Consider a sample of \(92.5 \mathrm{~g}\) of \(\mathrm{O}_{2}\) molecules. (a) How many moles of \(\mathrm{O}_{2}\) molecules are present? (b) How many moles of \(\mathrm{O}\) atoms are present?

Understanding molar mass is crucial when it comes to dealing with measurements in chemistry. Molar mass is defined as the mass of one mole of a substance, usually expressed in grams per mole (g/mol). It corresponds to the mass of 6.022 x 10²³ (Avogadro's number) particles of that substance. For elements, the molar mass is the mass of one mole of atoms and is numerically equivalent to the atomic weight given in the periodic table.

In our exercise, the calculation of the molar mass of an oxygen molecule (\r\(O_2\)) is performed by adding the molar masses of two oxygen atoms. Since one oxygen atom has a molar mass of approximately 16 g/mol, for the molecule \r\(O_2\), the molar mass is double this value: \r\[M_{O_{2}} = 2 \times 16 \mathrm{\ g/mol} = 32 \mathrm{\ g/mol}\]. Knowing the molar mass is the first step before we can convert between grams and moles, which is a foundational skill in chemical stoichiometry.

The mole concept is a bridge between the microscopic world of atoms and molecules with the macroscopic world we encounter in the laboratory. A mole is simply a certain number of particles (usually atoms or molecules) and is one of the seven SI base units. Avogadro's number (named after the scientist Amedeo Avogadro) is the number of particles in one mole, which is approximately 6.022 x 10²³ particles.

When dealing with compounds, moles refer to this fixed number of molecules. In our example with oxygen, we've determined that 92.5 g of \r\(O_2\) correspond to \r\(2.890625 \mathrm{\ mol}\) of oxygen molecules, using its molar mass. This helps us quantify the substance in terms of a number that connects to the amount of molecules present, rather than dealing with an incomprehensible number of individual atoms.

Stoichiometry is the area of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction, based on the principles of the mole concept and conservation of mass. It comes from the Greek words \r\(\text{\'stoicheion\'}\) (element) and \r\(\text{\'metron\'}\) (measure).

In practice, stoichiometry allows us to predict how much product will form from a given amount of reactants, or vice versa. In the given exercise, we calculated moles of \r\(O_2\) molecules and then converted that to moles of oxygen atoms. This step is a form of stoichiometric calculation because it involves the ratio of the number of molecules of \r\(O_2\) to the number of atoms of oxygen, which is 2:1, according to the chemical formula. Understanding the stoichiometric relationships in chemical compounds is essential for tasks including creating reaction mechanisms, determining theoretical yields of a reaction, and analyzing reactant-product conversion efficiency.