Final answer:
The mass of 6.02 x 10^23 atoms of zirconium is 91.22 grams. To find the mass of 4.2 x 10^13 atoms of zirconium, use a proportion based on Avogadro's number, resulting in approximately 0.0000063 grams, or 6.3 micrograms.
Step-by-step explanation:
To find the mass of atoms in a given sample, we employ Avogadro's number, which is 6.022 x 1023. This quantity represents one mole of atoms, correlating the microscopic world of atoms to macroscopic measurements in the laboratory.
1. The mass of 6.02 x 1023 atoms of zirconium can be determined using the atomic mass of zirconium from the periodic table, which is 91.22 amu (atomic mass units), or when considering one mole of Zr, it would be 91.22 grams. Since 6.02 x 1023 atoms are equivalent to one mole, the mass is simply the molar mass of one mole of zirconium which is 91.22 grams.
2. To find the mass of 4.2 x 1013 atoms of zirconium, the following proportion can be used: the mass of one mole of Zr atoms (6.02 x 1023 atoms) to 91.22 grams is equal to 4.2 x 1013 atoms to x grams. Solving for x gives a mass of approximately 0.0000063 grams, which is 6.3 micrograms of Zirconium.