Some Other Interpretations of Chemical Formulas

As we shall see when we discuss the composition of compounds in some detail, two (and sometimes more) elements may form more than one compound. The Law of Multiple Proportions summarizes many experiments on such compounds. It is usually stated  

When two elements, A and B, form more than one compound, the ratio of the masses of element B that combine with a given mass of element A in each of the compounds can be expressed by small whole numbers. 

What is the ratio of the numbers of oxygen atoms that are combined with a given number of nitrogen atoms in the compounds N2O3 and NO  

To compare the number of oxygen atoms, we need to have equal numbers of nitrogen atoms. Solution 

Because NO has half as many nitrogen atoms in its formula relative to N2O3, we must multiply it by a factor of 2 to compare the two elements on the basis of an equal number of nitrogen atoms. Once we show the number of atoms of each element present, we can cancel out the equal amounts of nitrogen atoms, leaving the ratio of oxygen atoms. 

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Some Other Interpretations of Chemical Formulas 2-12 Purity of Samples... 

Derivation of Formulas from Elemental Composition 2-9 Determination of Molecular Formulas 2-10 Some Other Interpretations of Chemical Formulas 2-11 Purity of Samples... 

After a brief bibliographical sketch, Duhem s professional interests in chemistry are distinguished from his several other interests and related to his general concerns with the development of thermodynamics. His account of chemical formulas is described in sufficient detail to convey why he thought no atomist presuppositions were involved, and some of his reasons for questioning atomism are discussed. The article concludes with a discussion of his imderstanding of the bearing of ancient alternatives to atomism on the interpretation of the science of his time. 

Conclusions as to how the atoms are joined together in any compound are reached from an interpretation of the way in which the compound interacts with other substances. Many cases will be described in the following chapters. Some chemists take exception to the view that a study of the reactions of a substance gives information as to the actual structure of its molecules. They hold that a constitutional formula is nothing more than a short way of expressing the reactions of a substance. Such formulas are a kind of chemical shorthand. Other chemists believe that, as so many facts are in accord with the theory, and as the theory has stood so many tests, it is as well established as the theory of atoms and molecules itself. Which ever view is correct, we can say, at least, that organic compounds react as if their molecules were constituted as represented by their graphic formulas. 

How, indeed, should one interpret the symbols in a molecular formula Dalton thought that each of the symbols in his formulas must signify an actual "atom," in the sense of an absolutely unsplittable entity, much like an invisibly small but very real billiard ball— which is why he chose to represent his atoms by distinctive iconic circles, or spherical wooden models. Few chemists thereafter took such an unre-flectively realist position. At the other extreme, some regarded chemical formulas purely conventionally, as a mere aid to memory in representing the empirical facts of chemical analysis and having no real referent in the microworld at all. 

In the language of linear algebra, N and b define vector spaces, and the dimension of a vector space corresponds to the number of linearly independent vectors, called basis vectors, that are needed to define the space. Then the multiplication in (7.4.2) can be interpreted as a transformation in which A maps a certain subspace of N into a subspace of b. In other words, only certain sets of mole numbers satisfy the elemental balances (7.4.2), and the possible sets of mole numbers depend on the chemical formulae for the species present in the system. That subspace of b, which is accessible to some N, is called the range of A the dimension of the range equals rank(A). According to (7.4.2), any basis vectors for the range automatically satisfy the elemental balances. For example, if we let N represent one particular basis vector for the range, then... 

We have chosen to restrict our stucfy to propagation by modelling of a aystal like nitromethane This choice of this compound was determined hy interest in the diversity of behaviOTs as regards detonations (e.g. in die liquid vs. solid phases sensitivity modified by some traces of additives), and the richness of eiqierimentk other physical and chemical data as well as tiie simplicity of the chemical formula which allow both, the interpretation of experiment and the accuracy of the calculations of the electronic structure in the differ t electronic states... A body of conditions wdiich gives a heuristic character to this compound and, consequmitiy, an opening to new ideas. 

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