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Bases are considered the chemical opposite of acids because of their ability to neutralize acids. In 1887 the Swedish physicist and chemist Svante Arrhenius defined a base as the chemical substance that produces hydroxide ions (OH) and cations. A typical base, according to the Arrhenius definition, is sodium hydroxide (NaOH). The neutralization of an acid with a base to yield salt and water may be represented as

HCl (aq ) + KOH (aq ) H2O (l ) + KCl (aq )          (1)

A major problem with Arrhenius's definition of bases is that several chemical compounds, such as NaHCO3, Na2CO3, Na3PO4, which produce basic solutions when dissolved in water, do not contain hydroxide ions. The Brønsted-Lowry theory, which was proposed independently by Danish chemist Johannes Brønsted and English chemist Thomas Lowry in 1923, states that a base accepts hydrogen ions and an acid donates hydrogen ions. This theory not only includes all bases containing hydroxide ions, but also covers any chemical species that are able to accept hydrogen ions in aqueous solution . For example, when sodium carbonate is dissolved in solution, the carbonate ion accepts a hydrogen ion from water to form the bicarbonate ion and hydroxide ion.


The Brønsted-Lowry theory includes water as a reactant and considers its acidity or basicity. In reaction (2) a new acid and base are formed, which are called the conjugate acid and conjugate base, respectively.

The strength of a base is determined by the extent of its ionization in aqueous solution. Strong bases, such as NaOH, are 100 percent ionized in aqueous solution and weak bases, such as ammonia, are only partially ionized in aqueous solution.


The partial ionization is a dynamic equilibrium , as indicated by the double arrow in equation (3).

The strength of acids and bases also determines the strength of their conjugate bases and conjugate acids, respectively. Weak acids and bases have strong conjugate bases and acids. For example, when ammonium chloride is dissolved in water, it gives an acidic solution because ammonium ion is a strong conjugate acid of the weak base ammonia, but chloride ion is a weak conjugate base of the strong acid hydrochloric acid.

NH4+ (aq ) + H2O (l ) NH3 (aq ) + H3O+ (aq )          (4)

The carbonate ion in equation (2) yields a basic solution because it is the strong conjugate base of the weak acid HCO3.

When NaHCO3 is dissolved in water, it gives a basic solution, even though a hydrogen ion is available. Predicting this requires one to consider the strength of carbonic acid, H2CO3, which is a very weak acid.

H2CO3 (aq ) + H2O (l ) HCO3 (aq ) + H3O+ (aq )          (5)

However, HCO3 will act as an acid if a strong base is added.

HCO3 (aq ) + OH (aq ) H2O (l ) + CO32 (aq )          (6)

This ability to act as a base or an acid is called amphoterism. Any anions of polyprotic acids, such as HCO3, H2PO4, and HPO42, which contain replaceable hydrogen ions, are amphoteric. Some hydroxides, such as Al(OH)3 and Zn(OH)2, are also amphoteric, reacting with a base or acid, as illustrated by the following equations:

Al(OH)3 (s ) + OH (aq ) Al(OH)4 (aq )          (7)

Al(OH)3 (s ) + 3 H3O+ (aq ) Al3+ (aq ) + 6 H2O (l )          (8)

Equations (7) and (8) can also be explained by American chemist Gilbert Lewis's acid-base theory. A Lewis acid is a substance that can accept a pair of electrons to form a new bond, and a Lewis base is a substance that can donate a pair of electrons to form a new bond.


All Arrhenius and Brønsted-Lowry bases are also Lewis bases. All metal cations are potential Lewis acids. Complexes of metal ions with water, ammonia, and hydroxide ion are examples of Lewis acid-base reactions. For example, [Al(H2O)6]3+ may be regarded as a combination of the Lewis acid, Al3+, with six electron pairs from six H2O molecules.

Buffer solutions contain a base and an acid that can react with an added acid or base, respectively, and they maintain a pH very close to the original value. Buffers usually consist of approximately equal quantities of a weak acid and its conjugate base, or a weak base and its conjugate acid. For example, one of the buffers used to keep the pH of the blood near 7.45 is the H2PO4/HPO42 acid/conjugate base system. Small amounts of an acid or base react with one of the components of the buffer mixture to produce the other component as follows:

H2PO4 (aq ) + OH (aq ) H2O (l ) + HPO42 (aq )          (10)

HPO42 (aq ) + H3O+ (aq ) H2O (l ) + H2PO4 (aq )          (11)

see also Acid-Base Chemistry; Arrhenius, Svante; BrØnsted, Johannes Nicolaus; Chemical Reactions; Lewis, Gilbert N.; Solution Chemistry.

Melvin D. Joesten


Joesten, Melvin D., and Wood, James L. (1996). The World of Chemistry, 2nd edition. Fort Worth, TX: Saunders College.

Moore, John W.; Stanitski, Conrad L.; Wood, James L.; Kotz, John C.; and Joesten, Melvin D. (1998). The Chemical World, 2nd edition. Philadelphia: Saunders.

Internet Resources

Carpi, Anthony. "Acids and Bases: An Introduction." Visionlearning. Available from <>.

"CHEMystery: An Interactive Guide to Chemistry." Available from <>.

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Although the number system commonly used for counting and measuring is based on the number 10 and is known as the decimal system, there are counting systems based on other numbers. For example, base-2 and base-60 number systems are also used for counting. Base-2, known as the binary number system, is used in electronic computers and other electrical devices. Time on a clock is partially measured in the base-60 system. Each hour is divided into 60 minutes and each minute is divided into 60 seconds. This entry will introduce the base-10 and base-2 number systems.

Base-10 Number System

Because humans have ten fingers, objects are naturally grouped in tens when counting. Counting a dozen apples with one's fingers consists of counting up to ten and then repeating the count, which results in one 10 plus two 1s. So all numbers in this base-10 system are made from just ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

For example, there are 365 days in a year. In the base-10 number system, the value of each of the three digits 3, 6, and 5 depends on their position. Starting from the left, the 3 stands for 3 hundreds; the 6 stands for 6 tens; the 5 stands for 5 ones, or units. So,

365 = (3 × 100) + (6 × 10) + (5 × 1).

Using exponents, 100 = 102, 10 = 101, and 1 = 100. So,

365 = (3 × 102) + (6 × 101) + (5 × 100).

In a similar fashion, 2,030 is expressed as (2 × 103) + (0 × 102) + (3 × 101) + (0 × 100).

Base-2 Number System

Whereas the base-10 number system is naturally suited to humans, base-2 is suited to computers and other devices that run on electricity. The electric current has two stateson and off. A computer is programmed to compute with groups of two using the binary number system.*

*The word "binary" means "comprised of two."

In base-10, a number is expressed in terms of the sum of multiples of 10: 100, 101, 102, and so on. But in base-2, a number is expressed in terms of the sum of multiples of 2: 20, 21, 22, and so on. This basically means that objects are grouped in twos. The following example shows how to express four base-10 digits in binary form.

2 (one group of two) (1 × 21) + (0 × 20) + 10

3 (one group of two plus one) = (1 × 21) + (1 × 20) = 11

4 (two groups of two; same as one group of four) = (1 × 22) + (0 × 21) + (0 × 20) = 100

5 (one group of four plus one) = (1 × 22) + (0 × 21) + (1 × 20) = 101

The binary number 1011, for example, is equal to (1 × 23) + (0 × 22) + (1 × 21) + (1 × 20), which in base-10 equals 11. So the binary (base-2) number 1011 and the decimal (base-10) number 1,011 represent totally different values.

see also Computers and the Binary System; Decimals; Powers and Exponents; Time, Measurement of.

Rafiq Ladhani


Amdahl, Kenn, and Jim Loats. Algebra Unplugged. Broomfield, CO: Clearwater Publishing Co., 1995.

Miller, Charles D., Vern E. Heeren, and E. John Hornsby, Jr. Mathematical Ideas, 9th ed. Boston: Addison-Wesley, 2001.

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Bases were a form of skirt, worn by upper-class members of the military, that were a striking departure from typical men's costume of the sixteenth century. During this period, most men wore a doublet, a slightly padded short overshirt, with hose and breeches. The bases replaced the hose and breeches. They were made of stiff, heavy cloth, and consisted of panels of fabric, often in alternating colors. The panels were attached to an inner lining in such a way as to make each of the panels either rounded or pleated. These skirts were worn for ceremonial purposes throughout Europe, especially for the large military reviews that allowed European armies to show off their strength. Men typically wore form-fitting leg stockings beneath the bases.


Payne, Blanche, Geitel Winakor, and Jane Farrell-Beck. The History of Costume. 2nd ed. New York: HarperCollins, 1992.

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ba·ses / ˈbāsēz/ • plural form of basis.

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