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Formula

Columbia Electronic Encyclopedia - Cite This Source

formula, in chemistry, an expression showing the chemical composition of a compound. Formulas of compounds are used in writing the equations (see chemical equations) that represent chemical reactions. Compounds are combinations in fixed proportions of the chemical elements. The smallest unit of an element is the atom.

Formulas for Compounds

The formula of a well-known compound, water, is H₂O. Water is made up of molecules, and the formula shows that each molecule consists of two atoms of hydrogen, H, bonded to an atom of oxygen, O. The subscript 2 indicates that there are two atoms of hydrogen in the molecule; where no subscript appears, as after the O, the subscript 1 is implied. It should be kept in mind that not all compounds are molecular. For example, sodium chloride, NaCl, is an ionic rather than a molecular compound. Solid sodium chloride consists of a collection of sodium ions and chloride ions arranged in a regular, three-dimensional pattern called a crystalline structure. One cannot say that a certain sodium ion and a certain chloride ion are grouped together into a unit, since each sodium ion is equally associated with all its neighboring chloride ions and each chloride ion is equally associated with all its neighboring sodium ions. The formula NaCl, therefore, cannot be taken as showing the composition of some particular unit, such as a molecule. Rather, it shows the proportion of the atoms of each element making up the compound—in this case, one atom of sodium to every atom of chlorine; such a formula is called an empirical formula.

Molecular and Empirical Formulas

If a compound is molecular, the molecular formula is preferred to the empirical formula since it gives more information. A molecule of glucose, for example, consists of 6 carbon atoms, 12 hydrogen atoms, and 6 oxygen atoms. Its molecular formula, C₆H₁₂O₆, displays this information explicitly; the empirical formula is CH₂O. From the formula one can also deduce the proportion of the atoms of each element making up the compound: one atom of carbon to every two atoms of hydrogen to every one atom of oxygen (6 : 12 : 6=1 : 2 : 1). The empirical formula of glucose, CH₂O, shows only the proportion, not the actual number of atoms.

Many compounds may have the same empirical formula. For example, formaldehyde, each molecule of which consists of one carbon atom, two hydrogen atoms, and one oxygen atom, has the molecular formula CH₂O, which is identical to the empirical formula of glucose. Another example is furnished by ethyne (acetylene), whose molecular formula is C₂H₂, and benzene, whose molecular formula is C₆H₆. Both have the same empirical formula, CH.

In addition to showing the actual number of atoms, molecular formulas are also more useful than empirical formulas in that they explicitly show radicals. For example, the molecular formula for the compound aluminum sulfate, Al₂(SO₄)₃, shows that it contains three sulfate radicals (SO₄). The empirical formula, Al₂S₃O₁₂, does not show this. When only one radical is present in the molecule, the parentheses and subscript are omitted, e.g., CuSO₄ for cupric sulfate. Other groups are also shown in molecular formulas, e.g., the water molecules in the mineral chalcanthite (blue vitriol), which consists of cupric sulfate atoms to each of which are attached five water molecules. Its molecular formula is CuSO₄·5H₂O, its empirical formula CuSO₉H₁₀.

Structural Formulas

In many cases, especially with organic compounds, even the molecular formula does not provide enough information to identify a compound, so that structural formulas are needed. For example, both ethanol (ethyl alcohol) and dimethyl ether have the molecular formula C₂H₆O (see isomer). Their structural formulas are:In these formulas each line represents a single covalent chemical bond. A double bond is represented by a double line and a triple bond by a triple line. In ethene (ethylene), C₂H₄, the carbon atoms are joined by a double bond. The structural formula of ethene is:(In many representations of structural formulas, the angles of the lines indicating bonds do not necessarily have meaning.) In ethyne (acetylene), C₂H₂, the carbon atoms are joined by a triple bond. The structural formula of ethyne is:

Semistructural Formulas

Structural formulas are often simplified so that they can be written on a single line; the simplified formulas are often called semistructural formulas. The semistructural formula for ethanol is CH₃CH₂OH, or more simply C₂H₅OH. In such a semistructural formula the OH is written explicitly to indicate that the oxygen has a hydrogen bonded to it. The C₂H₅ indicates that the two carbon atoms are bonded to one another. The semistructural formula for dimethyl ether may be written CH₃OCH₃. Here the O is placed between the two carbon atoms to show that the carbons are bonded to the oxygen. A carbon often has three hydrogens bonded to it, and the H₃ is written after the C. In some cases the H₃ is written before the C for clarity; thus the formula for dimethyl ether might be written H₃COCH₃.

Electron Dot Diagrams

Dots are used in a type of formula called the electron dot diagram, where each pair of dots represents a pair of shared electrons in a covalent bond. The diagrams for ethane (CH₃CH₃), ethene, and ethyne are:

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Formula

Columbia Electronic Encyclopedia - Cite This Source

formula, in mathematics and physics, equation expressing a definite fixed relationship between certain quantities. The quantities are usually expressed by letters, and their relationship is indicated by algebraic symbols. For example, A=πr² is the formula for the area A of a circle of radius r, and s=1/2at² is the formula for the distance s traveled by a body experiencing an acceleration a during a time interval t.

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