views updated

# Atomic weight

History

Isotopes

Interpretation of atomic weights

Uses

Resources

Atoms are exceedingly small, so small that actual weights of atoms were not able to be determined until early in the twentieth century. The weight of an atom of oxygen-16 (an oxygen atom with eight neutrons in the nucleus) was found to be 2.657 × 10-23 grams and an atom of carbon-12 (a carbon atom with six neutrons in the nucleus) was found to weigh 1.99 × 10-23grams. Because these units are so small, they are not practical and are seldom used in everyday laboratory work. Rather, the weight of an atom is usually calculated in units other than grams, units that are closer to the size of the particle being weighed and therefore more practical.

The table of atomic weights is based on a unit called an atomic mass unit, abbreviated u, or in older notation, amu. This unit is defined as 1/12 the mass of carbon-12 (12C) and is equal to 1.6606 × 10-24 grams. On this scale, carbon-12 weighs exactly 12 atomic mass units. Because even the smallest amount of matter contains enormous numbers of atoms, atomic weights are usually interpreted to mean grams of an element rather than atomic mass units. When interpreted in grams, the atomic weight of an element represents 6.02 × 1023atoms, which is defined as one mole. Thus, the atomic weight in grams is the mass of an element that contains one mole or 6.02 × 1023 atoms.

Atomic weights are actually atomic masses, but historically they were called atomic weights because the method used to determine them was called weighing. This terminology has persisted and is more familiar to most people even though the values obtained are actually atomic masses.

## History

Although the atomic theory of matter, in its various forms, existed a good two thousand years before the time of John Dalton (17661844), he was the first to propose, in his 1808 book A New System of Chemical Philosophy, that atoms had weight. Atoms, as Dalton defined them, were hard, solid, indivisible particles with no inner spaces, rather than something that could not be seen, touched, or tasted. They were indestructible and preserved their identities in all chemical reactions. Furthermore, each kind of element had its own specific kind of atom different from the atoms of other elements. These assumptions led him to propose that atoms were tangible matter and therefore had weight.

Because atoms were much too small to be seen or measured by any common methods, absolute weights of atoms could not be determined. Rather, these first measurements were made by comparing weights of various atoms to hydrogen. Hydrogen was chosen as the unit of comparison because it was the lightest substance known, and the weights of the other elements would be very close to whole numbers.

The weight of oxygen could then be calculated because of earlier work by Alexander von Humboldt (17691859) and Joseph-Louis Gay-Lussac (17781850), who found that water consisted of only two elements, hydrogen and oxygen, and that there were eight parts of oxygen for every one part of hydrogen. Lacking any knowledge about how many atoms of hydrogen and oxygen combine in a molecule of water, Dalton again had to make some assumptions. He assumed that nature is basically very simple and, therefore, one atom of hydrogen combines with only one atom of oxygen. Using this hypothesis, and the fact that hydrogen was assigned a weight of one unit, it follows that oxygen, which is eight times heavier than hydrogen, would have a weight of eight units. Of course, if the ratio between hydrogen and oxygen in water were not one to one, but some other ratio, the weight of oxygen would have to be adjusted accordingly. Dalton used experimental results and similar reasoning to prepare the very first table of atomic weights, but because of the lack of knowledge about the real formulas for substances, many of the weights were incorrect and had to be modified later.

Knowledge about absolute formulas of substances came mainly from the work of two chemists. In 1809, Gay-Lussac observed that gases react with each other in very simple proportions. For example, at the same temperature and pressure, two volumes of hydrogen react with one volume of oxygen and form two volumes of water. Then in 1811, Amedeo Avogadro (17761856) proposed that equal volumes of gases have the same number of particles if measured at the same temperature and pressure. The difficulty of explaining how one volume of oxygen could form two volumes of water without violating the current theory that atoms were indivisible was not resolved until the 1850s when Avogadros explanation that molecules of gases, such as hydrogen and oxygen, existed as diatomic molecules (molecules with two atoms joined together) was finally accepted. If each oxygen molecule was composed of two oxygen atoms, then it was the molecule and not the atom that split apart to form two volumes of water.

Although other scientists contributed to knowledge about atomic weights, much of the experimental work that was used to improve the table of atomic weights was done by J. J. Berzelius (17781848), who published his list of the weights of 54 elements in 1828. Unlike Daltons atomic weights, the weights published by Berzelius match quite well the atomic weights used today.

Until that time, all the knowledge about atomic weights was relative to the weight of hydrogen as one unit. The first of the experiments to uncover knowledge about the absolute weight of parts of the atom were done early in the twentieth century by J. J. Thomson (18561940) and Robert Millikan (18681953). Thomson studied rays of negative particles (later discovered to be electrons) in partially evacuated tubes. He measured how the beam deflected or bent when placed in a magnetic field and used this information to calculate mathematically the ratio of the charge on the electron to the mass of the electron.

Millikan devised an experiment in which he produced a very fine spray of charged oil droplets and allowed them to fall between two charged plates. By adjusting the charge as he observed the droplets under a microscope, he was able to suspend the droplets midway between the two plates; with this information he could calculate the charge of the electron. Now, along with the charge/mass ratio calculated by Thomson, the mass of the electron could be calculated and was found to equal 9.11 × 10-28 grams (a decimal with 27 zeros before the 9).

About five years later, the protons charge and mass were calculated. The proton was found to weigh 1.6726 × 10-24 grams, or about 1,836 times as much as an electron. Because most atoms (hydrogen being the only exception) were heavier than would be expected from the number of protons they had, scientists knew that there had to be another neutral particle in the atom. Because of the difficulty in observing neutral particles, the neutron was not discovered until 1932 by James Chadwick (18911974). Its mass was found to be 1.6749 × 10-24 grams, about the same as the mass of the proton.

## Isotopes

The atomic weight represents the sum of the masses of the particles that make up the atomprotons, neutrons, and electronsbut since the mass of the electron is so small and essentially all the weight of the atom comes from the protons and neutrons, the atomic weight is considered to represent the sum of the masses of the protons and neutrons present in the atom. These weights were given in relative units called atomic mass units (abbreviated u or, in older notation, amu) in which the protons and neutrons have nearly equal masses. Consequently, the sum of the protons and neutrons in the nucleus would be the same as the atomic weight of the atom.

Today, a very sophisticated instrument, called a mass spectrometer, is used to obtain accurate measurements of atomic masses. In this instrument, atoms are vaporized and then changed to positively charged particles by knocking off electrons. These charged particles are passed through a magnetic field, which causes them to be deflected in different amounts, depending on the size of the charge and mass. The particles are eventually deposited on a detector plate where the amount of deflection can be measured and compared with the charge. Very accurate relative masses are determined in this way.

When atoms of various elements were analyzed with the mass spectrometer, scientists were surprised to find that not all atoms of the same element had exactly the same mass. Oxygen, for example, was found to exist in three different forms, each differing by one atomic mass unit, or about the mass of one proton or one neutron. Since the number of protons in the nucleus was known because of the association with a + 1 charge, the three different masses for oxygen had to be caused by different numbers of neutrons in the nucleus. Atoms of this type were called isotopes. Both the identity of the element (since the number of protons remains the same) and the chemical properties (since the electrons remain unchanged) are identical in isotopes of the same element. However, the mass is different because of the different number of neutrons in the nucleus, and this sometimes makes the atom unstable and radioactive. Radioactive isotopes are frequently used in research because the radioactivity can be followed using a Geiger counter. They can be administered to living systems like plants or animals and the isotope is observed as it moves and reacts throughout the system. Oxygen has three isotopes with masses of 16, 17, and 18 (often written as oxygen-16, oxygen-17, and oxygen-18 [16O, 17O, and 18O ]). Similarly, carbon exists as carbon-12, carbon-13, and carbon-14 (12C,13C, and 14C ) and hydrogen as hydrogen-1, hydrogen-2, and hydrogen-3 (H,2H, and 3H ). Each of these successive isotopes has one more neutron in the nucleus than the preceding one.

## Interpretation of atomic weights

Early work on atomic weights used naturally occurring oxygen, with an assigned atomic weight of exactly 16 as the basis for the scale of atomic weights. All other atomic weights were found in relation to it. Confusion arose in 1929, when the three isotopes of oxygen were discovered. In 1961 it was finally decided to adopt carbon-12 as the basis for all other atomic weights. Under this system, still in use today, the atomic weight of carbon-12 is taken to be exactly 12 and the atomic mass unit is defined as exactly one-twelfth the mass of carbon-12. All other atomic weights are measured in relation to this unit.

Surprisingly, however, the weight of carbon in the table of atomic weights is not given as exactly 12 as would be expected, but rather 12.01. The reason is that the weights used in the table represent the average weight of the isotopes of carbon that are found in a naturally occurring sample. For example, most carbon found in nature, 98.89% to be exact, is carbon-12 and has a weight of exactly 12. The rest (1.11%) is carbon-13 (with an atomic weight of 13.00) and carbon-14 (which exists in quantities too minute to affect this calculation). The atomic weight of carbon is calculated by taking 98.89% of the weight of carbon-12 and 1.11% of the weight of carbon-13 to give 12.0112. All weights in the table of atomic weights are calculated by using the percentage of each isotope in a naturally occurring sample.

Because atoms are too impossibly small for chemists to observe or weigh, the weights of individual atoms are not very useful for experimentation. Very large numbers of atoms are involved in even the tiniest samples of matter. It is important to match the unit that is used to make a measurement to the size of the thing being measured. For example, it is useful to measure the length of a room in feet rather than miles because the unit, foot, corresponds to the length of a room. One would not measure the distance to London or Paris or to the sun in inches or feet, because the distance is so large in relation to the size of the unit. Miles are a much more appropriate unit.

A new unit, called a mole, was created as a more useful unit for working with atoms. A mole is a counting number much like a dozen. A dozen involves 12 of anything, 12 books, 12 cookies, 12 pencils, etc. Similarly, a mole involves 6.02 × 1023 (602 with 21 zeros after it) particles of anything. The mole is such a large number that it is not a useful measurement for anything except counting very, very small particles, too small to even imagine. For example, if a mole of dollars were divided evenly among all the people of the world (6.5 billion in 2006), every single person alive would receive 1.09 × 1014 dollars! That is enough money to last nearly 300 years if a billion dollars were spent every single day of the year. Yet a mole of carbon atoms is contained in a chunk of coal about as big as a marble.

Needless to say, atoms cannot be counted in the same way that cookies or books are, but they can be counted by weighing, and the mole is the unit that can express this quantity. If a ping-pong ball weighs one ounce, then 12 ounces of ping-pong balls would contain 12 balls. Twenty ounces would contain 20 balls. If golf balls weigh four ounces each, then 48 ounces are needed in order to obtain 12 balls, and 80 ounces are needed in order to obtain 20 balls. Since the golf ball weighs four times as much as the ping-pong ball, it is easy to obtain equal numbers of these two balls by weighing four times as much for the golf balls as you weigh for the ping-pong balls. Actually, it is easier to count small numbers of ping-pong balls or golf balls than to weigh them. But if 10 or 20 or 30 thousand of them were needed, it would be much easier figure the weight of the balls and weigh them than it would be to count them.

Likewise, the weighing method is more useful and, in fact, is the only method by which atoms can be counted. It was discovered in the early 1800s, mostly through the work of Avogadro, that when the atomic weight of an atom is interpreted in grams rather than atomic mass units, the number of atoms in the sample is always 6.02 × 1023 atoms or a mole of atoms. Thus, 12 grams of carbon contain one mole of carbon atoms and 16 grams of oxygen contain one mole of oxygen atoms. One mole of the lightest atom, hydrogen, weighs just one gram; one mole of the heaviest of the naturally occurring elements, uranium, weighs 238 grams.

Molecules are particles made up of more than one atom. The weight of the molecule, called the molecular weight, can be found by adding the atomic weights of each of the atoms that make up the molecule. Water is a molecule with the chemical formula H2 O. It is composed of two atoms of hydrogen, with an atomic weight of one, and one atom of oxygen with an atomic weight of 16. Water, therefore has a molecular weight of 18. When this molecular weight is interpreted as 18 atomic mass units, it represents the weight of one molecule in relation to one-twelfth of carbon-12. When the molecular weight is interpreted as 18 grams (fewer than 400 drops of water), it represents the weight of one mole, or 6.02 × 1023 molecules of water. Similarly, the molecular weight of carbon dioxide (CO2)is 44 a tomic mass units or 44 grams. A chunk of solid carbon dioxide (known as dry ice) about the size of a baseball contains one mole of molecules. If this chunk were allowed to change to a gas at room conditions of temperature and pressure, this mole of carbon dioxide would take up slightly over a cubic foot.

## Uses

When a new substance is found in nature or produced in the laboratory, the first thing chemists try to determine is its chemical formula. This new compound, a substance made of two or more kinds of atoms, is analyzed to find what elements it is composed of, usually by chemically separating the compound into its elements and then determining how much of each element was present. Chemical formulas tell how many atoms are in a compound, not the amount of mass. So the mass of each element must be expressed as a part of a mole by comparing it to the atomic weight. When expressed in this manner, the quantity is a way to represent how many atoms are present in the compound. These numbers of moles are expressed as ratios, reduced to the lowest whole numbers and then combined with the symbols for the elements to represent the simplest chemical formula.

Companies that produce raw materials or manufacture goods use atomic and molecular weights to determine the amounts of reactants needed to produce a given amount of product, or they can determine how much product they can produce from a given amount

### KEY TERMS

Atomic mass The mass of an atom relative to carbon-12 (which has a mass of exactly 12 atomic mass units); also the mass, in grams, of an element that contains one mole of atoms.

Atomic mass unit (u or amu) A unit used to express the mass of atoms equal to exactly one-twelfth of the mass of carbon-12.

Molecule The smallest particle of a compound that can exist, formed when two or more atoms join together to form a substance.

of reactant. Once again, the quantities involved in chemical reactions depend on how many atoms or molecules react, not on the amount of mass of each. So the known amount of reactant or product must be expressed as a part of a mole by comparing it to the molecular weight. Although other factors are involved in these determinations, this quantity, along with the balanced equation for the chemical reaction, allows chemists to figure out how much of any other reactant or product is involved in the reaction. Calculations of this type can save manufacturers many dollars because the amounts of chemicals needed to manufacture a product can be accurately determined. If a billion tires are produced in one year and a penny can be saved on each tire by not using more of a substance than can be reacted, it would be a substantial savings to the company of \$10,000,000 per year.

## Resources

### BOOKS

Brock, William H. The Norton History of Chemistry. New York: W. W. Norton & Company, 1993.

Feather, Ralph M., et al. Science Connections. Columbus, OH: Merrill Publishing Company, 1990.

### OTHER

International Union of Pure and Applied Chemistry; Inorganic Chemistry Division, Commission on Atomic Weights and Isotopic Abundances. History of the Recommended Atomic-Weight Values from 18821997: A Comparison of Differences from Current Values to the Estimated Uncertainties of Earlier Values <http://www.iupac.org/reports/1998/7001coplen/history.pdf#search=%22%22atomic%20weight%22%22> (accessed October 2006).

Leona B. Bronstein

views updated

# Atomic weight

Atoms are exceedingly small, so small that actual weights of atoms were not able to be determined until early in the twentieth century. The weight of an atom of oxygen-16 (an oxygen atom with eight neutrons in the nucleus) was found to be 2.657 × 10-23 grams and an atom of carbon-12 (a carbon atom with six neutrons in the nucleus) was found to weigh 1.99 × 10-23 grams. Because these units are so very small, they are not practical and are seldom used in everyday laboratory work. Rather, the weight of an atom is usually calculated in units other than grams, one that is closer to the size of the particle being weighed and is therefore more practical.

The table of atomic weights is based on a unit called an atomic mass unit, abbreviated u, or in older notation, amu. This unit is defined as 1/12 the mass of carbon-12 (12C) and is equal to 1.6606 × 10-24 grams. On this scale, carbon-12 weighs exactly 12 atomic mass units. But because even the smallest amount of matter contains enormous numbers of atoms, atomic weights are usually interpreted to mean grams of an element rather than atomic mass units. When interpreted in grams, the atomic weight of an element represents 6.02 × 1023 atoms, which is defined as one mole . Thus, the atomic weight in grams is the mass of an element that contains one mole or 6.02 × 1023 atoms.

Atomic weights are actually atomic masses but historically they were called atomic weights because the method used to determine them was called weighing. This terminology has persisted and is more familiar to most people even though the values obtained are actually atomic masses.

## History

Although the atomic theory of matter, in its various forms, existed a good two thousand years before the time of John Dalton, he was the first to propose, in his 1808 book A New System of Chemical Philosophy, that atoms had weight. Atoms, as Dalton defined them, were hard, solid, indivisible particles with no inner spaces, rather than something that could not be seen, touched, or tasted. They were indestructible and preserved their identities in all chemical reactions . Furthermore, each kind of element had its own specific kind of atom different from the atoms of other elements. These assumptions led him to propose that atoms were tangible matter and therefore had weight.

Because atoms were much too small to be seen or measured by any common methods, absolute weights of atoms could not be determined. Rather, these first measurements were made by comparing weights of various atoms to hydrogen . Hydrogen was chosen as the unit of comparison because it was the lightest substance known and the weights of the other elements would be very close to whole numbers.

The weight of oxygen could then be calculated because of earlier work by Humboldt and Gay-Lussac, who found that water consisted of only two elements, hydrogen and oxygen, and that there were eight parts of oxygen for every one part of hydrogen. Lacking any knowledge about how many atoms of hydrogen and oxygen combine in a molecule of water, Dalton again had to make some assumptions. He assumed that nature is basically very simple and, therefore, one atom of hydrogen combines with only one atom of oxygen. Using this hypothesis and the fact that hydrogen was assigned a weight of one unit, it follows that oxygen, which is eight times heavier than hydrogen, would have a weight of eight units. Of course, if the ratio between hydrogen and oxygen in water were not one to one, but some other ratio, the weight of oxygen would have to be adjusted accordingly. Dalton used experimental results and similar reasoning to prepare the very first Table of Atomic Weights, but because of the lack of knowledge about the real formulas for substances, many of the weights were incorrect and had to be modified later.

Knowledge about absolute formulas of substances came mainly from the work of two chemists. In 1809, Gay-Lussac observed that gases react with each other in very simple proportions. For example, at the same temperature and pressure , two volumes of hydrogen react with one volume of oxygen and form two volumes of water. Then in 1811, Amedeo Avogadro proposed that equal volumes of gases have the same number of particles if measured at the same temperature and pressure. The difficulty of explaining how one volume of oxygen could form two volumes of water without violating the current theory that atoms were indivisible was not resolved until the 1850s when Avogadro's explanation that molecules of gases, such as hydrogen and oxygen, existed as diatomic molecules (molecules with two atoms joined together) was finally accepted. If each oxygen molecule was composed of two oxygen atoms, then it was the molecule and not the atom that split apart to form two volumes of water.

Although other scientists contributed to knowledge about atomic weights, much of the experimental work that was used to improve the Table of Atomic Weights was done by J. J. Berzelius who published his list of the weights of 54 elements in 1828. Unlike Dalton's atomic weights, the weights published by Berzelius match quite well the atomic weights used today.

So far, all the knowledge about atomic weights was relative to the weight of hydrogen as one unit. The first of the experiments to uncover knowledge about the absolute weight of parts of the atom were done early in the twentieth century by J. J. Thomson and Robert Millikan. Thomson studied rays of negative particles (later discovered to be electrons) in partially evacuated tubes. He measured how the beam deflected or bent when placed in a magnetic field and used this information to calculate mathematically the ratio of the charge on the electron to the mass of the electron.

Millikan devised a clever experiment in which he produced a very fine spray of charged oil droplets and allowed them to fall between two charged plates. By adjusting the charge on the plates as he observed the droplets under a microscope , he was able to suspend the droplets midway between the two plates and with this information calculate the charge of the electron. Now, along with the charge/mass ratio calculated by Thomson, the mass of the electron could be calculated and was found to equal 9.11 × 10-28 grams (a decimal with 27 zeros before the 9).

About five years later, the charge and mass of the proton were calculated. The proton was found to weigh 1.6726 × 10-24 grams or about 1,836 times as much as an electron. Because most atoms (hydrogen being the only exception) were heavier than would be expected from the number of protons they had, it was known that there must be another neutral particle in the atom. Because of the difficulty in observing neutral particles, the neutron was not discovered until 1932 by James Chadwick. The mass was found to be 1.6749 × 10-24 grams, about the same as the mass of the proton.

## Isotopes

The atomic weight represents the sum of the masses of the particles that make up the atom, protons, neutrons, and electrons. But since the mass of the electron is so small and essentially all the weight of the atom comes from the protons and neutrons, the atomic weight is considered to represent the sum of the masses of the protons and neutrons present in the atom. These weights were given in relative units called atomic mass units (abbreviated u or, in older notation, amu) in which the protons and neutrons have nearly equal masses. Consequently, the sum of the protons and neutrons in the nucleus would be the same as the atomic weight of the atom.

Today, a very sophisticated instrument, called a mass spectrometer, is used to obtain accurate measurements of atomic masses. In this instrument, atoms are vaporized and then changed to positively charged particles by knocking off electrons. These charged particles are passed through a magnetic field which causes them to be deflected different amounts, depending on the size of the charge and mass. The particles are eventually deposited on a detector plate where the amount of deflection can be measured and compared with the charge. Very accurate relative masses are determined in this way.

When atoms of various elements were analyzed with the mass spectrometer, scientists were surprised to find that not all atoms of the same element had exactly the same mass. Oxygen, for example, was found to exist in three different forms, each differing by one atomic mass unit or about the mass of one proton or one neutron. Since the number of protons in the nucleus was known because of their association with a +1 charge, the three different masses for oxygen had to be caused by different numbers of neutrons in the nucleus. Atoms of this type were called isotopes. Both the identity of the element (since the number of protons remains the same) and the chemical properties (since the electrons remain unchanged) are identical in isotopes of the same element. However, the mass is different because of the different number of neutrons in the nucleus, and this sometimes makes the atom unstable and radioactive. Radioactive isotopes are frequently used in research because the radioactivity can be followed using a Geiger counter. They can be administered to living systems like plants or animals and the isotope is observed as it moves and reacts throughout the system. Oxygen has three isotopes with masses of 16, 17, and 18 (often written as oxygen-16, oxygen-17, and oxygen-18 [16O, 12O, 18O]). Similarly, carbon exists as carbon-12, carbon-13, and carbon-14 and hydrogen as hydrogen-1, hydrogen-2, and hydrogen(12C, 13C, 14C)-3(H, 2H, 3H). Each of these successive isotopes have one more neutron in the nucleus than the preceding one.

## Interpretation of atomic weights

Early work on atomic weights used naturally occurring oxygen, with an assigned atomic weight of exactly 16 as the basis for the scale of atomic weights. All other atomic weights were found in relation to it. Confusion arose when, in 1929, the three isotopes of oxygen were discovered. In 1961, it was finally decided to adopt carbon-12 as the basis for all other atomic weights. Under this system still in use today, the atomic weight of carbon-12 is taken to be exactly 12 and the atomic mass unit is defined as exactly one-twelfth the mass of carbon-12. All other atomic weights are measured in relation to this unit.

When examining the table of atomic weights, it is found that the weight of carbon is not given as exactly 12 as would be expected, but rather 12.01. The reason is that the weights used in the table represent the average weight of the isotopes of carbon that are found in a naturally occurring sample . For example, most of the carbon found in nature, 98.89% of it to be exact, is carbon-12 and has a weight of exactly 12. The rest of it (1.11%) is carbon-13 (with an atomic weight of 13.00) and carbon-14 (which exists in quantities too minute to affect this calculation). The atomic weight of carbon is calculated by taking 98.89% of the weight of carbon-12 and 1.11% of the weight of carbon-13 to give 12.0112. All weights in the table of atomic weights are calculated by using the percentage of each isotope in a naturally occurring sample.

Because atoms are so small, making it impossible for chemists to observe or weigh them, the weights of individual atoms are not very useful for experimentation. Very large numbers of atoms are involved in even the tiniest samples of matter. It is important to match the unit that is used to make a measurement to the size of the thing being measured. For example, it is useful to measure the length of a room in feet rather than miles because the unit, foot, corresponds to the length of a room. One would not measure the distance to London or Paris or to the sun in inches or feet because the distance is so large in relation to the size of the unit. Miles would be a much more appropriate unit.

A new unit, called a mole, was created as a more useful unit for working with atoms. A mole is a counting number much like a dozen. A dozen involves 12 of anything, 12 books, 12 cookies, 12 pencils, etc. Similarly, a mole involves 6.02 × 1023 (602 with 21 zeros after it) particles of anything. The mole is such a large number that it is not a useful measurement for anything except counting very, very small particles, too small to even imagine. For example, if a mole of dollars were divided evenly among all the people of the world (5.5 billion), every single person alive would receive 1.09 × 1014 dollars! That is enough money to last nearly 300 years if a billion dollars were spent every single day of the year. Yet a mole of carbon atoms is contained in a chunk of coal about as big as a marble.

Needless to say, atoms cannot be counted in the same way that cookies or books are counted. But they can be counted by weighing, and the mole is the unit that can express this quantity. If a ping-pong ball weighs one ounce, then 12 ounces of ping-pong balls would contain 12 balls. Twenty ounces would contain 20 balls. If golf balls weigh four ounces each, then 48 ounces are needed in order to obtain 12 balls, and 80 ounces are needed in order to obtain 20 balls. Since the golf ball weighs four times as much as the ping-pong ball, it is easy to obtain equal numbers of these two balls by weighing four times as much for the golf balls as you weigh for the ping-pong balls. Actually, it is easier to count small numbers of ping-pong balls or golf balls than to weigh them. But if 10 or 20 or 30 thousand of them were needed, it would be much easier figure the weight of the balls and weigh them than it would be to count them.

Likewise, the weighing method is more useful and, in fact, is the only method by which atoms can be counted. It was discovered in the early 1800s, mostly through the work of Amadeo Avogadro, that when the atomic weight of an atom is interpreted in grams rather than atomic mass units, the number of atoms in the sample is always 6.02 × 1023 atoms or a mole of atoms. Thus, 12 grams of carbon contain one mole of carbon atoms and 16 grams of oxygen contain one mole of oxygen atoms. One mole of the lightest atom, hydrogen, weighs just one gram and one mole of the heaviest of the naturally occurring elements, uranium , weighs 238 grams.

Molecules are particles made up of more than one atom. The weight of the molecule, called the molecular weight , can be found by adding the atomic weights of each of the atoms that make up the molecule. Water is a molecule with a formula, H2O. It is composed of two atoms of hydrogen, with an atomic weight of one, and one atom of oxygen with an atomic weight of 16. Water, therefore has a molecular weight of 18. When this molecular weight is interpreted as 18 atomic mass units, it represents the weight of one molecule in relation to one-twelfth of carbon-12. When the molecular weight is interpreted as 18 grams (less than 400 drops of water), it represents the weight of one mole or 6.02 × 1023 molecules of water. Similarly, the molecular weight of carbon dioxide (CO2) is 44 atomic mass units or 44 grams. A chunk of solid carbon dioxide (known as dry ice ) about the size of a baseball contains one mole of molecules. If this chunk were allowed to change to a gas at room conditions of temperature and pressure, this mole of carbon dioxide would take up slightly over a cubic foot.

## Uses

When new substances are found in nature or are produced in the laboratory, the first thing chemists try to determine is the chemical formula for the substance. This new compound, a substance made of two or more kinds of atoms, is analyzed to find what elements it is composed of. This is usually done by chemically separating the compound into its elements and then determining how much of each element was present. Chemical formulas tell how many atoms are in a compound, not the amount of mass. So the mass of each element must be expressed as a part of a mole by comparing it to the atomic weight. When expressed in this manner, the quantity is a way of representing how many atoms are present in the compound. These numbers of moles are expressed as ratios, reduced to the lowest whole numbers and then combined with the symbols for the elements to represent the simplest chemical formula.

Companies that produce raw materials or manufacture goods use atomic and molecular weights to help determine the amounts of reactants needed to produce a given amount of product. Or they can determine how much product they can produce from a given amount of reactant. Once again, the quantities involved in chemical reactions depend on how many atoms or molecules react, not on the amount of mass of each. So the known amount of reactant or product must be expressed as a part of a mole by comparing it to the molecular weight. Although other factors are involved in these determinations, this quantity, along with the balanced equation for the chemical reaction, allows chemists to figure out how much of any other reactant or product is involved in the reaction. Calculations of this type can save manufacturers many dollars because the amounts of chemicals needed to manufacture a product can be accurately determined. If a billion tires are produced in one year and one penny can be saved on each tire by not using more of a substance than can be reacted, it would be a substantial savings to the company of \$10,000,000 per year.

## Resources

### books

Brock, William H. The Norton History of Chemistry. New York: W. W. Norton & Company, 1993.

Feather, Ralph M. et al. Science Connections. Columbus, OH: Merrill Publishing Company, 1990.

Leona B. Bronstein

## KEY TERMS

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Atomic mass

—The mass of an atom relative to carbon-12 (which has a mass of exactly 12 atomic mass units); also the mass, in grams, of an element that contains one mole of atoms.

Atomic mass unit (u or amu)

—A unit used to express the mass of atoms equal to exactly one-twelfth of the mass of carbon-12.

Molecule

—The smallest particle of a compound that can exist, formed when two or more atoms join together to form a substance.

# relative atomic mass

views updated

relative atomic mass (atomic weight; r.a.m.) Symbol Ar. The ratio of the average mass per atom of the naturally occurring form of an element to 1/12 of the mass of a carbon–12 atom.