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When comparing substances at the atomic or molecular level, it's essential to understand the concept of molar mass. This value indicates the mass of one mole (approximately 6.022 x 10²³ entities) of a given substance. The molar mass is measured in grams per mole (g/mol) and is numerically equivalent to the substance's atomic or molecular weight.

Molar mass is a bridge between the mass of a material and the number of particles or entities present in that material. It allows us to count particles by weighing them. This is crucial in chemical reactions, where balancing equations requires equalizing the number of atoms of each element on both sides of the reaction.

In our exercise, molar mass helps us to answer which element, potassium or sodium, has a greater mass per mole. By consulting the periodic table, we confirm their molar masses and thus conclude that a mole of potassium is heavier than a mole of sodium due to its higher molar mass.

The periodic table is a tabular display of the chemical elements, organized by their atomic number, electron configuration, and recurring chemical properties. It's an invaluable tool for chemists and students alike, offering a wealth of information at a glance.

Each element in the periodic table is represented by its chemical symbol, and typically, the atomic mass is provided below this symbol. The layout of the periodic table groups elements with similar properties together, which can help predict the behavior of elements during chemical reactions.

For instance, in our potassium versus sodium mass comparison, the periodic table not just provides the atomic masses needed to determine their molar masses but also highlights that both elements belong to the same group (alkali metals), suggesting they have similar chemical properties, yet different atomic masses.

Diving into the very essence of chemical substances, atomic mass is fundamentally the mass of a single atom, usually expressed in atomic mass units (amu). For practical and historical reasons, atomic mass is typically averaged over all of an element's isotopes as they occur on Earth, and this average is known as the standard atomic weight.

The atomic mass takes into account both the mass of the protons and neutrons in the nucleus and the mass of the electrons that orbit the nucleus. Since the mass of electrons is negligible compared to that of protons and neutrons, the atomic mass is almost entirely the sum of the masses of protons and neutrons.

Our exercise utilized the atomic masses of potassium and sodium from the periodic table to determine which element has more mass per mole. Here, understanding atomic mass was crucial, as it directly relates to the concept of molar mass - the cornerstone of our comparison.