# 0.1 Relative atomic masses and empirical formulae

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## Foundation

We begin by assuming the central postulates of the Atomic-Molecular Theory . These are:

• the elements are comprised of identical atoms
• all atoms of a single element have the same characteristic mass
• the number and masses of these atoms do not change during a chemical transformation
• compounds consist of identical molecules formed of atoms combined in simple whole number ratios
. We also assume a knowledge of theobserved natural laws on which this theory is based: the Law of Conservation of Mass , the Law of Definite Proportions , and the Law of Multiple Proportions .

## Goals

We have concluded that atoms combine in simple ratios to form molecules. However, we don't know what thoseratios are. In other words, we have not yet determined any molecular formulae. In the second table of Concept Development Study #1 , wefound that the mass ratios for nitrogen oxide compounds were consistent with many different molecular formulae. A glance back atthe nitrogen oxide data shows that the oxide B could be $NO$ , $N{O}_{2}$ , ${N}_{2}O$ , or any other simple ratio.

Each of these formulae correspond to different possible relative atomic weights for nitrogen and oxygen. Sinceoxide B has oxygen to nitrogen ratio 1.14 : 1, then the relative masses of oxygen to nitrogen could be 1.14:1 or 2.28:1 or 0.57:1 ormany other simple possibilities. If we knew the relative masses of oxygen and nitrogen atoms, we could determine the molecular formulaof oxide B. On the other hand, if we knew the molecular formula of oxide B, we could determine the relative masses of oxygen andnitrogen atoms. If we solve one problem, we solve both. Our problem then is that we need a simple way to "count" atoms, atleast in relative numbers.

## Observation 1: volume relationships in chemical reactions

Although mass is conserved, most chemical and physical properties are not conserved during a reaction. Volume isone of those properties which is not conserved, particularly when the reaction involves gases as reactants or products. For example,hydrogen and oxygen react explosively to form water vapor. If we take 1 liter of oxygen gas and 2 liters of hydrogen gas, by carefulanalysis we could find that the reaction of these two volumes is complete, with no left over hydrogen and oxygen, and that 2 litersof water vapor are formed. Note that the total volume is not conserved: 3 liters of oxygen and hydrogen become 2 liters of watervapor. (All of the volumes are measured at the same temperature and pressure.)

More notable is the fact that the ratios of the volumes involved are simple whole number ratios: 1 liter ofoxygen : 2 liters of hydrogen : 2 liters of water. This result proves to be general for reactions involving gases. For example, 1liter of nitrogen gas reacts with 3 liters of hydrogen gas to form 2 liters of ammonia gas. 1 liter of hydrogen gas combines with 1liter of chlorine gas to form 2 liters of hydrogen chloride gas. These observations can be generalized into the Law of Combining Volumes .

## Law of combining volumes

When gases combine during a chemical reaction at a fixed pressure and temperature, the ratiosof their volumes are simple whole number ratios.

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