Empirical Formula
An empirical formula is a mathematical expression that represents the proportional relationships between different elements in a chemical compound, based on real-world observations rather than theoretical predictions. In chemistry, it is commonly used to indicate how the amounts of various chemical substances relate to one another, often expressed in ratios or percentages. For instance, the empirical formula for water is H2O, indicating a ratio of two hydrogen atoms to one oxygen atom. While it provides insight into the composition of a substance, the empirical formula does not specify the exact quantity of each element present in a sample.
Knowing an empirical formula can aid scientists in calculating the actual amounts of elements in a compound when combined with additional data, such as molecular weights. Importantly, empirical formulas do not reveal the molecular structure of compounds, meaning multiple compounds can share the same empirical formula, as seen with benzene and acetylene, both represented as CH. An analogy for understanding this distinction is comparing toy blocks used to create different structures; while the blocks may be the same, the arrangements yield very different results.
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Empirical Formula
An empirical formula is an equation that expresses an empirical relationship. An empirical relationship is based on real-world observations rather than on theoretical conjecture. The most common context in which empirical formulas are used is chemistry, where mathematical calculations are used to discover the amounts of various chemical substances required to produce the desired results.
The empirical formula does not give a precise indication of how much of a chemical ingredient is present in a particular sample. Instead, an empirical formula describes the proportional relationships that must exist between the various ingredients for them to be combined in a reaction that creates a given compound. These proportional relationships are usually expressed as either percentages or in ratio form. For example, one could say that the chemical composition of water is two hydrogen atoms for every one oxygen atom (hence, H2O) or that a given quantity of water will be approximately 66% hydrogen and 30% oxygen. These are both empirical formulas that tell an observer of a sample of material how much of one substance there is in relation to another substance. But they do not tell how much of the substance is present in the sample.
Overview
Knowing the empirical formula of a compound is useful to scientists because (while it does not directly tell exactly how much of a substance is present in a sample) it can be used to calculate this value with the addition of more information. If one knows the empirical formula of the compound C4H6O3, for example, and if there are 100 grams of the compound present—and then if one also knows the molecular weight of each element in the compound (for example, Cs molecular weight is 12.011)—it is possible to calculate an approximate value for the amount of each element present in the compound.
It is important to remember that an empirical formula does not tell one anything about the molecular structure of a compound; that is, the empirical formula does not indicate how the atoms of each element are arranged within a molecule of the compound. The empirical formula simply shows how much of each element will be present in a given molecule or sample. Thus, it is possible for a single empirical formula to describe more than one compound.
A well known example of this can be seen in the empirical formulas of acetylene and benzene. Each of these compounds contains equal amounts of carbon and hydrogen. Therefore, the empirical formula for both benzene and acetylene is CH. What accounts for the differences between the two substances is the way the atoms are arranged in each molecule. In acetylene, the molecular formula is C2H2, meaning that each acetylene molecule has two C and two H atoms. Benzene, though, has a molecular formula of C6H6.
A helpful analogy for remembering the difference between empirical and molecular formulas is that of children’s toy blocks. We can give a child five red blocks and seven blue blocks, which would have an empirical formula of R5B7. The child could then use these blocks to create two very different structures: one a truck and the other an airplane. The properties of these structures are as distinct as benzene and acetylene are from one another.
Bibliography
Berg, Hugo. Mathematical Models of Biological Systems. New York: Oxford UP, 2011.
Dahm, Donald J., and Eric A. Nelson. Calculations in Chemistry: An Introduction. New York: Norton, 2013.
Leszczynski, Jerzy. Handbook of Computational Chemistry. Dordrecht: Springer, 2012.
Monk, Paul, and Lindsey J. Munro. Maths for Chemistry: A Chemist's Toolkit of Calculations. New York: Oxford UP, 2010.
Nassiff, Peter, and Wendy A. Czerwinski. "Using Paperclips to Explain Empirical Formulas to Students." Journal of Chemical Education 91.11 (2014): 1934-38.