Chemical formulas and combinations

Type of physical science: Chemistry

Field of study: Chemical reactions

Chemical formulas are ways of indicating which elements are present in a substance and the relative numbers of atoms of the different elements. Such information is important in understanding the chemical and physical behavior of materials.

Overview

"Chemical combination" refers to the characterization of materials in terms of their constituent elements. This is accomplished via chemical formulas, which indicate the elements present in materials as well as the relative numbers of atoms of these elements.

When materials (or "substances") decompose, they break apart, usually into two or more different materials. Usually, decomposition is in response to some external action. If an electric current is passed through water, the water decomposes into two other gaseous substances, hydrogen and oxygen. Seemingly, the materials hydrogen and oxygen are "contained in" the substance water. Similarly, if ordinary table salt is heated to a temperature sufficient to melt it, and if an electric current is then passed through the melt, the salt decomposes into two other materials, chlorine and sodium. Again, it can be concluded that the substances sodium and chlorine are somehow bound together in salt.

Not all materials decompose as easily as water and salt. Neither the hydrogen nor the oxygen produced as a result of the decomposition of water is decomposable under ordinary chemical circumstances. The same is true of the chlorine and sodium generated via the decomposition of salt. Substances such as these are viewed as the building blocks of chemistry.

They apparently do not contain "simpler" substances, for if they did, they would be decomposable into them. Such building blocks are called elements. Slightly more than one hundred elements are currently known. Each is given a special one- or two-letter symbol: H for hydrogen, C for carbon, O for oxygen, Cl for chlorine, Na for sodium, and so on. Nearly 80 percent of all known elements are metals. Metals are materials that are good conductors of electricity and heat, and good reflectors of light. Sodium, iron, and calcium are common examples. The other roughly 20 percent of elements are nonmetals; nonmetals typically have properties opposite those of metals. Hydrogen, carbon, oxygen, and chlorine are examples.

If a substance can be decomposed into elements, the original material is called a compound. Water and salt are two familiar compounds. In fact, virtually all materials are compounds.

There is a close connection between the concept of an element and that of an atom.

Atoms are the most fundamental units that characterize elements. Each atom is an unimaginably small entity consisting of a very tiny, very massive, positively charged region called the nucleus, and, at great distance away and in very rapid motion, a set of light, negatively charged electrons.

The positive charge of the nucleus, as well as much of its mass, derives from protons. Each proton carries a single unit of positive charge (represented as +1). Each electron is much lighter than a proton, and each carries a single unit of negative charge (represented as -1). Charge-wise, protons and electrons cancel one another. Since all atoms are electrically neutral (that is, carry no net charge), each atom must have equal numbers of protons and electrons; this number is called the atomic number. The atomic number is what characterizes atoms of a particular element. For example, the atomic number of iron is 26, so every iron atom contains twenty-six protons and twenty-six electrons.

While each atom has an indescribably minuscule mass, if enough atoms are brought together, the mass of the entire collection may become substantial. For various reasons, it has become customary to consider a collection consisting of 6.02 x 10²³ atoms; his enormously large number is called Avogadro's number. Why such a seemingly peculiar number is chosen will not be of concern here. Suffice it to say that Avogadro's number of hydrogen atoms is found to have a mass of 1.0 gram. Similarly, Avogadro's number of carbon and oxygen atoms have masses of 12.0 grams and 16.0 grams, respectively. The mass of Avogadro's numbers of atoms is called the "gram-atomic mass" of the element.

It is convenient to define one mole of atoms as being equal to Avogadro's number of atoms. One mole of oxygen atoms contains Avogadro's number of oxygen atoms and has a mass of 16.0 grams; one mole of chlorine atoms contains Avogadro's number of chlorine atoms and has a mass of 35.5 grams, and so on. Fundamentally, moles are counting units for large numbers of items, much as dozen and gross are counting units for large numbers of things.

As was noted, water can be decomposed into the elements hydrogen and oxygen. This implies that water is composed of hydrogen and oxygen atoms. There are twice as many hydrogen atoms as oxygen atoms in the entire substance. To describe this circumstance, one associates an empirical formula with water. The empirical formula (also called the formula unit) is a listing of the elements present, with subscripts used to indicate the relative proportions of the atoms of these elements. The empirical formula of water is therefore H₂O. This means simply that there are two hydrogen atoms for each oxygen atom. The empirical formula of table salt is NaCl, indicating that for each sodium atom there is one chlorine atom. If compounds contain a mixture of metals and nonmetals, it is customary to list the metal(s) first in the formula unit; hence, Na precedes Cl in the empirical formula of table salt. Every compound has an empirical formula. Other common examples include: hydrogen peroxide, HO; Epsom salts, MgSO₄ (Mg and S are the element symbols for magnesium and sulfur, respectively); aspirin, C₉H₈O₄ and benzene (an important solvent), CH.

The mole concept can be extended to empirical formulas. One mole of NaCl means Avogadro's number of NaCl formula units, each unit consisting of one sodium and one chlorine.

One mole of water means Avogadro's number of H₂O formula units, each consisting of two hydrogens and one oxygen.

Every chemical substance has an empirical formula, which, as we have seen, is a listing of the elements present with subscripts indicative of the relative number of atoms of each element. Many substances have only an empirical formula. There are some compounds, however, that are molecular; chiefly, these are compounds composed only of nonmetals. In molecular compounds, there are no free, unattached atoms. Instead, the atoms coalesce to some extent to form larger entities called molecules. The atoms in a molecule are held to one another via covalent bonds (or "chemical bonds"). These bonds result from a sharing of electrons among the atoms in the molecule. Functionally, the bonds act like bits of atomic glue, binding the atoms together into a coherent, stable whole. Water is a molecular compound. While one speaks of water as containing hydrogen and oxygen atoms, in fact no free atoms exist in water. Rather, water consists of molecules, each having a central oxygen atom connected to two hydrogen atoms; schematically, H-O-H. The single lines, -, represent the covalent bonds that hold the atoms one to another. A glass of water consists of an enormously large number of these molecules, all stacked next to and around one another. Hydrogen peroxide is also molecular, each molecule consisting of two oxygen atoms bonded to each other, and each also connected to a hydrogen atom: schematically, H=O=O=H. Finally, benzene is a molecular compound. Each molecule consists of six carbon atoms, connected so as to form a hexagon; a single hydrogen atom is also connected to each carbon.

Molecular compounds can be assigned molecular formulas. These are a listing of the elements present, with subscripts indicating the number of each type of atom in a single molecule. Thus, the molecular formulas of water, hydrogen peroxide, and benzene are H₂O, H₂O₂, and C₆H₆, respectively. The molecular formula conveys all the information found in the empirical formula, and more. For example, both the empirical formula (CH) and the molecular formula (C₆H₆) of benzene show that carbon and hydrogen atoms occur in a 1:1 proportion. The molecular formula tells, in addition, how many of each type of atom are represented in a single molecule. Molecular formulas are more desirable than their empirical counterparts; remember, however, that not all compounds have molecular formulas. Some compounds (such as table salt) do not consist of molecules, and so have only empirical formulas.

A question now presents itself in the case of molecular compounds whose empirical and molecular formulas differ: Does "one mole of hydrogen peroxide," for example, mean Avogadro's number of HO formula units, which would have a mass of 17.0 grams, or Avogadro's number of real H₂O₂ molecules, which would have a mass of exactly twice as much? Likewise, does one mole of benzene mean Avogadro's number of CH formula units, with a mass of 13.0 grams, or does it mean Avogadro's number of real C₆H₆ molecules, with a mass of exactly six times as much? The general convention is that one mole of a molecular material indicates Avogadro's number of real molecules, and not Avogadro's number of formula units.

One final clarification is in order. Earlier, a correspondence was established between the concepts of atoms and elements, in that each element consists of basically one and only one kind of atom. All chlorine atoms have seventeen protons and electrons, for example. Perhaps the impression was given that elements, therefore, actually consist of free, unencumbered atoms.

This may or may not be true. Metallic elements do tend to consist of atoms packed closely together to form a solid, under ordinary conditions of pressure and temperature; mercury, a liquid, is the only common exception. A few nonmetals, notably the noble gases (helium, neon, argon, and a few others), exist as atomic gases under common conditions. But the remainder of the nonmetallic elements exist as molecules. A variety of nonmetals, including hydrogen, nitrogen, oxygen, and chlorine, exist as diatomic (or two-atom) molecules, and therefore have molecular formulas such as H₂, O₂, C_l2, and so on. Phosphorus (P) and sulfur exist as even larger molecules, P₄ and S₈, respectively. Carbon exists in two molecular forms, diamond and graphite, both of which represent such giant molecules that it is impossible even to give meaningful molecular formulas. For molecular elements, another paradox arises; namely, does one mole of hydrogen, say, mean Avogadro's number of hydrogen atoms, with a mass of 1.0 gram, or does it mean Avogadro's number of H2 molecules, with a mass of 2.0 grams? The usual convention here is that, unless specified otherwise, one mole of an element means Avogadro's number of molecules, if the element is molecular.

Applications

It is of great importance in chemistry to be able to characterize the nature and structures of materials at the atomic or molecular level. There exist a wide variety of experimental techniques for determining what certain regions or portions of a molecule might look like.

Evidence might suggest that, at one point in the molecule, there is a carbon atom bonded to an oxygen atom, or a hydrogen atom bonded to an oxygen atom. Other analysis might indicate the presence of a methyl group (a carbon atom linked to three hydrogens) adjacent to a methylene group (a carbon atom bonded to two hydrogen atoms). If enough of this sort of information is available, it is possible to make one or more guesses as to how all the pieces fit together, that is, to predict the precise substance of the molecule. One test of such hypotheses is to determine the molecular formula experimentally and see if it matches any of the predictions. Molecular formulas can be determined in a variety of ways. Commonly, one sets about first determining the percentage of each element, by mass, in the compound. This information, coupled with known gram-atomic masses for the elements, allows determination of the empirical formula. Other experiments permit one to determine how the empirical and molecular formulas are related, and so to determine, experimentally, the molecular formula. If the molecular formula so determined is consistent with that proposed by other studies, there is strong evidence that the proposed structure is correct. Besides offering corroborative evidence for the correctness of a proposed substance, empirical and molecular formulas often contain suggestions about the ultimate structure of the material under consideration, as in the following example. Molecules, like atoms, are electrically neutral. Sometimes, however, a group of atoms held together by covalent bonds can gain or lose one or more electrons. This gives the molecule a net negative or positive charge.

Such charged molecules are called polyatomic ions. The sulfate ion, for example, consists of a central sulfur atom bonded to four oxygen atoms. The group of five atoms also contains two extra electrons, and so, as a group, carries a -2 charge. The formula of sulfate is therefore SO₄ to the power of -2. Note that the net charge is included as a superscript. Many other polyatomic ions exist. For example, ammonium has a central nitrogen atom linked to four hydrogen atoms. Here, the collection has lost an electron, and carries a net plus-one charge: NH₄⁺. The plus-one charge derives from a proton whose charge is no longer canceled by the missing electron. Polyatomic ions such as sulfate and ammonium are common to many materials. Thus, if one had a compound that had as its empirical formula N₂H₈SO₄, one might guess (correctly) that the actual structure of the material consisted of two ammonium ions (which account for N₂H₈⁺²) and a sulfate ion (which contributes SO₄^-2). Note that the total charge on the two ammonium ions (+2) exactly cancels the charge on the sulfate (-2) so the compound is neutral overall.

Formulas also are capable of imparting tremendous insight into the chemical nature of a material. Nearly everyone has seen a demonstration of the "baking soda volcano," in which a mixture of vinegar and baking soda froths and bubbles quite vigorously. This behavior is easy to understand given the formulas of the participants. Baking soda is sodium bicarbonate, the empirical formula of which is NaHCO₃. It contains the polyatomic ion HCO₃. Vinegar, on the other hand, is a mixture of acetic acid and water. Acetic acid is a molecular compound having the molecular formula C₂H₄O₂. Acids, in general, are materials that can lose one or more hydrogen nuclei, especially when placed in water. Of the four hydrogen atoms in a molecule of acetic acid, only one has this property. Consequently, the formula of acetic acid is often written as HC₂H₃O₂. The acidic hydrogen is emphasized by placing it to the far left of the formula, away from the other, nonacidic hydrogens. The bicarbonate ion acts as a base, meaning it reacts chemically with acids--hence the "volcano." As the acid and base react, the original materials are consumed and are replaced with a new set of materials, carbon dioxide (CO₂), water, and sodium acetate (NaC₂H₃O₂). It is the CO₂ gas that causes the bubbling.

The important point is this: Now that the chemical behavior of these materials is understood, one can predict that anytime a substance containing bicarbonate (HCO₃) in its formula is mixed with a substance evidencing an acidic hydrogen, an exactly similar "volcanic" result can be expected.

Thus, the groupings evidenced in formulas can be tremendous predictors of the chemical behavior of the substances.

Context

In the early nineteenth century, John Dalton put forth the first modern, scientific view of the atom. He proposed that elements consist of minute, indivisible, and permanent entities, called atoms. The atoms of a particular element were assumed to be identical to one another in every regard, while atoms of different elements were dissimilar. Dalton then proposed that compounds consist of atoms of the elements contained in the compound, so that water, known to be decomposable into the elements hydrogen and oxygen, must consist of hydrogen and oxygen atoms. It was further assumed that the ratio of the numbers of atoms of the different elements in a compound was a definite, characteristic number. Thus, water would have a characteristic number of oxygen atoms per hydrogen atom. Using these postulates, Dalton was able to rationalize both the law of conservation of mass and the law of definite proportions, two experimental laws proposed during the latter part of the eighteenth century.

This work set the stage for the advent of chemical formulas. All samples of water, for example, were known to contain eight times as much mass from oxygen as from hydrogen.

Similarly, hydrogen peroxide was known to contain sixteen times as much mass from oxygen as from hydrogen. In other words, per some common amount of hydrogen, hydrogen peroxide must contain twice as much oxygen (both by mass and by number of atoms) as water. Thus, if one assumed the (empirical) formula of water to be HO, the formula of hydrogen peroxide would have to be HO2. Similarly, if one assumed the formula of water to be H₂O, then the formula of hydrogen peroxide would have to be HO. The problem was, nobody knew what the formula of water (or any other compound) was.

The missing piece of information was supplied in 1811 by Amedeo Avogadro, although most people did not appreciate its significance until almost a half-century later.

Avogadro proposed that if different gaseous materials, all under the same conditions of temperature and pressure, contained equal volumes, then the different materials would have to be composed of the same number of particles. For the first time, Avogadro understood that these particles need not be atoms, but could be larger entities, molecules. As never before, it became possible to arrive at unambiguous formulas. It was an experimental fact that two volumes of hydrogen gas reacted with one volume of oxygen gas to form two volumes of steam. By Avogadro's hypothesis, then, one volume of oxygen would have to contain the same number of particles as do two volumes of both hydrogen and steam. This, when coupled with the law of conservation of mass, the law of definite proportions, and Dalton's atomic theory, leads directly to the conclusion that the formulas of hydrogen, oxygen, and water are H₂, O₂, and H₂O, respectively. Suffice it to say that once the concepts of elements, compounds, atoms, molecules, and formulas were finally firmly established, chemistry blossomed as a science.

Currently, determining the formula of a new material is one of the most important ways to characterize it. There are standard ways of going about this. Determining the formula of a compound is also an important first step in understanding the chemical and physical properties of the material. One of the most challenging areas for future work is the establishment of reliable ways of determining the formulas of short-lived, or transient, chemical species during the course of a chemical reaction. These materials may have lifetimes of only a few picoseconds, yet a knowledge of their structures is indispensable for the understanding of the detailed mechanism whereby materials react chemically with one another.

Principal terms

ATOM: a minute, overall electrically neutral collection of particles, some positively charged and some negatively charged; each element can be considered to consist of atoms, all of which share a common atomic number

ATOMIC NUMBER: the integer number that characterizes atoms of a particular element

AVOGADRO'S NUMBER: that number of particles (or units) that is the same number as there are atoms in one gram-atomic mass of any element; the numerical value is 6.02 x 1023

COMPOUND: a material that can be considered to be derived from atoms of more than one element

COVALENT BOND: the entity that holds two or more disparate atoms together to form a molecule; also called chemical bonds, they originate in the sharing of electrons between atoms

ELEMENT: a substance comprised exclusively of atoms sharing a common atomic number

EMPIRICAL FORMULA: a listing of the elements present in a substance, with subscripts indicating the relative numbers of atoms of the different elements

GRAM-ATOMIC MASS: the mass, in grams, of Avogadro's number of atoms of a particular element

MOLE: a counting unit used to indicate Avogadro's number of items

MOLECULE: a collection of atoms held together by covalent bonds to form a coherent whole

MOLECULAR FORMULA: similar to the empirical formula, except subscripts are used to indicate the actual number of atoms of each element in a single molecule

Bibliography

Atkins, P. W. MOLECULES. New York: Scientific American Library, 1987. A beautifully written and illustrated book that focuses on the structure and importance of chemicals, ranging from the fairly mundane to the fairly exotic. The book also emphasizes the practical aspects of molecular structure by considering topics such as sight and color, taste, smell, pain, and acid rain. Excellent, and relatively nontechnical, reading.

Ihde, Aaron J. THE DEVELOPMENT OF MODERN CHEMISTRY. New York: Harper & Row, 1964. At 750 pages of textual material alone, this book is a vast historical resource. It traces chemistry from its earliest roots right up to the date of publication. The first six chapters are particularly pertinent to chemical formulas and combinations.

Lehmann, Walter J. ATOMIC AND MOLECULAR STRUCTURE. New York: Harper & Row, 1972. Based on a course given to liberal arts and other nonscience majors at the University of Massachusetts at Boston, the book is a clear exposition of the elementary nature of atoms, molecules, formulas, and combination. The mathematical knowledge necessary for comprehension is minimal.

Leicester, Henry M., and Herbert S. Klickstein. SOURCE BOOK IN CHEMISTRY, 1400-1900. New York: McGraw-Hill, 1952. A widely recognized classic. Individual chemists are highlighted. A short introductory note by the authors is followed by one or more reprints of seminal works authored by the featured individual. The articles on (and by) J. B. Priestley, Antoine Lavoisier, Joseph Louis Proust, John Dalton, Amedeo Avogadro, William Prout, and Joseph Louis Gay-Lussac are particularly pertinent to the topic of chemical combination.

Nye, Mary J., ed. THE QUESTION OF THE ATOM. Los Angeles: Tomash, 1984. A very interesting and diverse collection of original source material, much of which is concerned with mid-nineteenth century views on chemical combinations and formulas. The paper by Cannizzaro is especially interesting.

Quantum Mechanics of Chemical Bonding

Isomeric Forms of Molecules