Simple and multiple proportions

The development of chemistry itself has progressed significantly by analytical findings over several centuries. Fundamental knowledge of general chemistry is based on analytical studies, the laws of simple and multiple proportions as well as the law of mass action. Most of the chemical elements have been discovered by the application of analytical chemistry, at first by means of chemical methods, but in the last 150 years mainly by physical methods. Especially spectacular were the spectroscopic discoveries of rubidium and caesium by Bunsen and Kirchhoff, indium by Reich and Richter, helium by Janssen, Lockyer, and Frankland, and rhenium by Noddack and Tacke. Also, nuclear fission became evident as Hahn and Strassmann carefully analyzed the products of neutron-bombarded uranium. 

Hissins, WjlHam (1763-1825) Irish chemist who was the first to propose, although without any experimental data, that substances forming chemical compounds do so according to laws of simple and multiple proportions. The principle was later formulated by John Dalton. 

In the two decades between Lavoisier s Traite and Daltons New System of Chemical Philosophy, we find a conscious effort to accommodate chemical knowledge to a systematic compositional framework. This assimilation was organized through the new nomenclature and the operational concept of simple body. At the same time, there was a great increase in the gathering of quantitative data and attempts to find rational patterns to incorporate them. The results anticipated empirically the laws of constant composition and multiple proportion that reached full rationality in Dalton s atomic theory early in the next century. 

The assumed formulas are presented in line 1. The percent composition of each compovmd, calculated in the usual way, is presented in line 3, showing that these two compovmds, indeed, have different compositions, as required by the law of multiple proportions. Line 4 contains the ratio of the mass of mercury to the mass of oxygen, for each compound. Those ratios can be expressed as the ratio of simple whole numbers (2.25 4.5 = 1 2), fulfilling a condition required by the law of multiple proportions. Notice that Dalton s ideas do not depend upon the values assigned to the elements or the formulas for the compounds involved. Indeed, the question as to which compound, red or black, is associated with which formula cannot be answered from the data available. Thus, although Dalton was unable to establish an atomic mass scale, his general theory did provide an rmderstanding of the three mass-related laws conservation, constant composition, and multiple proportion. Other information was required to establish the relative masses of atoms. 

The Laws of Reciprocal and Multiple Proportions have ceased to have predictive scientific value. Their importance hes in the fact that they provided evidence that Dalton needed in 1807 to postulate his atomic theory. The reason for Richter s whole number ratios has since become obvious the simple ratios occur because atoms, although having different masses, react in simple ratios. Dalton s insistence that atoms cannot be split in chemical reactions holds true in modern chemistry. 

The atomic theory is based upon the laws of definite and multiple proportions. Exact analyses of many substances have shown that the constituent elements of these substances are combined in such quantities that definite amounts or their multiples are always combined with each other. The atomic theory gives a definite and simple theory to account for this. The molecular theory is based upon the existence of certain quantitative relationships between the chemical compositions of substances and their relative volumes in gas form or osmotic pressures in dilute solutions. These theories were based upon quantitative experimental data and accounted for them satisfactorily. In recent years the existence of atoms and molecules has... 

In last century the knowledge of defects in a solid, especially an oxide, has been explored comprehensively. The contribution of Schottky and Wagner successfully put the problem on a quantitative basis and promote the discovery of semiconductor transistor. The idea of non-stoichiometry was developed by Berthollet more than a hundred years ago and the controversy between berthollides, which do not obey the Dalton s law, and daltonides, which follow Dalton s law of constant and multiple proportions based originally upon the study of simple ionic and molecular species, encouraged the scientific debates on how existence of point defect in a compound is is it random statistic distribution or the structure related The experimental data are the best way to explore the truth. Indirect and direct observations of atom... 

Dalton s Law of Multiple Proportions meant that two elements combine in simple whole number ratios. Dalton believed that compounds found in nature would be simple combinations. Hence, knowing that hydrogen combines with oxygen to give water, Dalton s formula for water would consist of 1 H and 1 O. Its formula would be HO using modern nomenclature. Both Proust s Law of Definite Proportions and Dalton s Law of Multiple Proportions are outcomes of an atomic view of nature. In 1808 Dalton published his table of relative atomic weights along with his ideas on atomism in A New System of Chemical Philosophy. 

Biyan Higgins (1737 or 1741-1818) applied Newton s repulsion of atoms in air to simple and compound gases, and suggested that there were caloric atmospheres around molecules of compound gases (51). Many of his ideas were promoted by his nephew, William Higgins (1762/3-1825), who anticipated parts of Dalton s atomic theory and law of multiple proportions in 1789 (52). In 1814, he wrote (55) ... 

The term stoichiometry is often used and is well understood in Chemistry, and the law of definite proportions and the law of multiple proportion are well-known examples deduced from the stoichiometric relation. The existence of non-stoichiometric compounds cannot be explained by a simple interpretation of the above mentioned laws, however, it is no exaggeration that all inorganic compounds exhibit non-stoichiometry. 

By then the French chemist, Joseph Louis Proust, had discovered that whenever elements form compounds these are always of a very definite composition —- the Law of Definite Composition. Water molecules, for example, always contain the same number of hydrogen and oxygen atoms. And Dalton had found that when two elements combine in different ways they do this in simple proportions — the Law of Multiple Proportions. One atom of carbon and one atom of oxygen make carbon monoxide one atom of carbon and two atoms of oxygen make carbon dioxide. 

Additive nomenclature1 is based on the combination of element names or roots of element names and/or ligand names. The simplest and oldest additive nomenclature is binary nomenclature that expresses two components, e.g. sodium chloride. The cationic or electropositive portion of the compound expressed in a binary name is the element name unchanged or a group name ending in -ium , and the anionic or electronegative portion of a compound expressed in the name ends in -ide, -ite or -ate. The proportions of cations and anions in neutral compounds are indicated by Stock numbers or simple or multiplicative prefixes (see Section 3.3.2). Additive nomenclature denotes composition. For examples see Table 1. 

Elements are made of tiny particles called atoms, which can combine in simple numerical ratios according to the law of multiple proportions. Atoms are composed of three fundamental particles Protons are positively charged, electrons are negatively charged, and neutrons are neutral. According to the nuclear model of an atom proposed by Ernest Rutherford, protons and neutrons are clustered into a dense core called the nucleus, while electrons move around the nucleus at a relatively large distance. 

The law of multiple proportions was an important contribution to the credibility of Dalton s atomic theory. It was discovered before relative atomic masses were well known (note that Ar values were not involved in the calculation above). However, it follows logically that all atoms of the same element have the same mass (which is unchangeable) and that compounds contain elements in the relative proportions of simple whole numbers. 

In this formulation of CTCB the off-diagonal orbital communications have been shown to be proportional to the corresponding Wiberg [52] or related quadratic indices of the chemical bond [53-63]. Several illustrative model applications of OCT have been presented recently [38,46-48], covering both the localized bonds in hydrides and multiple bonds in CO and C02, as well as the conjugated n bonds in simple hydrocarbons (allyl, butadiene, and benzene), for which predictions from the one- and two-electron approaches have been compared in these studies the IT bond descriptors have been generated for both the molecule as whole and its constituent fragments. 

The composition of compounds is usually expressed in per cent. If, however, a definite weight is adopted as a unit for one component, and the composition is expressed in terms of this unit, the simple integral relation existing between the different proportions of the other element is clearly seen. The following table illustrates the law of multiple proportions —... 

HISTORICAL REMARKS. THE LAWS OF CONSTANT PROPORTIONS, SIMPLE MULTIPLE PROPORTIONS, AND COMBINING WEIGHTS... 

Three laws of stoichiometry may now be considered The Laio of Constant Proportions, The Law of Simple Multiple Proportions, and The Law of Combining V/eights. These were originally empirical laws, based upon experiment. At the time that the laws were formulated it was seen that the atomic theory provides a simple explanation of them and although the laws do not require that the atomic theory be true most chemists accepted the theory as providing the simplest explanation of chemical weight relations. 

Historical development the laws of constant proportions, simple multiple proportions, and combining weights. 

When many ionic compounds are crystallized from a water solution, they include individual water molecules as part of their crystalline structure. If the substances are heated, this water of crystallization may be driven off and leave behind the pure anhydrous form of the compound. Because the law of multiple proportions also applies to crystalline hydrates, the number of moles of water driven off per mole of the anhydrous compound should be a simple whole-number ratio. You can use this information to help you determine the formula of the hydrate. 

One of the tasks closely related to documentation is simple calculations that have to be performed to prepare an experiment. The number of calculations performed, for instance, in the organic synthesis laboratory is quite small, but those calculations required are very important. The calculations associated with conversion of the starting materials to the product are based on the assumption that the reaction will follow simple ideal stoichiometry. In calculating the theoretical and actual yields, it is assumed that all of the starting material is converted to the product. The first step in calculating yields is to determine the limiting reactant. The limiting reactant in a reaction that involves two or more reactants is usually the one present in lowest molar amount based on the stoichiometry of the reaction. This reactant will be consumed first and will limit any additional conversion to product. These calculations, which are simple rules of proportions, are subject to calculation errors due to their multiple dependencies. 

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