In the density formula ρ = (sum_i N_i M_i) / (N_A V_cell), what is the role of N_A?

• A. Converts molar masses to masses per atom
• B. Converts cell volume to mass units
• C. Serves as the atomic mass unit
• D. Acts as a conversion factor with no physical meaning

Answer: (A)

The essential idea is that Avogadro’s number links amounts of substance to individual atoms. In this density formula, M_i is the molar mass of species i (mass per mole, in g/mol) and N_i is how many atoms of that species are in one unit cell. To get the mass contributed by those N_i atoms, you need the mass of a single atom, which is M_i divided by N_A (since one mole contains N_A atoms). Summing N_i times (M_i/N_A) over all species gives the total mass of one unit cell. Dividing that mass by the unit-cell volume V_cell yields the density.

So, Avogadro’s number serves to convert molar masses to masses per atom, enabling the mass per unit cell to be computed. It has physical meaning as the bridge between the amount of substance (moles) and the number of individual atoms.