If the atomic weight of an element is x, what is the mass in grams of 3.17 * 1020 atoms of the element?

Verified step by step guidance

1. Determine the number of moles of the element using Avogadro's number, which is approximately $6.022 \times 10^{23}$ atoms per mole. Use the formula: \( \text{moles} = \frac{\text{number of atoms}}{\text{Avogadro's number}} \).
2. Calculate the mass of the element in grams by multiplying the number of moles by the atomic weight of the element in grams per mole. Use the formula: \( \text{mass in grams} = \text{moles} \times \text{atomic weight} \).
3. Substitute the given values into the formulas. First, substitute $3.17 \times 10^{20}$ for the number of atoms and $x$ for the atomic weight in the formulas.
4. Perform the division to find the number of moles from the number of atoms and Avogadro's number.
5. Finally, multiply the number of moles by the atomic weight to find the mass in grams.

Key Concepts

Atomic Weight

Atomic weight, often expressed in atomic mass units (amu), is the weighted average mass of an element's isotopes relative to 1/12th the mass of a carbon-12 atom. It reflects the mass of a single atom of the element and is crucial for converting between the number of atoms and mass in grams.

Avogadro's Number

Avogadro's number, approximately 6.022 x 10^23, is the number of atoms, ions, or molecules in one mole of a substance. This constant allows chemists to relate the macroscopic scale of substances (grams) to the microscopic scale (number of atoms), facilitating calculations involving quantities of matter.

Mass Calculation from Atoms

To calculate the mass of a specific number of atoms, one can use the formula: mass = (number of atoms / Avogadro's number) x atomic weight. This formula bridges the gap between the atomic scale and macroscopic measurements, enabling the conversion of a given number of atoms into grams.