Discussion: Early in the transition from alchemy to the science of chemistry, researchers recognized the consistency in the mass relationships that exist between the elements present in compounds. Beginning with Lavoisier establishing the Law of Conservation of Mass, the investigation into the composition of matter led Joseph Louis Proust in 1799 to propose the Law of Definite Proportions. In this postulate, Proust states the ratio by mass of elements present in a chemical compound always contains the elements in certain constant proportions, independent of the source. For example, Proust always found copper carbonate to contain 5.3 parts copper to 4.0 parts oxygen to 1.0 part carbon by mass, whether prepared in the laboratory or from natural sources such as in the mineral malachite. The compositional makeup of the copper carbonate can be expressed as its percent composition by appropriate conversion of the parts by mass relationship. While working on his study of gases, John Dalton discovered that several elements could combine with one another in different proportions and the ratios of these combinations always reduced to a simple whole number. This extension of Proust's law become know as the Law of Multiple Proportions. According to the Law of Multiple Proportions, the ratio of the compound ratios of the elements present in the related compounds can be expressed as a small whole number. Experimental evidence such as this led Dalton to postulate that compounds are formed through the combination of the fundamental particles of elements, the atom, from which they are comprised. This observation and others eventually led Dalton to formulate his atomic theory, which is recognized as the beginning of the modern era of chemistry. Stoichiometry, a term first used by Jeremias Benjamin Richter in describing his Law of Equivalent Proportions (1792 - 1794), gives the quantitative relationships between reactants and products in any balanced equation. In applying this law to the formation of water and hydrogen peroxide from their elements, for 100g of oxygen, the formation of water requires 12.6g of hydrogen, a 7.94 mass equivalency, while production of hydrogen peroxide from an equivalent mass of oxygen requires 6.3g, a 15.9 mass equivalency. While this law of equivalency was useful in understanding the mass relationships between reactants and products, it did not provide any insight to the formation of compounds in terms of their molecular composition. Improvements in the determination of the atomic masses of the elements and the reaffirmation of Avogadro's principles by Stanisloa Cinnazzaro in 1858 lead to the general acceptance of the distinction between atomic and molecular mass. Cinnazzaro's work in distinguishing the atomic mass of elements from the molecular mass of their compounds proved useful in deriving the stoichiometric relationships within molecules, enabling the determination of the chemical formula of the compound. The application of Avogadro's mole relationships, through the molar mass equivalencies, permits conversion of the atomic or molecular quantities to the macroscopic quantities used in the laboratory. The formation of water from its elements can therefore be restated as two moles of hydrogen combine with one mole of oxygen yielding two moles of water - a 2:1 or 1:1 stoichiometry, respectively. These mole quantities are expressly related to the equivalent proportions ascribed by Richter: 4.03g of hydrogen react stoichiometrically with 32.0g of oxygen, a 7.94 mass equivalency, forming 36.0g of water. In this laboratory exercise, an oxide is tin is synthesized and its empirical formula determined based on the concepts previously discussed. Tin, a vary stable element with respect to oxidation, cannot be converted directly to an oxide by simple combustion in air. To form the tin oxide, the tin will be oxidized by reaction with concentrated nitric acid, a strong oxidizing agent. The resulting compound, metastannic acid, is converted to Page - 1 Inorganic Chemistry Empirical Formula R2T the tin oxide at elevated temperatures. The overall reaction is represented in the following unbalanced equation: a Sn(s) + b HNO3 (aq) c SnxOy (s) + d H2O(g) + e NO2 (g) In order to facilitate the high temperature conversion of the metastannic acid, the tin is added directly to a porcelain crucible that has been brought to constant mass by repetitive heating and cooling until two subsequent massings agree to within 0.5mg. Working in the fume hood, concentrated nitric acid is added dropwise to the tin and evidence of a chemical reaction is noted by the generation of brown nitrogen dioxide gas. This reaction is performed in the hood to reduce any potential exposure to the toxic nitrogen dioxide. Nitric acid is added in small amounts until there is no evidence of continued reaction. During the addition of nitric acid, the crucible is placed on a hot plate at a low temperature to accelerate the reaction and to help drive off the water. The crucible and reaction mass are subsequently place above a Bunsen burner which is heated gently to evaporate any remaining water. Once the water has been removed, the burner is adjusted for high temperature heating of the crucible, evidenced by the bottom of the crucible glowing red-orange. Heating at this point is maintained for 3 to 5 minutes. Reacting and heating the sample mass in this manner is continued until a constant mass is achieved. The mass of oxygen that has combined with the tin is determined by difference the increase in mass of the crucible and tin is due to the oxygen in the product. This mass is converted to moles of oxygen and the oxygen to tin ratio calculated. The ratio obtained is transformed to a small whole number ratio. The empirical formula of the compound is determined based on this small whole number ratio.

Question: Mathematically determine the identity of the two hydrogen-oxygen compounds presented in the discussion section. Show your work.