A 1.0 -g sample of carbon dioxide \(\left(\mathrm{CO}_{2}\right)\) is fully decomposed into its elements, yielding \(0.273 \mathrm{~g}\) of carbon and \(0.727 \mathrm{~g}\) of oxygen. (a) What is the ratio of the mass of \(\mathrm{O}\) to \(\mathrm{C} ?(\mathbf{b})\) If a sample of a different compound decomposes into \(0.429 \mathrm{~g}\) of carbon and \(0.571 \mathrm{~g}\) 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?

To find the ratio of the mass of Oxygen to Carbon in CO2, we simply divide the mass of Oxygen by the mass of Carbon. Mass of Carbon = 0.273 g Mass of Oxygen = 0.727 g Ratio of O to C = Mass of Oxygen / Mass of Carbon Calculate the ratio: Ratio of O to C = 0.727 g / 0.273 g = 2.66

Similarly, for the second compound, we will find the mass ratio of Oxygen to Carbon by dividing the mass of Oxygen by the mass of Carbon. Mass of Carbon = 0.429 g Mass of Oxygen = 0.571 g Ratio of O to C = Mass of Oxygen / Mass of Carbon Calculate the ratio: Ratio of O to C in the second compound = 0.571 g / 0.429 g = 1.33

To find the empirical formula of the second compound, we will first convert the mass ratio of O to C into the mole ratio by dividing the mass of each element by its molar mass. Molar mass of Carbon = 12.01 g/mol Molar mass of Oxygen = 16.00 g/mol Moles of Carbon = 0.429 g / 12.01 g/mol = 0.0357 mol Moles of Oxygen = 0.571 g / 16.00 g/mol = 0.0357 mol Now, we will find the simplest whole-number ratio of the moles of each element by dividing the moles of each element by the smallest number of moles. In this case, the smallest number of moles is 0.0357 mol. Simplest ratio of moles of Carbon = 0.0357 mol / 0.0357 mol = 1 Simplest ratio of moles of Oxygen = 0.0357 mol / 0.0357 mol = 1 Thus, the empirical formula of the second compound is \(CO\).