Emilija Randjelovic/iStock/GettyImages
In chemistry, translating a count of atoms into mass is a foundational skill that underpins more advanced quantitative analyses. The conversion hinges on Avogadro’s number, atomic weights, dimensional analysis, and the mole concept. By applying these principles, you can convert any known quantity of atoms into grams with precision.
Assume we are working with 14 atoms of carbon. Write 14 atoms C at the top left of your scratch paper.
Avogadro’s number (6.02 × 10^23) represents the number of particles in one mole of a substance. Write the fraction 1 mol C / 6.02 × 10^23 atoms C to the right of the previous line so that your working sheet looks like this:
14 atoms C × (1 mol C / 6.02 × 10^23 atoms C)
Refer to the periodic table to find the atomic weight of carbon, which is 12.0 amu. Since the molar mass in grams equals the atomic mass in amu, one mole of carbon is 12.0 g. Extend the fraction:
14 atoms C × (1 mol C / 6.02 × 10^23 atoms C) × (12.0 g C / 1 mol C)
Cancel the common units: the “atoms C” cancel, and the “mol C” cancel, leaving grams (g) as the final unit. This cancellation serves as a quick check of your setup.
Multiply across the numerators: 14 × 1 × 12.0 = 168 g. The denominator remains 6.02 × 10^23.
Divide 168 g by 6.02 × 10^23, respecting significant figures. The result is 2.8 × 10^22 g of carbon for 14 atoms.
Multiply the number of atoms by the molar mass and divide by Avogadro’s number; that yields the mass in grams.
Always limit the result to the fewest significant figures in the input data. In this example, 14 has two significant figures, so the answer is reported with two significant figures.
