Fundamental laws of chemical reactions and chemical equations

1.

The law of conservation of mass (Lavoisier, 18th century): Lavoisier was one of the first to carry out quantitatively accurate chemical measurements. He demonstrated that combustion required oxygen, and he demonstrated oxygen's role in the rusting of metals. His observations led him to deduce the following general law known as the law of conservation of mass:

In every chemical transformation, an equal quantity of matter exists before and after the reaction.

(Because he was a tax collector and nobleman, Lavoisier was branded a traitor during the French Revolution and beheaded in 1794.)

2.

law of definite proportions (Joseph Proust, shortly after Lavoisier): Proust studied metal compounds, including metal oxides, carbonates and sulfides. From the work of Robert Boyle in the 17th century, it was understood that substances that could be broken down into more fundamental components were mixtures or compounds. Substances that could not be further broken down were referred to as elements. Thus, Proust deduced the so-called law of definite proportions:

In a given chemical compound, the proportion by mass of the elements that compose it are fixed, independent of the origin of the compound or its mode of preparation.

This is basically saying that sodium chloride, for example, is always NaCl, no matter how it is obtained, made, or prepared. There are no ``intermediate'' compounds.

3.

The law of multiple proportions: (John Dalton, shortly after Proust): Studied gases and gaseous mixtures under different external conditions. Building on Proust's work, he noted that mathematically discrete manner in which elements combined to form different compounds. For example, in carbon monoxide (CO), the mass ratio of oxygen to carbon $m_{\rm O}/m_{\rm C} = 1.33$ and in carbon dioxide (CO$_2$) $m_{\rm O}/m_{\rm C} = 2.66$. Thus, since the amount of carbon is fixed in each compound, we can look at how the amount of oxygen varies, and we find that $m_{\rm O}({\rm in\ CO}_2)/m_{\rm O}({\rm in\ CO}) = 2$. The generalization of this idea is the law of multiple proportions:

When two elements form a series of compounds, the masses of one that combine with a fixed mass of the other are in the ratio of (small) integers to each other.

This law is obeyed by all gaseous compounds, which is what Dalton studied. Certain solids are exceptions to both this rule and the law of definite proportions. An example is the solid wüstite, which can range from Fe$_{0.95}$O to Fe$_{0.85}$O, depending on the mode of preparation. These formulae express the incommensurate compositions possible in this solid. But, since atoms are essentially indestructible (we have to work hard to get them to fission!), this explains why we do not find compounds such as C$_{13/7}$H$_{5/3}$ in nature. Dalton's observations led him to propose the notion of the atom as the fundamental and indestructible building blocks of matter.

4.

The law of combining volumes (Joseph Gay-Lussac, Amedeo Avagadro, Stanislao Cannizzaro, early 19th century following Dalton): Again, based on studies of gases and how they combine, the law of combining volumes has been attribued to these three. The generalization of the observations is stated as follows:

When two gases are allowed to react, such that the gases are at the same temperature and pressure, the volumes of each gas consumed will be in the ratio of small integers. Moreover, the ratio of the volume of each product gas to the volume of either reacting gas will be a ratio of simple integers.

Example: 3 volumes of hydrogen + 1 volume of nitrogen $\rightarrow$ 2 volumes of ammonia.

Although this is a statement about gases, its implications can be deduced: the coefficients in chemical equations expressions how much of different reactants combine to give products will be integers.

5.

Avogadro's hypothesis (1811):

Equal volumes of different gases (at the same temperature and pressure) contain equal numbers of particles.

Example: How many particles are in 1 L of O$_2$ gas, and how many particles are in 1 L of H$_2$ gas? The density of O$_2$ is 1.429 g/L, and the density of H$_2$ gas is 0.0899 g/L.

Solution:

$${\rm mass\ of\ O_2} = (1 {\rm L}) (1.429 {\rm g/L}) = 1.429 {\rm g}$$

$${\rm moles\ of\ O_2} = {1.429 {\rm g} \over 31.998 {\rm g/mol}} = 0.04466 {\rm mol}$$

$${\rm molecules of O_2} = (0.04466 {\rm mol})(6.022\times 10^{23} {\rm molecules/mol}) = 2.69\times 10^{22} {\rm molecules}$$

$${\rm mass\ of\ H_2} = (1 {\rm L}) (0.0899 {\rm g/L}) = 0.0899 {\rm g}$$

$${\rm moles\ of\ H_2} = {0.0899 {\rm g} \over 2.0158 {\rm g/mol}} = 0.04466 {\rm mol}$$

$${\rm molecules of H_2} = (0.04466 {\rm mol})(6.022\times 10^{23} {\rm molecules/mol}) = 2.69\times 10^{22} {\rm molecules}$$

Combining Avogadro's hypothesis with the law of combining volumes allows the statement written above about volumes of hydrogen and nitrogen combining to give ammonia as a statement about definite numbers of molecules rather then volumes. This number could be expressed as moles, or even as individual molecules. The statement then reads:

$$3{\rm H}_2 + {\rm N}_2 \longrightarrow 2 {\rm NH}_3$$

This is an example of a balanced chemical equation. What does it mean to be balanced? It means that the law of conservation of mass is obeyed - equal quantities of hydrogen and nitrogen exist on both sides of the reaction. Furthermore, the coefficients, i.e., the numbers multiplying H$_2$, N$_2$ and NH$_3$ in the above equation, are expressible as simple integers. When balancing chemical equations, this serves as an important check.