Modern Engineering Thermodynamics

15.2 Stoichiometric Equations 593
15.2 STOICHIOMETRIC EQUATIONS
In the early 19th century, the English chemist John Dalton (1766–1844) devised a system of chemical symbols
and determined the relative masses of some elemental atoms. He also formulated a theory that combinations of
different chemical elements occur in simple mass ratios, which led him to the development of a way of writing
a chemical formula that mathematically represented chemical reactions. For example, if elements A and B combine
in a two to one ratio by mass to form chemical C, Dalton wrote this as
2 atoms of A + 1 atom of B = 1 atom of C (15.1)
In modern notation, this would simply be
2A + B !
C
Reactants
where the equality has been replaced by an arrow that indicates the direction of the reaction. The items on the left
side of this equation are called the reactants, and those on the right side are called the products of the reaction.
A description of the net combining properties of atoms and compounds that occur in a chemical reaction is
known today as the stoichiometry of the reaction. Dalton’s chemical equation notation provides a shorthand mathematical
version of such a description, and the numerical values that precede the chemical symbols in these equations
are called the stoichiometric coefficients of the reaction. These coefficients represent the number of atoms or
molecules involved in the reaction, and since mass is conserved in ordinary chemical reactions, the number of
atoms of each chemical element must be the same in both the reactants and the products. Therefore, a chemical
equation can be balanced (i.e., mass balanced) by requiring stoichiometric coefficients that produce the same number
of atoms of each chemical species on both sides of the reaction equation. For example, the reaction that occurs
in burning hydrogen to completion in a pure oxygen atmosphere can be written in modern notation as
aðH 2 Þ + bðO 2 Þ!cðH 2 OÞ
where a, b, andc are the stoichiometric coefficients for the reaction. An individual atomic species balance now gives
Product
Atomic hydrogen ðHÞbalance: 2a = 2c
Atomic oxygen ðOÞbalance: 2b = c
thus producing two equations in the three unknowns, a, b, andc. Since such reactions are usually of interest per
unit mass of fuel supplied, we can arbitrarily set a = 1: then, the atomic hydrogen and oxygen balances gives c = 1
and b = 1 2
= 0.5. Therefore, our final balanced equation would read
H 2 + 0:5ðO 2 Þ!H 2 O (15.2)
After an extensive period of experimentation, the Italian chemist Count Amado Avogadro (1776–1856)
proposed in 1811 that equal volumes of different gases at the same temperature and pressure contain equal
numbers of molecules.
WHAT DOES THE WORD STOICHIOMETRY MEAN?
The term stoichiometry comes from the Greek words stoicheion (component) and metron (measure). It was introduced in
1792 by the German chemist Jeremias Benjamin Richter, when he suggested that substances react chemically according to
relations that resemble mathematical formulae.
WHAT IS AVOGADRO’S LAW?
Avogadro’s law states that equal volumes of different gases at the same temperature and pressure contain equal numbers of
molecules. The Avogadro constant, N A (originally called Avogadro’s number), is the number of atoms in exactly 12 kg of
carbon-12. The 2006 value is
N A = 6:022 1 × 10 26 atoms/kgmole = 2:731 6 × 10 26 atoms/lbmole
Although Avogadro introduced this law in 1811, it was not generally accepted by the scientific community until after 1858.
Incidentally, André Marie Ampère (1775–1836) popularized the term molecule for an assembly of atoms in about 1814.