In 1680, Robert Boyle noted that acids dissolve many substances, that they change the color of certain natural dyes (litmus) from blue to red, and that they lose these characteristic properties after coming in contact with alkalis (bases). In the eighteenth century it was recognized that acids have a sour taste, that they react with limestone producing a gaseous substance (CO2), and that neutral substances result from their interaction with bases. Lavoisier in 1787 proposed that acids are binary compounds of oxygen, and he considered oxygen to be responsible for the acidic properties of that class of substances. The necessity of oxygen was disproved by Sir Humphry Davy in 1811 when he showed that hydrochloric acid (HCl) contains no oxygen. Davy made a great step forward in the development of the acid-base concept by concluding that hydrogen, rather than oxygen, is the essential constituent of acids.

In 1814 Gay-Lussac concluded that acids are substances which can neutralize alkalis and that these two classes of substances can be defined only in terms of each other. The idea of Davy and Gay-Lussac provide the foundation for our modern concepts of acids and bases in water solution.


In 1887, a young Swedish chemist, Svante Arrhenius, published a paper concerning acids and bases. He knew that solutions containing acids or bases conducted an electric current, and he tried to explain why. He concluded that these substances released charged particles when dissolved; he called these charged particles Ions (wanderers). He concluded that acids were substances which separated (ionized) in solution to produce hydrogen ions (H+) and that bases were substances which ionized to produce hydroxide ions (OH-).

HCl H++ Cl-(1)

NaOH Na++ OH-(2)

While it is true that the OH- ion is responsible for the basic properties of solutions it is technically incorrect in attributing acidic properties to the hydrogen ion. Its small radius and unit charge give the hydrogen ion an extremely high charge density. Thus, it is highly reactive and will be strongly attracted to any molecule, such as water, which has pairs of unshared electrons. Free hydrogen ions cannot exist in water and cannot be responsible for acidic properties. In fact, they exist as hydrated protons called Hydronium Ions.

The hydrated proton is usually represented as H3O+. Spectroscopic analysis confirms the existence of the hydronium ion. We can conclude on the basis of experimental evidence that it is the hydrated proton, represented as a hydronium ion, that imparts acidic characteristics to water solutions of acids.

A better representation for the ionization in equation (1) above is:

H2O + HCl H3O++ Cl-(3)

in which a proton is transferred from HCl to the water molecule, where it is bonded to the oxygen atom by a stable coordinate covalent bond (Section 4.7). The dissociation of HCl is more correctly represented as the transfer of a proton from the acid to the solvent molecule.


As chemistry developed, knowledge of catalysts and nonaqueous solutions increased, and it became necessary to redefine the terms acid and base. In 1923, an English scientist, T.M.Lowry, and a Danish scientist, J.N.Bronsted (see Article), independently proposed that in a chemical reaction, any substance which donates a proton is an acid and any substance which accepts a proton is a base. When hydrogen chloride gas is dissolved in water, ions are formed:

HCl (g) + H2O (l) H3O+(aq) + Cl- (aq) (4)

In this reaction, hydrogen chloride is an acid, and water is a base. Note that the hydrogen ion (H+) has combined with a water molecule to form the polyatomic ion H3O+. There is strong evidence that the hydrogen ion is never found free as H+ in water solution.

In general, any acid-base reaction is described as:

acid + base conjugate acid + conjugate base (5)

The CONJUGATE BASE of an acid is the remainder of the acid after the proton has been released by the acid. The CONJUGATE ACID of a base is formed when the base acquires a proton from the acid.

NH3 (g) + H2O (l) NH4+(aq) + OH-(aq) (6)

base + acid conjugate acid + conjugate base

In this reaction, water acts as an acid because it donates a proton to the ammonia molecule. The ammonium ion is the conjugate acid of ammonia, a base, which receives a proton from water. Hydroxyl ion is the conjugate base.


In 1923, the same year that Bronsted and Lowry proposed their theories, Gilbert Newton Lewis, an American chemist, proposed an even broader definition of acids and bases. The same type of reasoning as Bronsted's and Lowry's led to his proposals, but Lewis focused on electron transfer instead of proton transfer. He defined an acid as an electron-pair acceptor, and a base as an electron-pair donor. This definition is more inclusive than the previous, and applies to solutions and reactions which do not even involve hydrogen and hydrogen ions. Consider the reaction between ammonia and boron trifluoride:

BF3 (g) + NH3(g) F3BNH3(g) (7)

The electron structure of boron trifluoride is:



Note that boron has an empty orbital, and can accept two more electrons in its valence level. Since boron trifluoride can accept an electron pair, it is a Lewis acid. Now consider the structure of ammonia:

ammonia.gif (1416 bytes)

Note that the nitrogen atom has an unshared electron pair, which can be donated to the boron. Ammonia is therefore a Lewis base, because it can donate an electron pair.

H3N + BF3 H3N:BF3


None of the preceding theories is incorrect. Each succeeding theory includes that of its predecessors. What is true for the most specialized (Arrhenius theory) is also true for the most general (Lewis theory).

The Arrhenius theory defines an acid as any substance which produces H+ ions in solution, and a base as any substance which produces OH- in solution. The Bronsted-Lowry theory defines an acid in the same way the Arrhenius theory defines an acid (as a proton donor), but widens the definition of base to include any substance which will accept a free proton. The Lewis theory does not enlarge the Bronsted-Lowry theory of a base, although it shifts the emphasis from protons to electrons. The Lewis theory broadens the Bronsted-Lowry theory of acids to include any substance which can accept an electron pair. Therefore, according the Lewis theory, any elements or compounds which form compounds by coordinate-covalent bonding may be thought of as acids or bases. Consider the ammonia in the ammonia gas-water reaction.

NH3 (g) + H2O (l) NH4+(aq) + OH-(aq) (8)

According to Arrhenius' theory, ammonia is a base because it produces OH- ion when placed in water. The Bronsted-Lowry theory classifies ammonia as a base because it accepts a proton from H2O. The Lewis theory classifies NH3 as a base because it donates an electron-pair to a proton. What is considered an acid or base in the simplest theory is also considered an acid or base in the more complex theories.


For our purposes, we will consider the Arrhenius theory of acids and bases because beginning chemists are primarily concerned with aqueous solutions involving either hydronium ions or hydroxide ions, or both. There is one exception: we will use the H3O+ ion instead of the H+ ion, because it is now accepted that free protons are so strongly attracted by the electrons of the water molecule that free hydrogen ions are effectively nonexistent. If we use the other theories, we will designate the acid or base as a Lewis acid or a Bronsted base, as example.

  1. All Arrhenius acids are compounds composed of hydrogen chemically united with a nonmetallic element or polyatomic ion.
  2. All acids turn blue litmus (an organic dye) red.
  3. Acids taste sour. Examples are lemon, grapefruit, and vinegar. It is possible to detect the presence of acid by tasting the solution. However, even in dilute solutions, this can be dangerous; it is not good laboratory procedure to say the least.
  4. A salt and water are produced when an acid reacts with a base.

    acid + base salt + water

    HBr + KOH KBr + H2O

    The resulting solution will be neutral (theoretically, neither acidic nor basic). This type of reaction is called a NEUTRALIZATION REACTION.

  5. Acids react with certain metals to form hydrogen gas.

    acid + metal H2(g) + salt

    2 HCl + Zn H2(g) + ZnCl2

  6. Acids react with metallic oxide to form salt and water.

    acid + metallic oxide salt + water

    2 HCl + CaO CaCl2+ H2O

  7. Acids react with carbonates to form a salt, water, and carbon dioxide gas.

    acid + carbonate salt + water + CO2

    2HCl + K2CO3 2 KCl + H2O + CO2

  8. Acids are produced by the action of water on oxides of nonmetals.

    Nonmetallic oxide + water acid

    CO2 + H2O H2CO3

    SO3 + H2O H2SO4

    P2O5+ H2O 2H3PO4


The hydroxides of the alkali metals (potassium and sodium) are called alkali bases, and those of the alkaline earth metals (barium, strontium, and calcium) are known as alkaline earth bases. The hydroxides of sodium, potassium, and barium are referred to as strong bases because they give a high concentration of hydroxide ions in aqueous solution. The hydroxides of the alkali metals are very soluble in water, those of the alkaline earth metals are moderately soluble, and all of the other metal hydroxides are only sparingly soluble. The properties which are common to hydroxide bases in aqueous solution are due to the presence of the hydroxide ion (OH-).

  1. All Arrhenius bases are compounds composed of hydroxide ion chemically united with a metallic element or polyatomic ion.
  2. All bases turn red litmus blue.
  3. Bases taste bitter. Examples are soap and lye. Solutions of bases often feel slippery.
  4. Salt and water are formed when a base is added to an acid.
  5. A base will react with a nonmetallic oxide to form salt and water.

    Base + nonmetallic oxide salt + water

    2 KOH + SO3 K2SO4+ H2O

  6. Bases are produced by the action of water on the oxides of alkali or alkaline earth metals.

    metallic oxide + water base

    Na2O + H2O 2 NaOH

    CaO + H2O Ca(OH)2


Acids react with bases to form salt and water. The water is formed by the union of hydrogen ion from the acid and hydroxide ion from the base. An acid is composed of positive hydrogen ion(s) combined with negative nonmetallic ion(s); a base is composed of negative hydroxide ion(s) combined with positive metallic ion(s). If the water formed when the hydrogen and hydroxide ions unite is evaporated, the negative ions of the acid will unite with the positive ions of the base to form a new compound. This ionic compound is called a SALT. A SALT IS A CRYSTALLINE COMPOUND COMPOSED OF THE NEGATIVE ION OF AN ACID AND THE POSITIVE ION OF A BASE.

acid + base water + salt

H2SO4+ 2 NaOH 2 H2O + Na2SO4

3 H2SO4+ 2 Al(OH)3 6 H2O + Al2(SO4)3

H3PO4+ 3 KOH 3 H2O + K3PO4


BINARY ACIDS are acids containing only two elements. Binary acids always contain the prefix HYDRO- and the suffix -IC. The stem is determined by the element combined with hydrogen. To name a binary acid, we determine what stem to use by finding what element is combined with hydrogen, For instance, chlorine will have the stem CHLOR, and fluorine the stem FLUOR. To this stem, the prefix HYDRO- and the suffix -IC are added. There are a few exceptions to the rule that binary acids begin with HYDRO- and end with -IC. One example is hydrocyanic acid, HCN, which really is ternary. These exceptions must be learned separately, but since they are not of great importance to us, HCN is the only one we will mention.

H2S Hydrosulfuric acid HF Hydrofluoric acid
HCl Hydrochloric acid HBr Hydrobromic acid
HI Hydroiodic acid


TERNARY ACIDS ARE ACIDS WHICH CONTAIN THREE ELEMENTS. Because almost all of the ternary acids we will be working with have oxygen as the third element, these are the only ones we will consider. We find the stem by determining what element is combined with oxygen and hydrogen in the acid molecule. We determine the prefix (if there is one) and the suffix by the number of oxygen atoms in each molecule. Generally, the most common form of the acid is given the suffix -IC. No prefix is used. Examples are sulfuric acid (H2SO4), chloric acid (HClO3), phosphoric acid (H3PO4), and nitric acid (HNO3). If a second acid is formed containing the same three elements, but having less oxygen, this acid is given the suffix -OUS. There is no prefix. Examples are sulfurous acid (H2SO3), chlorous acid (HClO2), phosphorous acid (H3PO3), and nitrous acid (HNO2).

If a third acid containing still less oxygen is formed, it is given the prefix HYPO- and the suffix -OUS. An example is hypochlorous acid (HClO).

Acids containing more oxygen than the common form are named by adding the prefix PER- to the common name. For example, perchloric acid (HClO4).


It is not possible, without experiment or previous knowledge, to know which form of acid is most common; or, for that matter, whether any given form exists. If the name of one form is known, the other ternary acid containing the same elements can usually be named. If only two acids are known to exist, the one which contains the most oxygen is usually given the suffix -IC, and the one having less oxygen is given the suffix -OUS. Examples are nitric acid (HNO3) and nitrous acid (HNO2). These rules, however, do not always hold. For instance, bromine forms only two acids with hydrogen and oxygen: HBrO and HBrO3. Instead of being named bromous and bromic acids, they are named hypobromous acid and bromic acid, because they contain the same number of oxygen atoms as hypochlorous acid and chloric acid.


Arrhenius bases are composed of metallic, or positively charged polyatomic ions, and negatively charged hydroxide ions. Bases are named by adding the word HYDROXIDE to the name of the positive ion. Examples are sodium hydroxide (NaOH), ammonium hydroxide (NH4OH), aluminum hydroxide Al(OH)3, and calcium hydroxide Ca(OH)2.


When sulfur dioxide (SO2) is dissolved in water, sulfurous acid is formed. When sulfur trioxide (SO3) is dissolved in water, some sulfuric acid is formed. Any oxygen-containing substance which will produce an acid, when dissolved in water, is called an ACID ANHYDRIDE. If sodium oxide (Na2O) is added to water, sodium hydroxide, a base, is formed. Any oxygen-containing substance which will produce a base, when dissolved in water, is called a BASIC ANHYDRIDE. The equations for the reactions just mentioned are:

SO2 + H2O H2SO3

SO3 + H2O H2SO4

Na2O + H2O 2 NaOH

Anhydride means "without water", so anhydrides may be classified as acids or bases with all the water removed. It might be more accurate and understandable if we say anhydrides are acids or bases with all the hydrogen removed in the form of water. Given a particular acid or base, we can determine its anhydride by removing two hydrogen atoms and one oxygen atom from its molecule (or molecules). For example:

2 HClO Cl2O + H2O

Ca(OH)2 CaO + H2O

The acid anhydride for hypochlorous acid, HClO, is Cl2O. The basic anhydride for calcium hydroxide is CaO.

In predicting anhydrides, two hydrogen atoms and one oxygen atom must always be removed as a unit. ENOUGH H2O UNITS MUST BE REMOVED TO LEAVE THE ANHYDRIDE WITHOUT ANY HYDROGEN. To form the anhydride for an acid like H3PO4, remove three water molecules from two phosphoric acid molecules to produce the anhydride, P2O5.

2 H3PO4 P2O5+ 3 H2O


Substances that give aqueous solutions which conduct an electric current are known as ELECTROLYTES. Molten salts which conduct an electric current are electrolytes also. The process of conducting an electric current through a solution or through a molten salt, which results in the decomposition of the electrolyte or the solvent, is called ELECTROLYSIS. Most electrolytes are acids, bases, or salts. Aqueous solutions of substances that give nonconducting solutions are called NONELECTROLYTES. The classification of substances as electrolytes and nonelectrolytes may be carried out experimentally by setting up a simple electrolytic cell. The terminals of a storage battery or a 100 volt circuit are connected through an electric lamp to two electrodes in a beaker. When the beaker is filled with pure water, and the current applied, the electric lamp bulb will fail to emit light. If, however, hydrochloric acid, sodium hydroxide, or sodium chloride is dissolved in the water, the lamp glows brightly. When an aqueous solution of sugar, alcohol, or glycerin is tested, the lamp does not glow.

If the beaker is filled with a 0.1 N solution of hydrochloric acid, the lamp in the circuit will glow brightly, showing that the solution is a good conductor of electricity. The same is true of 0.1 N solutions of nitric acid and sulfuric acid, as well as bases such as potassium, sodium, and barium hydroxides. Most salts behave in a similar fashion. Substances whose aqueous solutions are good conductors of electricity are known as STRONG ELECTROLYTES. When a 0.1 N solution of acetic acid or ammonium hydroxide is placed in the beaker, it is found that the lamp glows much less brightly than it does with acids like hydrochloric or bases like sodium hydroxide. Substances whose aqueous solutions are poor conductors of electricity are called WEAK ELECTROLYTES. Originally, the term weak electrolyte was given to liquid solutions which conducted an electric current only slightly. This definition has been extended as chemists have learned more about these substances. Now, a WEAK ELECTROLYTE is defined as a substance which ionizes only slightly in solution. In other words, equilibrium is established before much product is formed. Since such a solution contains few ions, and ions are what carry a current through a liquid, weak electrolytes are poor conductors. Strong acids and basesionize completely. Weak acids and bases ionize only slightly. Fortunately, there are few acids or bases which ionize almost completely or in some other partial way. This makes it possible for us to group acids and bases as either strong or weak with no intermediate groups.


A CONDITION OF EQUILIBRIUM IS REACHED IN A SYSTEM WHEN TWO OPPOSING CHANGES OCCUR SIMULTANEOUSLY AT THE SAME RATE. Most of our examples of equilibrium have been systems involving physical changes rather than chemical changes. For example, we have defined the vapor pressure of a liquid as the pressure exerted by a vapor in equilibrium with its liquid at a given temperature. The two opposing changes in this case are evaporation and condensation. An example of a chemical equilibrium is the reduction of steam by hot iron.

2 Fe + 3 H2O Fe2O3+ 3 H2

At equilibrium these two opposing chemical changes occur at the same rate. The equilibrium state of a given reversible reaction varies with the conditions under which the reaction takes place. A clear understanding of chemical equilibrium is possible only after reaction rates and the factors which influence them are studied.

THE RATE OF A CHEMICAL REACTION MAY BE DEFINED AS THE NUMBER OF MOLES OF A SUBSTANCE WHICH DISAPPEAR OR ARE FORMED BY THE REACTION PER UNIT VOLUME IN A UNIT OF TIME. The rates of reactions vary greatly. Most reactions involving ions in solution proceed vary rapidly. When solutions of sodium hydroxide and hydrochloric acid are mixed, neutralization occurs nearly instantaneously, and involves the union of hydronium ions and hydroxide ions with the formation of water. Reactions involving molecules in general are slower than those involving ions.

Before two or more molecules (or ions) can react, they must collide with one another. The only collisions which are effective are those involving molecules possessing an energy content higher than a certain minimum value, which is called ENERGY OF ACTIVATION. The collisions between the fast moving molecules are most apt to be effective ones. The total energy for a given reaction may involve the breaking of bonds in the reacting molecules as well as the formation of the new bonds which are present in the product molecules. Often in the process of breaking and forming bonds, a situation, referred to as a TRANSITION STATE for the reaction, arises in which an intermediate substance is formed. This intermediate substance is one which can then either change back to the original substance or go on to form the new products.

Most reactions involving ions in solution are rapid because the ions have a large attraction for each other and no additional energy is required to cause them to react. Practically every collision between ions which tend to combine is an effective one. Reaction rates depend upon many factors, some of the more important ones are:

  1. NATURE OF THE REACTION SUBSTANCES - Similar reactions involving different substances have different reaction rates under the same conditions. Calcium and sodium both react with water at ordinary temperatures, calcium at a moderate rate and sodium so rapidly that the reaction is of almost explosive violence.
  2. STATE OF SUBDIVISION - Except for substances in the gaseous state or in solution, the rate of reaction depends to a great extent on the size of the surface of contact between the two phases. Finely divided solids, because of their more extensive surfaces, react more rapidly than massive specimens of the same substance. For example, large pieces of coal burn slowly, smaller pieces more rapidly, and powdered coal may burn at an explosive rate.
  3. TEMPERATURE - It is common observation that chemical reactions are accelerated by increases in temperature. The oxidation of iron or coal is very slow at ordinary temperatures but proceeds rapidly at high temperatures. The student uses a burner in the laboratory to increase the speed of reactions which proceed slowly or even at an imperceptible rate at ordinary temperatures. It is a familiar fact that foods cook faster at higher temperatures than at lower ones. In many cases, the rate of a reaction in a homogeneous system is approximately doubled by an increase in temperature of only 10o.
  4. CATALYSIS - Many reactions can be accelerated or retarded by the presence of small amounts of substances which are not themselves permanently used up by the reaction. Such substances, called CATALYSTS, may be divided into two general classes: a) contact catalysts and b) those which form intermediate substances which in turn react and regenerate the catalyst.

    Contact catalysts act by furnishing a surface at which the reacting molecules are adsorbed and concentrated. Adsorption of molecules on the surface of the catalyst effectively reduces the energy necessary for activation and more collisions are therefore effective. In addition, the increase in concentration resulting from adsorption results in more collisions per unit of time, this increasing the velocity of the reaction.

    Many reactions of organic compounds are catalyzed by enzymes, which are complex proteins produced by living organisms. For example, the production of alcohol from sugars by fermentation is catalyzed by the enzyme zymase which is produced by yeast cells. The many chemical reactions that take place in living organisms, called METABOLIC PROCESSES, are catalyzed by enzymes.

  5. CONCENTRATION - At a fixed temperature and in the absence of a catalyst (or in the presence of a catalyst if the catalyst is present in fixed amount), the rate of a given reaction in solution is largely dependent upon the concentrations of the reacting substances. THE RATE OF A SIMPLE REACTION IS DIRECTLY PROPORTIONAL TO THE CONCENTRATION OF THE REACTION SUBSTANCES. This generalization is referred to as the LAW OF MASS ACTION.


Whenever the products of a chemical reaction are capable of reacting to form the reactants, two reactions are taking place simultaneously, the one tending to offset the other. As a consequence, such reactions do not go to completion and a state of equilibrium is attained. Most chemical reactions possess the quality of reversibility and do not go to completion.



If we apply the law of chemical equilibrium the constant for this equation may be expressed as follows:

K = (CH3COO-)(H3O+)/(CH3COOH)(H2O)

Acetic acid is a weak electrolyte and ionizes only slightly. This means that the CH3COO- and H3O+ ion concentrations are small, and the concentration of CH3COOH is almost unaffected by the ionization. When acetic acid ionizes, hydrogen ions are set free. These hydrogen ions attach to a water molecule and form the hydronium ion, H3O+. However, because acetic acid is a weak acid and ionizes only slightly few hydrogen ions are formed, and the concentration of water remains nearly constant. Since the concentration of water remains almost constant, we can multiply the concentration of water times the equilibrium constant and produce the equation:

K(water) = (CH3COO-)(H3O+)/(CH3COOH)

Because (H2O) is constant, K(water), the product of the equilibrium constant and the concentration of water, produces a new constant. This new constant is called the IONIZATION CONSTANT, and is given the symbol Ka. For any weak acid

HA + H2O A-+ H3O+

the ionization constant is:

Ka = (A-)(H3O+)/(HA)


The equilibrium existing in a chemical system may be shifted by increasing the rate of the forward or the reverse reaction. For the reversible reaction

A + B C + D

when the system is in equilibrium and an additional quantity of A or B is added, the rate of the forward reaction is increased because the concentration of the reacting molecules is increased. This means that the rate of the forward reaction will momentarily be greater than that of the reverse reaction; the system, then, is temporarily out of equilibrium. However, as the concentrations of C and D increase, the rate of the reverse reaction increases, whereas the decrease in the concentrations of A and B causes the rate of the forward reaction to decrease. The rates of the two reactions thereby soon become equal again and a new state of equilibrium is attained in which the molar concentrations of A,B,C, and D have changed; however, the ratio (C) (D) to (A)(B) is again equal to the original value of K. It is worth noting that at equilibrium the value of K remains unchanged even though the values of the reactants and the products have changed.

The effect of a change in concentration upon a system in equilibrium is an important application of the PRINCIPLE OF LE CHATELIER, which may be stated as follows: IF A STRESS, SUCH AS A CHANGE IN CONCENTRATION, PRESSURE, OR TEMPERATURE, IS APPLIED TO A SYSTEM IN EQUILIBRIUM, THE EQUILIBRIUM IS SHIFTED IN A WAY THAT TENDS TO UNDO THE EFFECT OF THE STRESS.


All chemical changes involve either the evolution of energy or the absorption of energy. In every system in equilibrium, an ENDOTHERMIC (absorption of heat) and EXOTHERMIC (release of heat) reaction is taking place simultaneously. The endothermic reaction is favored by an increase in temperature, the exothermic reaction by a decrease in temperature.

The effect of temperature changes upon systems in equilibrium may be summarized by the statement: WHEN THE TEMPERATURE OF A SYSTEM IN EQUILIBRIUM IS RAISED, THE EQUILIBRIUM IS DISPLACED IN SUCH A WAY THAT HEAT IS ABSORBED. This generalization is known as VAN'T HOFF'S LAW, which is a special case of Le Chatelier's principle.


When a weak electrolyte is dissolved in water, it ionizes only slightly. It is often desirable in such cases to know just how much of a certain kind of ion will be produced. The amount of ion present is usually expressed in terms of percent, and is called the PERCENT OF IONIZATION. For example, if we know the ionization constant of 0.1 M formic acid (HCOOH) to be 2.1 X 10-4, and we know that

Ka = (HCOO-)(H3O+)/(HCOOH)

we can find the molar concentration of either H3O+ OR HCOO-.

2.1 X 10-4 = (X)(X)/(0.1)

X2 = (2.1 X 10-4)(0.1)

X2 = 2.1 X 10-5

X2 = 21.0 X 10-6

X = 4.6 X 10-3

This value represents the molar concentration of either H3O+ OR HCOO-. We can now find the percent of ionization by the following method.

Percentage = Partial/Total X 100

% of ionization = (X)(0.1) X 100

% of ionization = (4.6 X 10-3)/(0.1) X 100

% of ionization = 4.6%


Water is an extremely weak electrolyte which undergoes self-ionization.

H2O + H2O H3O++ OH-

or simply

H20 H++ OH-

Application of the law of chemical equilibrium yields the expression

Ke = (H+)(OH-)/(H2O)

Conductivity experiments have indicated that pure water contains 1 X 10-7 moles of H+ (and the same amount of OH-) per liter. Therefore:

Ke = (10-7)(10-7)/(H2O)

We can find Ke if we can arrive at some value for (H2O). Since water ionizes so slightly, we can approximate the molar concentration of water in pure water by assuming that no ionization occurs. We assume that pure water contains no ions and no impurities, only un-ionized H2O molecules.

One mole of water weighs 18 grams (16 + 2). Concentration is expressed in moles per liter. One liter of pure water weighs 1000 grams. We can find the concentration of water in pure water by dividing 18 into 1000. Thus, a liter container will hold 55.6 moles of water.

We can now find Ke for water:

Ke = (10-7)(10-7)/(55.6)

Since the concentration of water remains almost constant, we can multiply the concentration of water times the equilibrium constant and produce the equation:

Ke = (10-7)(10-7)

Ke = 10-14

We will call this new constant the ION PRODUCT CONSTANT OF WATER, Kw.

Kw = (H+)(OH-)

Kw = 10-14

Kw is a constant for all aqueous solutions. This indicates that, although the concentration of H3O+ and OH- may change when acids or bases are added to water, the product of H3O+ and OH- remains the same:

(H3O+)(OH-) = 10-14


The ionization of water is so slight that it is almost never considered in the actual production or use of acids and bases. Why, then, was it introduced? Knowledge of the ion product constant for water has enabled chemists to develop a simple scale, called the pH scale, which can be used to indicate the acidity or basicity of any water solution. pH is an expression of the hydrogen ion concentration in terms of the negative logarithm of the hydrogen ion concentration.

pH = -log(H+)

EXAMPLE: Calculate the pH of 0.01 M HCl. Hydrochloric acid is completely ionized in dilute solution so the concentration of the hydrogen ion is 0.01 M, or 10-2 M.

pH = -log(H+)

pH = -log(10-2)

pH = -(-2)

pH = 2

EXAMPLE: Calculate the pH of 0.0050 M HNO3. The hydrogen ion concentration of nitric acid is the same as the molar concentration of the acid, for it is a strong electrolyte.

pH = -log(H+)

pH = -log(5.0 X 10-3)

pH = -(log 5.0 + log 10-3)

pH = -(0.6990 + (-3))

pH = -(0.6990 - 3)

pH = -0.6990 + 3

pH = 2.3010

The pH scale indicates the degree of acidity or basicity of a solution. This scale extends from the numerical values of 1 to 14 with 1 indicating a relatively strong acid and 14 a relatively strong base, 7 being the pH of water or a neutral solution.

Acid Neutral Base

1 7 14

It should now appear evident that by the utilization of the equation for the law of chemical equilibrium and the formula for finding pH we can determine the pH of weak acids and bases as well as strong acids and bases.

EXAMPLE: What is the molar concentration of the hydrogen ion (H+) and the pH of a 0.02 M solution of acetic acid (CH3COOH)? The Ka for acetic acid is 1.8 X 10-5.


Ka = (CH3COO-)(H+)/(CH3COOH)

1.8 X 10-5/(0.02) = (X)(X)

X2 = (1.8 X 10-5)(0.02)

X2 = 3.6 X 10-7

X2 = 36 X 10-8

X = 6 X 10-4

This value represents the molar concentration of the hydrogen ion, 0.0006 M. We can now find the pH using the following method.

pH = -log(H+)

pH = -log(6 X 10-4)

pH = -(log 6.0 + log 10-4)

pH = -(0.7782 + (-4))

pH = -(0.7782 - 4)

pH = -0.7782 + 4

pH = 3.2218

This value represents the pH of a 0.02 molar solution of acetic acid. In order to determine the pH of a weak acid it is necessary to apply the law of chemical equilibrium to determine first the (H+), because weak acids only partially ionize.


Certain organic substances have the property of changing color in dilute solution when the hydrogen ion concentration of the solution attains a definite value. Such substances like phenolphthalein, which is colorless in an acid solution but becomes pink or red in a basic solution, are called ACID-BASE INDICATORS. Chemical indicators are acid-base conjugate pairs whose acid form and base form are different in color. They are often employed for the determination of the pH of solutions. The most common indicators in addition to phenolphthalein are litmus and methyl orange. Litmus is an organic dye which is red as an acid and blue as a base. Methyl orange forms an orange solution which turns yellow in basic solution and red in acidic solutions. Solutions in which they are to be successfully used must be colorless, or the color of the solution may mask the color changes of the indicator.

A large number of acid-base indicators are known, covering a wide range of pH values. A number of indicators may be used in determining the pH of any solution, and by the process of elimination the pH of a solution can be fixed within rather narrow limits. The following is a partial listing.

Methyl violet yellow 0-1.6 violet
Thymol blue pink 1.2-2.8 yellow
Methyl yellow red 2.9-4.0 yellow
Brom-phenol blue yellow 3.0-4.7 violet
Methyl Orange pink 3.1-4.4 yellow
Brom-cresol green yellow 3.8-5.4 blue
Methyl red red 4.2-6.2 yellow
Litmus red 4.7-8.2 blue
Chlorophenol red yellow 4.8-6.4 red
Brom-cresol purple yellow 5.2-6.8 purple
Bromothymol blue yellow 6.0-7.6 blue
Phenol red yellow 6.4-8.0 red
Cresol purple yellow 7.4-9.0 purple
Thymol blue yellow 8.0-9.6 blue
Phenolphthalein colorless 8.0-9.8 pink
Thymolphthalein colorless 9.3-10.5 blue
Alizarin yellow G colorless 10.1-12.1 yellow
Indigo Carmine blue 11.4-13.0 yellow
Trinitrobenzene colorless 12.0-14.3 orange

The measurement and control of the hydrogen ion concentration is important in scientific investigations, in industry, and in agriculture. In analytical chemistry the separation and identification of many of the metallic ions depend upon the pH of the solutions containing these ions.



The determination of the concentration of acidic solutions of unknown normality (Section 7.13) by means of standard basic solutions is known as ACIDIMETRY. If an acid is added to a base, a neutralization reaction occurs. The acid unites with the base to form salt and water:

Acid + Base Salt + Water

The quantity of acid in a solution of known volume is determined by measuring the volume of base of known normality (standard solution) required to neutralize the acid. An indicator which changes color at the point of neutralization or END POINT is used to indicate that equivalent amounts of acid and base have been brought together. A pH indicator is a material, usually an orgainc dye, that is one color above a characteristic pH and another color below that pH. There are many materials that can serve as pH indicators, each with its own pH range at which it changes color. Some have more than one color change at distinct pH's. Litmus and phenolphthalein are common pH indicators. Litmus is red in acid (below pH 4.7) and blue in base (above pH 8.1). Phenolphthalein is clear in acid (below pH 8.4) and pink-purple in base (above pH 9.9). These ranges may seem large, but near the EQUIVALENCE POINT, the point at which the materials are equal, there is a large change in pH. The equivalence point may not occur at pH 7, neutral pH, so the appropriate pH indicator must be chosen for the type of acid and base being titrated. The base is added drop by drop to the acid from a BURET (shown at left); this process is called TITRATION. The use of standard acid solutions to determine the concentration of basic solutions of unknown normality is called ALKALIMETRY. The most commonly used indicator in running a titration is phenolphthalein because of its ability to change color at a pH near neutrality. 

A measured amount of the unknown material in a flask with indicator is usually combined with the known material from a buret.  The buret is marked with the volume of liquid by a scale with zero on top and (usually) fifty milliliters on the bottom. The buret has some type of valve at the bottom that can dispense the contained liquid.

It is not necessary to begin the titration with the level in the buret at the zero mark, but the level must be within the portion of the buret that is marked. The buret on the left represents about 48.2 ml of the yellow liquid. Most laboratory burets can be read to an accuracy of one hundredth of a milliliter. (Most burets show the ten divisions of a milliliter allowing one to interpolate between the marks.) One reads the buret by getting at eye level to the bottom of the meniscus (curve in the liquid) and comparing the bottom of the meniscus to the marks on the glass. A reading of the buret is taken before and at the end of the titration. The amount of known concentration liquid used is the difference between the beginning and ending buret reading.

The volume of the material of unknown concentration is known by how much is put into the reaction vessel. The concentration of the standard is known, and its volume is known from the measurement of liquid used in the titration.

The equivalents of acid can be calculated by multiplying the normality of the acid solution by its volume:

Na x Va= equivalents of acid

The equivalents of base in the titrated solution are equivalent to the normality of the basic solution times the volume of the solution:

Nb x Vb= equivalents of base

If you have a monobasic base and a monoprotic acid, you can simplify the formula for titration to: if Na = the concentration of the acid and Nb = the concentration of the base and Va = the volume of acid solution and Vb = the volume of base.  At the point of neutralization, or end point (also known as STOICHIOMETRIC POINT), the number of equivalents of acid equals the number of equivalents of base. This may be represented in formula form as:

Na x Va= Nb x Vb


EXAMPLE: What concentration (Na) will 48.2 ml (Va) of CH3COOH have if it requires 96.4 ml (Vb) of 0.25 N (Na) KOH to neutralize the solution?

Na x Va= Nb x Vb

(Na)(48.2 ml) = (0.25 N)(96.4 ml)

Na = (0.25 N)(96.4 ml)/(48.2 ml)

Na = .5 N

An acid-base titration is good to consider when learning the method, but there are more uses for the technique.  The measure of oxalate ion using potassium permanganate in a warm acid environment is a good example of a redox titration. The Mohr titration is a determination of chloride concentration using known silver nitrate solution and sodium dichromate as indicator.

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Copyright May 1987 James R. Fromm (mailto:jfromm@3rd1000.com) (Revised March 2000)