Stoichiometry
That chemical elements are made of atoms (the smallest piece of matter that still retained the chemical features of the element) was an idea first put forth by Greek philosophers. Revitalization of the atomic theory was, in part, credited to John Dalton, an English school tutor and practicing chemist, during the early 1800s. The reason that his work on chemical atomism, if not physical atomism, was so widely accepted was that it worked to explain the relationships that had been noted and tested by the chemists of the latter part of the 1700s. In particular, it gave a rationale for the work of an obscure German chemist, Jeremias Richter.
Richter "invented" stoichiometry, which can be described as the systematic study of the quantitative changes between substances undergoing a chemical transformation or reaction. Just as Johannes Kepler had provided a mathematical harmony to the stars, Richter was determined to provide a mathematical basis for chemistry. Without an understanding of the atomic basis of matter, it was a task that was doomed for failure but Richter did generate considerable insight into the definite proportions of chemical reagents for reactions. His analysis led him to the conclusion that in, for example, a double decomposition of a salt, the proportions of the products was provided by the proportions of the reagents. That is, he recognized that a chemical reaction such as the combination of sodium sulfate with barium chloride resulted in precipitated barium sulfate and soluble sodium chloride, and that the proportions or ratios of the constituent groups was fixed by the starting materials.
Richter's work laid the foundation for other chemists to establish the laws of proportionality. For example, Ernst Gottfried Fisher published a table demonstrating the amount of base required to neutralize 1,000 parts of sulfuric acid. Further, he expanded the table to then show much of each acid was required to neutralize the corresponding bases. From this table, it is easy to see that 672 parts of ammonia require 712 parts of muriatic acid or 979 parts of phosphoric to be neutralized. This was the start of the systematization of analytical chemistry and the beginning of rationalization of the atomic mass of the elements. The implication is that each "atom" of muriatic acid weighs more than each atom of ammonia but less than each atom of phosphoric acid. Of course, it was not until much later that Dalton proposed an Atomic Theory of Matter.
The Atomic Theory provided a method for determining and systematizing the changes between reactants and products. Chemical equations began to emerge. This required symbols for the elements but that was not a critical issue. Rather, simply being able to begin to express reactions as mathematical entities with a view to balancing the various reagents impelled chemistry forward. Stoichiometry enabled chemists to begin to make sense of myriad equations and compounds.
Consider, for example, cooking food. Within any cookbook, there are invariably recipes which instructs the used to "add two cups of flour" or "mix in three tablespoons of vanilla." These are empirically derived instructions that originate from the trial and error process that is consider a good recipe. But once a recipe has been established, the ratios are fixed and the product is defined. The question remains, however, why is it two cups of flour and not three cups? There is no underlying atomic theory of cooking equivalent to the atomic theory of matter, although there is an understanding of the chemistry that occurs during cooking. Stoichiometry provides this understanding by showing that each and every time, specific ratios are required for proper reaction.
This, of course, is fundamentally important to the practice of chemistry from the laboratory bench top to the multi-ton producing chemical manufacturing sites. If a solution needs to be neutralized, excess acid or base is not only wasteful of the chemical compound but can actually change the results of the reaction. Too much acid in neutralizing a basic solution can result in acid catalyzed cleavage of the product, and with too little acid the solution remains alkaline and unusable. Understanding stoichiometry allows chemical engineers to carefully balance all of the demands of a chemical process.
Most chemists encounter stoichiometry as high school or undergraduate students studying chemistry. It is presented in the form of balancing equations. "Why do equations balance? Because they are stoichiometric." is a fairly common question and response. Ultimately, equations balance because of the law of conservation of matter. Atoms can be neither created nor destroyed, so if they occur on one side of a reaction, they must be found, somewhere, on the other side. Learning how to properly balance equations is one of the most important skills that chemists acquire.
Furthermore, equations are scale invariant. This is important. Consider the following reaction:
2H2 + O2 ⇛ 2H2O
Taken literally, this reaction says that two molecules of hydrogen will react with one molecule of oxygen and yield two molecules of water. But it also tells us that if we react four molecules of hydrogen with two molecules of oxygen, we will end up with four molecules of water. All that we have done is multiple the coefficients of the equation by two. And we can actually use any number. One of the most convenient is Avogadro's number, 6.022 x 1023 molecules per mole. This number has one unusual property. It is the number of atoms or molecules that make up the gram molecular weight. That is, 12.011 grams of carbon contains 6.022 x 1023 atoms of carbon. Similarly, 15.9994 grams of oxygen is composed of 6.022 x 1023 atoms of oxygen but, because each molecule of oxygen is composed of two atoms, it is only 3.011 x 1023 molecules of oxygen. This is an important distinction to remember in dealing with stoichiometry. There is an equivalence of the atomic and molecular mass as determined by the formula with the mole quantity of a substance. Thus, the above combustion of hydrogen requires two moles of the hydrogen molecule, each of which weighs 2.0159 grams per mole. Thus, the reaction is the combination of 4.0318 grams of hydrogen with 31.9988 grams of oxygen, which produces exactly 36.0306 grams of water.
Further, that the ideal ratio for hydrogen to oxygen is almost 1 to 8. But what happens to a chemical reaction if the reagents are not in an ideal ratio? For example, if there is more than 31.9988 grams of oxygen present? The answer is that the remainder does not react. It remains as oxygen, usable in some future reaction but not at the present. This is an important concept as it leads to the idea of a limiting reagent. One of the more important considerations in any industrial process is to use up enough chemicals to cause the reaction to proceed with out using up more than necessary. Any more than necessary wastes money and effort. The limiting reagent in any reaction is the species that will run out first. It is the one that is in short supply.
It is also the species that any discussion of yield is based on. The percentage yield is the number of molecules or moles of the limiting reagent that are turned into product(s). In our above reaction, if we have exactly two moles of hydrogen and it is the limiting reagent, then producing two moles of water mean that the reaction had a 100% yield, regardless of how many moles of oxygen are present. The limiting reagent always limits the yield of product and defines the yield for the reaction. This is also of importance to industry as the yield of a reaction can vary under different circumstances and any industrial process should be optimized to give the best yield of the product, thus minimizing waste.
The concept of stoichiometry emerged out of the analytical techniques of the chemists of the 18th century. It provided the necessary mathematical relations for the development of the atomic theory and ultimately provided the basis for the development of the balance chemical equation to describe a reaction. Stoichiometry provides the chemist with an understanding of the quantities of reactants required for a reaction to occur and the amount of product that will be formed. But, in a subtle way, it has also provided us with the element masses of the periodic table and is one of the fundamental practical tools of chemistry.
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