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. (a) What is the ratio of the mass of O to C?

Verified step by step guidance

1. Identify the masses of carbon and oxygen obtained from the decomposition: 0.273 g of carbon and 0.727 g of oxygen.
2. To find the ratio of the mass of oxygen to carbon, use the formula: \( \text{Ratio} = \frac{\text{mass of oxygen}}{\text{mass of carbon}} \).
3. Substitute the given masses into the formula: \( \text{Ratio} = \frac{0.727}{0.273} \).
4. Simplify the fraction to find the ratio of the mass of oxygen to carbon.
5. Express the ratio in its simplest form to understand the proportion of oxygen to carbon in the decomposed sample.

Key Concepts

Mass Ratio

The mass ratio is a comparison of the mass of one substance to the mass of another. In this context, it refers to the ratio of the mass of oxygen to the mass of carbon in the decomposition of carbon dioxide. This ratio is calculated by dividing the mass of oxygen by the mass of carbon, providing insight into the relative amounts of each element in the compound.

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 crucial in understanding that the total mass of the products (carbon and oxygen) must equal the mass of the original compound (carbon dioxide). It ensures that when CO2 decomposes, the masses of the resulting elements can be accurately accounted for.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It allows chemists to predict the amounts of substances consumed and produced in a reaction. In this case, stoichiometry helps in understanding how the masses of carbon and oxygen relate to each other after the decomposition of CO2.