Allicin is the compound responsible for the characteristic smell of garlic. An analysis of the compound gives the following percent composition by mass: C: 44.4 percent; \(\mathrm{H}: 6.21\) percent; \(\mathrm{S}: 39.5\) percent; \(\mathrm{O}\) 9.86 percent. Calculate its empirical formula. What is its molecular formula given that its molar mass is about \(162 \mathrm{~g} ?\)

Determining the percent composition by mass of an element within a compound involves calculating what fraction of the total mass of a compound is made up by each constituent element. This concept is foundational in understanding chemical composition. In a problem related to percent composition by mass, you are typically given percentages for element masses and asked to compute their ratios in a compound.

For instance, in the allicin example, you're provided with percentages for carbon, hydrogen, sulfur, and oxygen. To solve for the empirical formula, it's convenient to assume a 100g sample of allicin, which directly translates the percent into grams. This conversion streamlines the process, allowing us to move effortlessly into the next steps of empirical formula calculation.

Molar mass is a vital concept in chemistry that refers to the mass of one mole of a substance, usually expressed in grams per mole (g/mol). It's the sum of the atomic masses of all atoms in a molecule. In practical applications, the molar mass allows chemists to convert between the amount of substance (in moles) and its mass in grams, providing a bridge between the microscopic world of atoms and the macroscopic quantities we measure in the lab.

In our example with allicin, the molar mass helps determine the molecular formula because it can be compared with the molar mass of the empirical formula. If they match, the empirical and molecular formulas are the same. The accurate determination of molar mass is crucial since it will influence the final molecular formula and thus our understanding of the compound's structure.

Converting moles to grams is an essential skill in chemistry. It involves taking the mole quantity of a substance and multiplying it by the substance's molar mass. One mole always contains Avogadro's number (\(6.022 \times 10^{23}\)) of particles, be they atoms, molecules, ions, or other entities, and the molar mass is the mass of one mole of those particles.

For example, in calculating the moles of carbon (C) from allicin, with 44.4g of carbon present, we use carbon's molar mass (12.01 g/mol) to find that we have 3.7 moles of carbon. This conversion from grams to moles is critical as it permits us to engage in stoichiometric calculations, which are often based on mole ratios rather than mass ratios.

Stoichiometric calculations are at the heart of chemical reactions. They involve using the relationships between reactants and products in a reaction, expressed in moles, to calculate various quantities of interest. When determining the empirical formula, stoichiometry comes into play by using mole ratios. Once we have the amount of moles for each element, we divide all amounts by the smallest mole quantity to find the simplest whole number ratio of atoms in the compound.

In the case of allicin, after converting to moles, we determine the smallest number of moles present among the elements (here, it's oxygen with 0.62 moles) and divide other elements' mole quantities by this number. The resulting ratios provide the subscripts in the empirical formula. Mastering stoichiometric calculations is essential for a wealth of chemical analyses, including empirical formula determination.