Complete the table. \(\begin{array}{lll}\text { Element } & \text { Moles } & \text { Number of Atoms } \\ \mathrm{Cr} & \- & 9.61 \times 10^{23} \\ \mathrm{Fe} & 1.52 \times 10^{-5} & \- \\ \mathrm{Ti} & 0.0365 & \- \\ \mathrm{Hg} & \- & 1.09 \times 10^{23}\end{array}\)

One of the fundamental constants in chemistry is Avogadro's number, which is essential when dealing with mole to atoms conversions. It is defined as the number of constituent particles, usually atoms or molecules, that are contained in one mole of a substance. The value of Avogadro's number is approximately \(6.022 \times 10^{23}\) particles per mole. This constant provides a bridge between the microscopic world of atoms and the macroscopic world we observe, allowing us to count atoms by weighing the substance in grams instead of trying to count each individual atom.

To illustrate, if you have one mole of carbon, you have \(6.022 \times 10^{23}\) carbon atoms, and this is the same number of atoms as there would be in a mole of any other element. However, the mass of these moles would differ because the elements have different molar masses. Avogadro's number is a pivotal concept in understanding stoichiometry and performing chemical calculations, as you'll see next.

Stoichiometry lies at the heart of the mole to atoms conversion, serving as the cornerstone of chemical calculations. Put simply, stoichiometry involves the quantitative relationship between reactants and products in a chemical reaction. It is based on the conservation of mass where the mass of the reactants equals the mass of the products.

In practice, stoichiometry allows chemists to predict the amounts of substances consumed and produced in a given reaction. One mole of a substance will react with a stoichiometric equivalent of another substance, based on the reaction coefficients in a balanced chemical equation. Furthermore, the concept of stoichiometry extends beyond the quantities of reactants and products in a chemical reaction to encompass the calculation of concentrations, volumes, and, as seen in our example, the conversion between moles and the number of atoms.

Chemical calculations often require the conversion between different units of measurement, such as moles to number of atoms, to understand the quantities involved in a chemical reaction. In our example problem, we performed these conversions by making use of Avogadro's number and the concept of stoichiometry. The process requires a clear understanding of the relationships and units involved.

For instance, when given a number of atoms and asked to find the number of moles, dividing the number of atoms by Avogadro's number yields the number of moles. Conversely, to find the number of atoms from moles, one would multiply the number of moles by Avogadro's number. These calculations are essential because substances react according to their mole ratios, not individual particles, and measuring in moles allows chemists to work with quantities that can be practically measured in a laboratory.