weight-average molecular weight: see molecular weight.

weight lifting, international sport, also a training technique for athletes in other sports. From the earliest times men have lifted weights as a test of strength. Long popular as a competitive sport in Europe, Egypt, Turkey, and Japan, weight lifting became increasingly popular in the United States after 1900.

Weight classes govern competition, which is won by the lifter with the greatest total of weight for two standard lifts—the clean-and-jerk, in which the lifter hoists the bar temporarily to the shoulders, pauses, and then thrusts it overhead, and the snatch, in which the lifter squats, then draws the bar overhead in a single motion. These Olympic lifts require delicate technique as well as great strength. A world championship for women was first held in 1987, and female lifters competed in the Olympics for the first time in 2000.

In recent decades, the use of illegal strength-building drugs—anabolic steroids—by some competitors has marred the sport's reputation. Their use is also widespread among power lifters who compete in a less technically demanding variation in which the dead lift, bench press, and squat determine weight totals. Bodybuilders, although not competitive lifters, rely almost solely upon weight training to shape their bodies. The number of women bodybuilders, like women weight lifters, rose dramatically in the late 20th cent.

weight, measure of the force of gravity on a body (see gravitation). Since the weights of different bodies at the same location are proportional to their masses, weight is often used as a measure of mass. However, the two are not the same; mass is a measure of the amount of matter present in a body and thus has the same value at different locations, and weight varies depending upon the location of the body in the earth's gravitational field (or the gravitational field of some other astronomical body). A given body will have the same mass on the earth and on the moon, but its weight on the moon will be only about 16% of the weight as measured on the earth. The distinction between weight and mass is further confused by the use of the same units to measure both—the pound, the gram, or the kilogram. One pound of weight, or force, is the force necessary at a given location to accelerate a one-pound mass at a rate equal to the acceleration of gravity at that location (about 32 ft per sec per sec). Similar relationships hold between the gram of force and the gram of mass and between the kilogram of force and the kilogram of mass.

number-average molecular weight: see molecular weight.

molecular weight, weight of a molecule of a substance expressed in atomic mass units (amu). The molecular weight may be calculated from the molecular formula of the substance; it is the sum of the atomic weights of the atoms making up the molecule. For example, water has the molecular formula H₂O, indicating that there are two atoms of hydrogen and one atom of oxygen in a molecule of water. Rounded to three decimal places, the atomic weight of hydrogen is 1.008 amu and that of oxygen is 15.999 amu. The molecular weight of water is thus (2×1.008)+(1×15.999)=2.016+15.999=18.015 amu. Since atomic weights are average values, molecular weights are also average values. On the average, a molecule of ordinary water weighs 18.015 amu. Both hydrogen and oxygen are made up of several isotopes. One isotope of hydrogen is deuterium, or heavy hydrogen. Atoms of deuterium are about twice as massive as the average for all hydrogen atoms in ordinary water. Therefore water that contains only atoms of deuterium, called heavy water, has a higher molecular weight than ordinary water. Some substances, especially ionic compounds such as common salt, are not made up of molecules and thus have neither a molecular formula nor a molecular weight.

Molecular weights of substances may be determined experimentally in various ways, the method employed usually depending on the state (solid, liquid, or gas) of the substance. Methods for determining the molecular weights of gaseous substances are based on Avogadro's law, which states that under given conditions of temperature and pressure a given volume of any gas contains a specific number of molecules of the gas; thus a comparison of the weights of equal volumes of different gases under the same conditions of temperature and pressure is equivalent to a direct comparison of the weights of molecules of the gases. The molecular weights of substances that are not normally gaseous and do not evaporate without decomposition are sometimes determined from their effects on the melting point, boiling point, vapor pressure, or osmotic pressure of some solvent (see colligative properties). However, if the substance ionizes or does not completely separate into molecules, the molecular weight so determined will be erroneous. Highly accurate molecular weights are sometimes determined by using the mass spectrograph.

Some substances, e.g., proteins, viruses, and certain synthetic polymers, have very high molecular weights. These molecular weights may be determined by measurement of sedimentation rate in an ultracentrifuge, by light-scattering photometry, or by other methods. The methods may give different results, since usually the molecules of a substance such as a polymer do not all have exactly the same molecular weight. These methods determine an average molecular weight for the molecules in the sample. The number-average molecular weight determined by the ultracentrifuge method gives a value that is equal to the weight of the sample divided by the number of molecules in the sample. This number-average molecular weight can also be determined by other methods based on measurement of colligative properties. The light-scattering method determines what is called the weight-average molecular weight. Although this may be the same value as the number-average molecular weight if all the molecules have nearly the same weight, it will be higher if some of the molecules are heavier than others.

gram-molecular weight, amount of a molecular substance whose weight, in grams, is numerically equal to the molecular weight of that substance. For example, one gram-molecular weight of molecular oxygen, O₂ (molecular weight approximately 32), is 32 grams, and one gram-molecular weight of water, H₂O (molecular weight approximately 18) is 18 grams. The term mole is often used in place of gram-molecular weight. See gram-atomic weight.

gram-atomic weight, amount of an atomic substance whose weight, in grams, is numerically equal to the atomic weight of that substance. For example, 1 gram-atomic weight of atomic oxygen, O (atomic weight approximately 16), is 16 grams. See gram-molecular weight.

formula weight, in chemistry, a quantity computed by multiplying the atomic weight (in atomic mass units) of each element in a formula by the number of atoms of that element present in the formula, and then adding all of these products together. For example, the formula weight of water (H₂O) is two times the atomic weight of hydrogen plus one times the atomic weight of oxygen. Numerically, this is (2×1.00797)+(1×15.9994)=2.01594+15.9994=18.01534. If the formula used in computing the formula weight is the molecular formula, the formula weight computed is the molecular weight. The percentage by weight of any atom or group of atoms in a compound can be computed by dividing the total weight of the atom (or group of atoms) in the formula by the formula weight and multiplying by 100. For example, the weight percentage of hydrogen in water is determined by taking two times the atomic weight of hydrogen, dividing it by the formula weight of water, and multiplying by 100. Numerically, this is 100×(2×1.00797)/18.01534=11.19% hydrogen in water by weight. Formula weights are especially useful in determining the relative weights of reagents and products in a chemical reaction. For example, it is known that two molecules of hydrogen gas, H₂, react with one molecule of oxygen gas, O₂, to form two molecules of water, H₂O. This reaction may be represented by the chemical equation 2H₂+O₂→2H₂O. The formula weight of hydrogen gas is 2.01594, that of oxygen gas 31.9998, and that of water 18.01534. Our chemical equation is numerically equivalent to 2×2.01594+31.9998=2×18.01534 or 4.03188+31.9998=36.03068 if the formula weight of each reactant is substituted for the formula of that reactant. From this equation we know, for example, that 4.03188 grams of hydrogen gas will react with 31.9998 grams of oxygen gas to yield 36.03068 grams of water. The relative proportions by weight of these reactants is the same in any reaction of hydrogen and oxygen to form water. These relative weights computed from the chemical equation are sometimes called equation weights.

equivalent weight. The equivalent weight of an element or radical is equal to its atomic weight or formula weight divided by the valence it assumes in compounds. The unit of equivalent weight is the atomic mass unit; the amount of a substance in grams numerically equal to the equivalent weight is called a gram equivalent. Hydrogen has atomic weight 1.008 and always assumes valence 1 in compounds, so its equivalent weight is 1.008. Oxygen has an atomic weight of 15.9994 and always assumes valence 2 in compounds, so its equivalent weight is 7.9997. The sulfate radical (SO₄) has formula weight 96.0636 and always has valence 2 in compounds, so its equivalent weight is 48.0318. Some elements exhibit more than one valence in forming compounds and thus have more than one equivalent weight. Iron (atomic weight 55.845) has an equivalent weight of 27.9225 in ferrous compounds (valence 2) and 18.615 in ferric compounds (valence 3). The weight proportion in which elements or radicals combine to form compounds can be determined from their equivalent weights. For example, hydrogen can combine with oxygen to form water; the weight proportion of oxygen to hydrogen in water is the same as the proportion of their equivalent weights, 7.9997 to 1.008 or 7.946 to 1; there is 1 weight of hydrogen for every 7.946 weights of oxygen, or water is about 11.2% hydrogen (by weight). Iron forms two oxides: ferrous oxide (FeO), in which there are 27.9225 weights of iron for each 7.9997 weights of oxygen, and ferric oxide (Fe₂O₃), in which there are 18.615 weights of iron for every 7.9997 weights of oxygen.

combining weight, the proportion (by weight) in which a chemical element combines with other elements to form compounds. The determination of combining weights was a very important part of early chemical endeavor. The atomic theory of John Dalton (see atom) was based in part on his determinations of combining weights, which he called atomic weights. Combining weights were usually measured by early chemists on a scale in which hydrogen had a combining weight of 1. See equivalent weight.

atomic weight, mean (weighted average) of the masses of all the naturally occurring isotopes of a chemical element, as contrasted with atomic mass, which is the mass of any individual isotope. Although the first atomic weights were calculated at the beginning of the 19th cent., it was not until the discovery of isotopes by F. Soddy (c.1913) that the atomic mass of many individual isotopes was determined, leading eventually to the adoption of the atomic mass unit as the standard unit of atomic weight.

Effect of Isotopes in Calculating Atomic Weight

Most naturally occurring elements have one principal isotope and only insignificant amounts of other isotopes. Therefore, since the atomic mass of any isotope is very nearly a whole number, most atomic weights are nearly whole numbers, e.g., hydrogen has atomic weight 1.00797 and nitrogen has atomic weight 14.007. However, some elements have more than one principal isotope, and the atomic weight for such an element—since it is a weighted average—is not close to a whole number; e.g., the two principal isotopes of chlorine have atomic masses very nearly 35 and 37 and occur in the approximate ratio 3 to 1, so the atomic weight of chlorine is about 35.5. Some other common elements whose atomic weights are not nearly whole numbers are antimony, barium, boron, bromine, cadmium, copper, germanium, lead, magnesium, mercury, nickel, strontium, tin, and zinc.

Atomic weights were formerly determined directly by chemical means; now a mass spectrograph is usually employed. The atomic mass and relative abundance of the isotopes of an element can be measured very accurately and with relative ease by this method, whereas chemical determination of the atomic weight of an element requires a careful and precise quantitative analysis of as many of its compounds as possible.

Development of the Concept of Atomic Weight

J. L. Proust formulated (1797) what is now known as the law of definite proportions, which states that the proportions by weight of the elements forming any given compound are definite and invariable. John Dalton proposed (c.1810) an atomic theory in which all atoms of an element have exactly the same weight. He made many measurements of the combining weights of the elements in various compounds. By postulating that simple compounds always contain one atom of each element present, he assigned relative atomic weights to many elements, assigning a weight of 1 to hydrogen as the basis of his scale. He thought that water had the formula HO, and since he found by experiment that 8 weights of oxygen combine with 1 weight of hydrogen, he assigned an atomic weight of 8 to oxygen. Dalton also formulated the law of multiple proportions, which states that when two elements combine in more than one proportion by weight to form two or more distinct compounds, their weight proportions in those compounds are related to one another in simple ratios. Dalton's work sparked an interest in determining atomic weights, even though some of his results—such as that for oxygen—were soon shown to be incorrect.

While Dalton was working on weight relationships in compounds, J. L. Gay-Lussac was experimenting with the chemical reactions of gases, and he found that, when under the same conditions of temperature and pressure, gases react in simple whole-number ratios by volume. Avogadro proposed (1811) a theory of gases that holds that equal volumes of two gases at the same temperature and pressure contain the same number of particles, and that these basic particles are not always single atoms. This theory was rejected by Dalton and many other chemists.

P. L. Dulong and A. T. Petit discovered (1819) a specific-heat method for determining the approximate atomic weight of elements. Among the first chemists to work out a systematic group of atomic weights (c.1830) was J. J. Berzelius, who was influenced in his choice of formulas for compounds by the method of Dulong and Petit. He attributed the formula H₂O to water and determined an atomic weight of 16 for oxygen. J. S. Stas later refined many of Berzelius's weights. Stanislao Cannizzaro applied Avogadro's theories to reconcile atomic weights used by organic and inorganic chemists.

The availability of fairly accurate atomic weights and the search for some relationship between atomic weight and chemical properties led to J. A. R. Newlands's table of "atomic numbers" (1865), in which he noted that if the elements were arranged in order of increasing atomic weight "the eighth element, starting from a given one, is a kind of repetition of the first." He called this the law of octaves. Such investigations led to the statement of the periodic law, which was discovered independently (1869) by D. I. Mendeleev in Russia and J. L. Meyer in Germany. T. W. Richards did important work on atomic weights (after 1883) and revised some of Stas's values.

apothecaries weight: see English units of measurement.

System of conditioning involving lifting weights, especially for strength and endurance. It may include the use of barbells and dumbbells, a Nautilus or similar machines, or a combination of these. Athletes use it to improve their performance, nonathletes use it for general conditioning or bodybuilding, and those recovering from an injury may use it as part of an overall rehabilitation program.

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Sport in which barbells are lifted competitively or as an exercise. The two main events are (1) the snatch, in which the barbell is lifted from the floor to arm's length overhead in a single, continuous motion; and (2) the clean and jerk, in which it is lifted first to the shoulders and then, after a pause, to arm's length overhead. Contestants are divided into 10 body-weight categories ranging from flyweight to superheavyweight. Lifts may range to over 1,000 lbs (455 kg) in the heavyweight divisions. The origins of modern competition are to be found in 18th- and 19th-century strongman contests. The first three Olympic Games (1896, 1900, 1904) included weight lifting, as have all games after 1920.

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Gravitational force of attraction on an object, caused by the presence of a massive second object, such as the Earth or Moon. It is a consequence of Isaac Newton's universal law of gravitation, which states that the force of attraction between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between them. For this reason, objects of greater mass weigh more on the surface of the Earth. On the other hand, an object's weight on the Moon is about one-sixth of its weight on Earth, even though its mass remains the same, because the Moon has less mass and a smaller radius than the Earth and therefore exerts less gravitational force. Weight math.W is the product of an object's mass math.m and the acceleration of gravity math.g at the location of the object, or math.W = math.mmath.g. Since weight is a measure of force rather than mass, the units of weight in the International System of Units are newtons (N). In common usage, weight is measured by the gram in the metric system and by the ounce and pound in the U.S. and British systems.

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Sum of the atomic weights of all atoms in a chemical formula. The term is generally applied to a substance that consists of ions (see ionic bond) rather than individual molecules (and thus does not have a molecular weight). An example of such a substance is sodium chloride (table salt). Such a substance's chemical formula describes the simplest ratio of the number of atoms of the constituent elements. Seealso stoichiometry.

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or combining weight

Quantity of an element that exactly reacts with (equals the combining value of) 1 g of hydrogen, 8 g of oxygen, or a corresponding amount of any other element. An element's equivalent weight is its atomic weight divided by its valence. In general, for oxidation-reduction, including electrolysis, the equivalent weight is the weight associated with the loss or gain of 6.02 × 10²³ electrons (Avogadro's number) or 96,500 coulombs of electric charge; this is also the molecular weight divided by the number of electrons lost or gained. The equivalent weight of a substance with several valences differs depending on the number of electrons transferred in the given reaction. The number of equivalent weights of any substance dissolved in one litre of solution is called the solution's normality (math.N). Seealso stoichiometry.

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Ratio of the average mass of a chemical element's atoms to 112 the mass of an atom of the carbon-12 isotope. The original standard of atomic weight, established in the 19th century, was hydrogen, with a value of 1. From circa 1900 until 1961, the reference standard was oxygen, with a value of 16, and the unit of atomic mass was defined as 116 the mass of an oxygen atom. Oxygen, however, contains small amounts of two isotopes that are heavier than the most abundant one, and 16 is actually a weighted average of the masses of the three isotopes of oxygen. Therefore, the standard was changed to one based on carbon-12. The new scale required only minimal changes to the values that had been used for chemical atomic weights.

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