Find the total number of atoms in a sample of cocaine hydrochloride, C17H22CINO4, of mass 23.5 mg.

Stoichiometry is akin to a recipe for chemical reactions. It allows chemists to calculate the relative quantities of reactants and products involved in a chemical process. At its core, stoichiometry is about balance and proportion. It provides the quantitative relationship between reactants and products in a balanced chemical equation, ensuring that atoms are conserved during the reaction.

For example, in the exercise, we used stoichiometry to link the mass of cocaine hydrochloride to the number of moles, and subsequently to the number of atoms. This process starts by computing the molar mass, which is essential for converting mass to moles, and then to the total number of molecules and atoms in the sample.

Avogadro's number is a fundamental constant in chemistry, representing the number of elementary entities (usually atoms or molecules) in one mole of a substance. Avogadro's number is approximately equal to \(6.022 \times 10^{23}\) entities per mole. This large number is crucial when dealing with microscopic particles on a macroscopic scale.

When chemists have the number of moles for a substance, as we calculated in the exercise, they can then use Avogadro's number to determine the exact number of molecules present. In our case, knowing the number of moles of cocaine hydrochloride from the sample's mass allowed us to use Avogadro's number to find out how many molecules made up that sample.

The molecular formula of a compound provides the specific number and type of atoms in a single molecule of that compound. It's like a blueprint for the molecule's structure, indicating not only the types of atoms present but also their precise amounts. The molecular formula for cocaine hydrochloride is \(C_{17}H_{22}ClNO_{4}\), detailing that each molecule contains 17 carbon atoms, 22 hydrogen atoms, one chlorine atom, one nitrogen atom, and four oxygen atoms.

Understanding the molecular formula is essential when determining the total number of atoms in a sample. This is shown in step 5 of our exercise where the total number of molecules is multiplied by the number of atoms in a single molecule, according to the molecular formula, to yield the final count of atoms in the sample.