Which has the greatest mass: 1 mole of ethylene gas \(\left(\mathrm{C}_{2} \mathrm{H}_{4}\right), 1\) mole of carbon monoxide gas, or 1 mole of nitrogen gas \(\left(\mathrm{N}_{2}\right) ?\)

Understanding how to calculate molar mass is fundamental in chemistry, as it connects the mass of a substance to the amount used in chemical reactions. When we talk about molar mass, we're referring to the mass of one mole of a substance, and it's measured in grams per mole (g/mol).

To calculate the molar mass of a compound, such as ethylene gas \(\mathrm{C}_{2}\mathrm{H}_{4}\), you'll sum up the atomic masses of all the atoms in the molecule. For ethylene, this means adding together the mass of two carbon atoms and four hydrogen atoms. The atomic masses are easily retrievable from the periodic table: carbon has an atomic mass of 12.01 g/mol, and hydrogen has an atomic mass of 1.01 g/mol.

When this calculation is carried out, the molar mass of ethylene is found to be 28.06 g/mol. It's this straightforward method that lets us understand the mass relationships in chemistry, and forms the basis for stoichiometry in chemical equations.

The concept of atomic mass lies at the core of chemistry and molar mass calculation. Atomic mass is the mass of a single atom of a chemical element, typically expressed in unified atomic mass units (u) where one atomic mass unit is defined as one-twelfth of the mass of a carbon-12 atom. On the periodic table, the atomic mass of each element is given, usually as an average value to account for the presence of isotopes.

For instance, carbon has an atomic mass of approximately 12.01 u, which represents the weighted average of its various isotopes. When you are dealing with a compound, you need to consider the atomic mass of each atom that constitutes the molecule. This is important when we want to convert between mass and moles in chemistry, allowing us to perform calculations for reactions and compound formation.

The mole is a fundamental concept in chemistry, providing a bridge between the microscopic world of atoms and molecules and the macroscopic world we measure in the laboratory. One mole represents Avogadro's number of particles, which is approximately \(6.022 \times 10^{23}\) entities, whether they are atoms, ions, or molecules.

This vast number allows chemists to count atoms by weighing, effectively linking atomic scale to real-world scale. When we say we have one mole of ethylene gas, we mean we have Avogadro's number of ethylene molecules. Through the moles concept, it's possible to discuss the amounts in chemical reactions in a meaningful way, since we can't count out individual atoms or molecules due to their tiny size and immense numbers.

The periodic table is an invaluable tool for chemists, carrying a wealth of information within a structured layout of all the known chemical elements. This table isn't just about listing elements; it presents them in a way that showcases patterns of chemical properties and helps predict the behavior of elements in chemical reactions.

For the purpose of molar mass calculation, the periodic table provides the atomic masses of the elements, which are critical for determining the molar mass of compounds. As seen with the exercise involving ethylene, carbon monoxide, and nitrogen gases, by consulting the periodic table, one can find the atomic masses needed for these calculations. Elements are organized by increasing atomic number, but they're also grouped by similar properties, which can hint at how they may combine and react with other elements. It's the periodic table that allows us to draw conclusions about reactivity, bonding, and many other important chemical concepts.