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?

Verified step by step guidance

1. Calculate the mass ratio of oxygen to carbon for the second compound by dividing the mass of oxygen by the mass of carbon: \( \frac{0.571 \, \text{g O}}{0.429 \, \text{g C}} \).
2. Simplify the ratio obtained in step 1 to find the simplest whole number ratio. This can be done by dividing both the numerator and the denominator by the smaller of the two values.
3. Use the simplified ratio to determine the empirical formula. The ratio represents the relative number of moles of oxygen and carbon atoms in the compound.
4. Convert the mole ratio into subscripts in a chemical formula. If the ratio from step 2 is, for example, 1.33, this would suggest a subscript of 1 for carbon and approximately 1.33 for oxygen in the empirical formula.
5. Round the subscripts to the nearest whole number if necessary, to get the empirical formula of the compound. This rounding is based on the assumption that the empirical formula represents the simplest whole-number ratio of atoms in the compound.

Key Concepts

Mass Ratio Calculation

To determine the ratio of the mass of oxygen to carbon in a compound, divide the mass of oxygen by the mass of carbon. This ratio provides insight into the relative proportions of elements in a compound, which is essential for understanding its composition and can help in deriving the empirical formula.

Dalton's Atomic Theory

Dalton's atomic theory posits that matter is composed of indivisible atoms, and compounds are formed when atoms of different elements combine in fixed ratios. This theory underpins the concept of empirical formulas, which represent the simplest whole-number ratio of the elements in a compound, reflecting the relative amounts of each element present.

Empirical Formula

The empirical formula of a compound is the simplest integer ratio of the elements present in that compound. To derive it, one must first calculate the moles of each element from their masses, then simplify the ratio of these moles to the smallest whole numbers, which provides a clear representation of the compound's composition.