Question

What is the average atomic mass of an element if, out of 100 atoms, 5 have a mass of 176 amu, 19 have a mass of 177 amu, 27 have a mass of 178 amu, 14 have a mass of 179 amu, and 35 have a mass of 180 amu?

Answer 1

`"Average Atomic Mass" = 178.55 color(white)(l) "amu"`

Explanation:

The `"Average Atomic Mass"` of an element is defined as "the weighted average mass of all naturally-occurring (occasionally radioactive) isotopes of the element." (and hence the name "average") [1]

Dividing the sum of the product of the `color(purple)("relative atomic mass of each of the isotope")` and `color(grey)("the occasion of their presence in the sample")` by `"the sum of atoms in the sample"` gives the weighted average of the relative atomic mass.

`"Average Atomic Weight"`
`= (color(grey)(5) xx color(purple)(176) + color(grey)(19) xx color(purple)(177) + color(grey)(27) xx color(purple)(178) + color(grey)(14) xx color(purple)(179) + color(grey)(35) xx color(purple)(180)) / (color(black)(100))`
`= 178.55 color(white)(l) "amu"`

Reference
[1] Vitz, Ed, et al. “4.13: Average Atomic Weights.” Chemistry LibreTexts, Libretexts, 5 Sept. 2017,
chem.libretexts.org/Textbook_Maps/General_Chemistry/Book:_ChemPRIME_(Moore_et_al.)/04The_Structure_of_Atoms/4.13:_Average_Atomic_Weights.