Stoichiometric Laws
Stoichiometry is the study of quantitative relationships between substances involved in chemical changes. That the Universe is a constantly changing place is readily apparent from any walk down the street. People and cars pass by, the sky is filled with moving clouds, the businesses and storefronts keep changing, and everything seems to be in motion. It is, in some ways, surprising that ancient philosophers often argued for the permanence of the Universe and unchanging nature. Some even argued against motion itself, saying it was but an illusion. In many ways, these thought experiments inhibited the development of science. But in understanding the constant nature of the Universe, they were right; just not in the way that they thought.
Underlying chemistry are a number of principles or laws that provide the basis for the relationships between the reactants and products in a chemical reaction. This relationship, called the stoichiometry of a reaction, can be used to predict how much reactant is needed to create a certain amount of product or to predict how much of the product will be formed from a certain amount of reactant. It also defines the proportions in which reactants will combine and the proportion in which products will be formed. It should be noted, emphatically, that while the expression of these stoichiometric laws is a human trait (so far, we are the only animal that seems to care about such things!), they are not of human invention.
The "Law of Conservation of Matter" was first expounded by the Russian chemist, Lomonosov, who investigated the reactions of compounds with air in closed containers. The weight, before and after the reaction, remained constant despite the observable change. Matter was neither being created nor destroyed, merely converted from one form to another. Unfortunately, working in Russia in the 1750s, his results did not get the attention nor he the recognition that he most likely deserved. The great French chemist, Antoine Lavoisier (late 1700s), is most often credited with the formulation of this law. Prior to the development of atomic theory, it was simply the absolute statement that there is no measureable change in the total mass of the chemical compounds upon reaction.
Methods of verifying this law required the careful observation of chemical reactions in sealed vessels. For example, the calcination of metals in sealed containers demonstrated that no change in mass occurred. Further, opening the vessels demonstrated the presence of a vacuum within and increase in weight only upon exposure to air. That is, when air is not the limiting reagent within the vessel, the reaction can proceed to a much greater extent. Arguably, this simple experiment - which Lavoisier repeated and refined - provides much of the basis for an understanding of stoichiometric relationships and laws, from the concept of stoichiometric quantities and limiting reagents to the conservation of matter.
The Law of Conservation of Mass can be seen using the simple decomposition of water, according to the equation:
2H2O 2H2 + O2
The data for this experiment demonstrate that 11.2 g of hydrogen and 88.8 g of oxygen are produced by 100 g of water, regardless of the water's source. Furthermore, these elements can be converted back into 100 g of water if the experiment is done carefully (particularly as hydrogen and oxygen form an explosive mixture!). Similarly, the burning of a candle, the rusting of a metal, or the act of living all obey the conservation law and this can be demonstrated, provided the reactions are carried out in a closed system to prevent the loss of gaseous products.
With the advent of the Atomic Theory, it was soon realized that it is not just matter or mass that is conserved but atoms as well. The more modern formulation of the law states that atoms can be neither created nor destroyed during a chemical reaction, only converted or rearranged into new substances. But this was pre-dated by the Laws of Constant Composition and Definite Proportion. The first says that the elemental composition of a compound is the same, regardless of the source of the compound. That is, water is water is water and is alway "H2O", whether it is obtained from the snow pack of a Himalayan mountain or the bathroom tap. The second law is an alternative way of looking at the same thing: "When elements combine to form a chemical compound, they do so in a definite proportion by mass." That is, all molecules of calcium carbonate are the same, consisting of a calcium ion and carbonate ion, and the carbonate ion is further composed of a carbon atom and three oxygen atoms. The composition is invariant; the mass proportions are fixed.
The realization of these laws facilitated chemical analysis. Instead of looking for a variety of different compounds in, for example, each sample of calcium carbonate, chemists now knew the composition that was to be expected. This realization also posed the question of why this should be so. The Atomic Theory explains both propositions if it is assumed that atoms are indivisible and form complexes in fixed ratios. That is, one oxygen atom is capable of picking up two hydrogen atoms in forming water. This, of course, lead to questions on the nature of molecules and the interaction of atoms which, in turn, lead to the question of bonding. As with most of science, the answer to one question is invariably the starting point for the next one.
One other subtle point that the Law of Constant Composition makes but that is often lost on the general public is that chemicals know no providence. Given a molecule of, for example, acetic acid, it is impossible to determine whether that specific molecule was made via the Wacker Process in a chemical plant, as the by-product of a biochemical pathway, or through the gradual oxidation of ethanol in wine into vinegar (acetic acid by a different name). The distinction between natural and artificial chemical is a false one, used by advertisers to market a product and usually at a higher cost!
The Law of Multiple Proportions states that "in different compounds containing the same elements, the masses of one of the elements compared with the fixed mass of one of the other elements will always be in a ratio of small whole numbers." This principle was first expounded by Dalton and the subsequent verification by experiment provided the strongest support, at the time, for his atomic theory.
In order to understand the Law of Multiple Proportions, consider the compounds carbon monoxide and carbon dioxide. If the first is composed of 12 g of carbon and 16 g of oxygen, then for the second, if 12 g of carbon are present, there must be some small number multiple of 16 g of oxygen. In this case, the small number is "2" and leads to the chemical formula of CO2. With our advanced understanding of chemistry and atomic theory, this result may seem a little redundant but when it was first proposed, an understanding of chemical composition and molecular formulae did not exist. Rather, this law provided a method for determining the chemical formula from observation.
As an example, consider the problem of three unknown compounds. Each is composed of chlorine and oxygen. Chemical analysis tells us that if we have 17.8 g of chlorine, then the first has 8 g of oxygen, the second 16 g of oxygen, and the third 24 g of oxygen. Clearly, then, the simplest whole number ratio for these three compounds is 1:2:3, implying the presence of one oxygen atom in the first, two in the second, and three in the third, or at least some multiple of these numbers as the analysis will only give us the empirical formula. Furthermore, if we know that chlorine has a molar mass of 35.5 g (give or take), we can easily come to the conclusion that these three compounds are: ClO, ClO2, and ClO3. By studying multiple proportions for a variety of compounds, it is possible to actually come up with a consistent set of atomic weights for all of the elements involved.
The Stoichiometric Laws were fundamental observations for chemical reactions. They allowed for the systematic classification of reactions and the development of the atom as the building block of molecules. They transformed chemistry from a collection of observations to a consistent and theoretically sound discipline. They provided the basis for understanding the atomic nature of chemistry and, in many ways, are the pillars upon which modern chemistry has been built.
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