Opening Essay
“When the disengaged gasses are carefully examined, they are found to weigh 113.7 grs.; these are of two kinds, viz. 144 cubical inches of carbonic acid gas, weighing 100 grs. and 380 cubical inches of a very light gas, weighing only 13.7 grs.…and, when the water which has passed over into the bottle [labeled] H is carefully examined, it is found to have lost 85.7 grs. of its weight. Thus, in this experiment, 85.7 grs. of water, joined to 28 grs. of charcoal, have combined in such a way as to form 100 grs. of carbonic acid, and 13.7 grs. of a particular gas capable of being burnt.” (Bold emphasis added.)
In this paragraph from the Elements of Chemistry, Antoine Lavoisier (1743–94) is explaining an experiment in which he was trying to demonstrate that water is not an element but instead is composed of hydrogen (the gas “capable of being burnt”) and oxygen. This is a historical account of a groundbreaking experiment and illustrates the importance of amounts in chemistry. Lavoisier was pointing out that the initial total mass of water and charcoal, 85.7 g plus 28 g, equals the final total mass of carbonic acid and the particular gas, 100 g plus 13.7 g. In this way, he was illustrating the law of conservation of matter, which was introduced in Chapter 5 “Introduction to Chemical Reactions”.
Amounts do matter and in a variety of circumstances. The chapter-opening essay in Chapter 1 “Chemistry, Matter, and Measurement” tells the story of a nurse who mistakenly read “2–3 mg” as “23 mg” and administered the higher and potentially fatal dose of morphine to a child. Food scientists who work in test kitchens must keep track of specific amounts of ingredients as they develop new products for us to eat. Quality control technicians measure amounts of substances in manufactured products to ensure that the products meet company or government standards. Supermarkets routinely weigh meat and produce and charge consumers by the ounce or the pound.
So far, we have talked about chemical reactions in terms of individual atoms and molecules. Although this allows us to visualize stoichiometry at a molecular level, in the real, macroscopic world, we do not see atoms and molecules and in general have no way to count them. Even a tiny sample of a substance will contain millions, billions, or a hundred billion billions of atoms and molecules. How do we compare amounts of substances to each other in chemical terms when it is so difficult to count to a hundred billion billion?
In the real world, we often determine the quantity of a substance by determining its mass. Yet in reactions, the amounts of reactants and products are related by number of atoms and molecules shown in the coefficients of balanced equations, not by mass. In this chapter, we will look at calculations that build bridges between the world of atoms and molecules, the masses we can measure in the lab, and the equation coefficients relating one chemical to another. In doing so, we will increase our understanding of stoichiometry, which is the study of the numerical relationships between the reactants and the products in a balanced chemical reaction.
