Calculate the moles of NaCl, Au, glucose, and N2 given their respective amounts in formula units, atoms, and molecules.

To find the number of moles, divide the number of formula units by Avogadro's number ($6.022 \times 10^{23}$ formula units/mol).

The number of moles of sodium chloride is $\boxed{\text{2.499 mol}}$.

To find the number of moles, divide the number of atoms by Avogadro's number ($6.022 \times 10^{23}$ atoms/mol).

The number of moles of gold is $\boxed{\text{0.4000 mol}}$.

To find the number of moles, divide the number of molecules by Avogadro's number ($6.022 \times 10^{23}$ molecules/mol).

The number of moles of glucose is $\boxed{\text{14.01 mol}}$.

To find the number of moles, divide the number of molecules by Avogadro's number ($6.022 \times 10^{23}$ molecules/mol).

The number of moles of nitrogen gas is $\boxed{\text{0.01000 mol}}$.

A mole is the SI unit for the amount of substance. It is defined as the amount of substance that contains exactly $6.022 \times 10^{23}$ elementary entities (atoms, molecules, ions, or formula units). It is important in chemistry because it provides a convenient way to count extremely large numbers of atoms or molecules and to relate macroscopic quantities (like mass) to microscopic quantities (like the number of particles) in chemical reactions.

The mole is directly related to Avogadro's number ($6.022 \times 10^{23}$). One mole of any substance contains exactly Avogadro's number of particles (atoms, molecules, ions, or formula units). This means that Avogadro's number is the conversion factor between the number of particles and the number of moles.