Estrone, which contains only carbon, hydrogen, and oxygen, is a female sexual hormone that occurs in the urine of pregnant women. Combustion analysis of a 1.893-g sample of estrone produces 5.545 g of CO2 and 1.388 g H2O. The molar mass of estrone is 270.36 g>mol. Find its molecular formula.

Understanding the empirical formula of a compound is a fundamental aspect of chemistry, particularly in the field of analytical chemistry. An empirical formula represents the simplest whole-number ratio of elements within a compound. For instance, the empirical formula for water is H₂O, which indicates two hydrogen atoms for every oxygen atom.

In the exercise provided, the empirical formula is derived from the combustion analysis data. The calculation begins by determining the moles of each element. Moles are a crucial concept in chemistry; they allow us to relate the mass of a substance to the number of particles it contains. Once the moles of carbon and hydrogen are found from the mass of CO₂ and H₂O produced respectively, the moles of oxygen are calculated by subtracting the mass of carbon and hydrogen from the original sample's mass.

By comparing the mole ratio of the elements, we arrive at the simplest ratio, which is the empirical formula. If, for example, the elements are present in a ratio that appears as 1.5:3:1, we would multiply the numbers by 2 to get whole numbers, resulting in an empirical formula with a whole-number ratio, such as 3:6:2.

After establishing the empirical formula, the next step is to determine the molecular formula. The molecular formula provides information on the exact number of each type of atom present in a molecule of the compound. It can be a multiple of the empirical formula. For example, the empirical formula of benzene is CH, but the molecular formula is C₆H₆, revealing that each molecule of benzene contains 6 carbon and 6 hydrogen atoms.

The exercise involves calculating the moles of carbon, hydrogen, and oxygen, and from these, determining the empirical formula. To find the molecular formula, the molar mass of the compound (given as 270.36 g/mol for estrone) is divided by the mass of the empirical formula unit. This results in a number that is used to multiply the subscripts in the empirical formula to give the precise number of atoms of each element in one molecule of the compound. By carefully comparing these numbers, the molecular formula that reflects the actual molecular composition is obtained.

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It is based on the law of conservation of mass and the concept of moles. Stoichiometry allows us to predict the amounts of substances consumed and produced in a reaction and is essential for calculating yields and for scaling up reactions from the laboratory to industrial scales.

In the given exercise, stoichiometry comes into play when calculating moles from the masses of CO₂ and H₂O produced during combustion. Each mole of CO₂ implies the presence of one mole of carbon atoms, while each mole of H₂O implies the presence of two moles of hydrogen atoms. These stoichiometric relationships allow for the accurate determination of the amounts of carbon and hydrogen in the estrone sample.

Importance of Stoichiometry in Combustion Analysis

Stoichiometry's role is crucial when it comes to analyzing combustion reactions, as it helps in deducing the amount of each element present within the original compound. By converting the mass of products (CO₂ and H₂O) to moles, and hence to moles of the original elements, stoichiometry bridges the gap between reactants and products, providing a full picture of the compound's composition.