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Stoichiometry is the branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. Understanding stoichiometry is vital for predicting the outcomes of reactions and for calculating the amounts of substances needed or produced. For instance, in the exercise given, we are asked to compare the weights of two substances, which directly relates to stoichiometric calculations.

When observing stoichiometry in a practical sense, it ensures that if we know the quantity of one substance, we can compute the quantity of another substance that reacts with or is produced from the first. In the exercise, knowing how many molecules of \(\mathrm{SO}_3\) we have allows us to calculate the equivalent number of \(\mathrm{O}_2\) molecules through stoichiometric principles. The fundamental concept to grasp here is the mole ratio, established by balanced chemical equations or, as in this case, by molecular weights, which acts as conversion factors between different substances.

Chemical composition refers to the identity and ratio of the elements that make up any particular compound. Each compound has a specific chemical formula that can be used to determine its composition and, subsequently, its molecular weight. For example, the chemical formula \(\mathrm{SO}_3\) represents sulfur trioxide, indicating that each molecule is composed of one sulfur atom and three oxygen atoms.

The knowledge of chemical composition is crucial when performing molecular weight calculations. It tells us directly how many atoms of each element are present in a molecule, which is the first step in determining the molecular weight. For our exercise, understanding that \(\mathrm{SO}_3\) contains three oxygen atoms compared to the two in an \(\mathrm{O}_2\) molecule provides the information needed to draw a comparison in weight between a known number of \(\mathrm{SO}_3\) and \(\mathrm{O}_2\) molecules.

Molar mass, often referred to as molecular weight, is the mass of one mole of a substance and is expressed in grams per mole (g/mol). It is calculated by summing the atomic masses of all the atoms in its chemical formula. For instance, in the exercise, the molar mass is found by taking the atomic weights of sulfur and oxygen from the periodic table to find the weight of a single sulfur trioxide molecule.

To calculate the molar mass of \(\mathrm{SO}_3\), we add one sulfur atom (with an atomic mass of 32) to three oxygen atoms (each with an atomic mass of 16), totaling to 80 u for \(\mathrm{SO}_3\). Similarly, \(\mathrm{O}_2\)’s molar mass is 32 u. These molar masses are pivotal in stoichiometric calculations as they allow us to relate and convert different substances' quantities together intelligibly. This is exactly what's applied in determining that 20 \(\mathrm{SO}_3\) molecules weigh as much as 50 \(\mathrm{O}_2\) molecules, linking the concept of stoichiometry, chemical composition, and molar mass.