A 1.0-g sample of carbon dioxide (CO2) is fully decomposed into its elements, yielding 0.273 g of carbon and 0.727 g of oxygen. (b) If a sample of a different compound decomposes into 0.429 g of carbon and 0.571 g of oxygen, what is its ratio of the mass of O to C?

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Identify the masses of carbon and oxygen from the decomposition of the different compound: 0.429 g of carbon and 0.571 g of oxygen.

Calculate the ratio of the mass of oxygen to the mass of carbon by dividing the mass of oxygen by the mass of carbon.

Use the formula: \( \text{Ratio} = \frac{\text{Mass of Oxygen}}{\text{Mass of Carbon}} \).

Substitute the given values into the formula: \( \text{Ratio} = \frac{0.571}{0.429} \).

Simplify the calculated ratio to find the mass ratio of oxygen to carbon in the compound.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Law of Conservation of Mass

The Law of Conservation of Mass states that mass is neither created nor destroyed in a chemical reaction. This principle is fundamental in stoichiometry, as it allows us to account for all the mass of reactants and products in a reaction. In the context of the question, it ensures that the total mass of carbon and oxygen produced from the decomposition of a compound equals the mass of the original sample.

Mass Ratio

The mass ratio is a comparison of the mass of one element to the mass of another element in a compound. It is calculated by dividing the mass of one element by the mass of another. In this question, determining the mass ratio of oxygen to carbon in the second compound is essential for understanding its composition and comparing it to the first compound.

Stoichiometry

Stoichiometry is the area of chemistry that deals with the quantitative relationships between the substances involved in a chemical reaction. It allows chemists to predict the amounts of products formed or reactants consumed based on balanced chemical equations. In this question, stoichiometry is used to analyze the decomposition of compounds and calculate the mass ratios of the resulting elements.

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Textbook Question

A 1.0-g sample of carbon dioxide (CO2) is fully decomposed into its elements, yielding 0.273 g of carbon and 0.727 g of oxygen. If a sample of a different compound decomposes into 0.429 g of carbon and 0.571 g of oxygen, what is its ratio of the mass of O to C? (c) According to Dalton's atomic theory, what is the empirical formula of the second compound?

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