Question

What is the atomic mass of Hafnium if out of 200 atoms, 10 have mass 176.00g/mol, 38 have mass 177.00g/mol, 54 have mass 178.00g/mol, 28 have mass 179.00g/mol, and 70 have mass 180.00g/mol?

a) 178.2 g/mol
b) 178.4 g/mol
c) 178.6 g/mol
d) 178.8 g/mol

Answer 1

Option (C): The atomic mass of Hafnium is calculated by multiplying the mass of each isotope by its relative abundance, summing those products, and dividing by the total number of atoms. The result gives an average atomic mass of 178.6 g/mol when rounded to the nearest tenth place.

Step-by-step explanation:

The atomic mass of Hafnium can be calculated by using the weighted average formula which takes into account the mass of each isotope and its relative abundance. To find the average atomic mass, each isotope's mass is multiplied by its relative number of atoms, and those products are summed and then divided by the total number of atoms. The calculations are as follows:

(10 atoms x 176.00 g/mol) / 200 atoms = 8.8 g/mol

(38 atoms x 177.00 g/mol) / 200 atoms = 33.66 g/mol

(54 atoms x 178.00 g/mol) / 200 atoms = 48.06 g/mol

(28 atoms x 179.00 g/mol) / 200 atoms = 25.06 g/mol

(70 atoms x 180.00 g/mol) / 200 atoms = 63.00 g/mol

Adding these values together gives us the average atomic mass:

8.8 + 33.66 + 48.06 + 25.06 + 63.00 = 178.58 g/mol

Rounding to the nearest tenth place, the atomic mass of Hafnium is 178.6 g/mol.