bases, that is, if you could recognize their conjugate acids. Assuming that HA is a weak acid, any source of A- ions in solution (say a sodium salt of A-) will tend to combine with any acids (water in the below eq. 4) present to form HA molecules. In a solution of NaA, therefore, the A- ions will tend to extract protons from the solvent water molecules, according to the reaction:

A- + H2O  OH- + HA(aq) Equation 4

In the solution, the above reaction usually will not go very far toward the right, since the equilibrium constant for this reaction is typically very small. Even though it proceeds to only a small extent, however, enough hydroxide ions are produced (more than 1 x 10-7 M), and the solution will be basic. Thus according to Bronsted’s definition of acids and bases, the A- ion is a weak base and water in eq. 4 is an acid. In general, we can say that the sodium salts formed from the negative ion of deprotonated weak acids (e.g. the conjugate base of a weak acid) behave as weak bases.

A common weak base that is molecular and should be remembered as such is ammonia, NH3. The aqueous reaction in which ammonia participates is

NH3(aq) + H2O  NH4+ + OH-

Ammonia is the weak base most commonly encountered in the laboratory. In 0.1 M NH3, less than one percent of the NH3 reacts according to the above reaction. In that solution, therefore, the hydroxide ion concentration is about 0.0004 M, the ammonium ion concentration also is about 0.0004 M, and the ammonia concentration is very nearly 0.1 M.

a.) What type of compounds are 1, 2, and 3 (strong/weak acid/base) in the above table and why doesn’t HCl have rows for % ionization or K’s?
b.) Construct 6 ICE tables, 3 tables for HC2H3O2 and 3 tables for NH3, one at each of the concentrations 1.0, 0.10 and 0.010 M solutions. Use these ICE tables to find the K and % ionization values for each of the 6 cases and use them to fill out Table A.
c.) What are the average Ka and Kb values and calculate their % error? (you need to look up their K values to compare to).
d.) What is the trend for % ionization as a function of concentration for weak electrolytes? Does the above trend for NH3 and HC2H3O2 in % ionization as a function of concentration make sense?