To find the atomic weight of an element, we need to use the relationship between the number of atoms, the atomic weight, and the mass of the sample. The atomic weight is defined as the average weight of one atom of an element compared to one-twelfth the weight of one carbon-12 atom.
Given: Number of atoms (N) = 1.58 × 10^22 atoms Mass of the sample (m) = 1.05 g
We can use the following formula to calculate the atomic weight (W) of the element X:
W = m / N
Substituting the values:
W = 1.05 g / (1.58 × 10^22 atoms)
To obtain the answer in atomic mass units (u), we need to divide the atomic weight by the Avogadro constant (6.022 × 10^23 atoms/mol):
W (in u) = (1.05 g / (1.58 × 10^22 atoms)) / (6.022 × 10^23 atoms/mol)
W (in u) = (1.05 g / 1.58 × 10^22) × (1 / 6.022 × 10^23) mol
W (in u) ≈ 1.05 / (1.58 × 6.022) u
Calculating the value, we get:
W (in u) ≈ 0.1097 u
Therefore, the atomic weight of element X is approximately 0.1097 atomic mass units (u).