Question

The element X occurs naturally to the extent of 67.83% 30X and

the rest 32X. What is the atomic mass of X? (Use 4 sig. fig.)

Answer 1

The atomic mass of x is approximately 30.62 amu.

Define the isotopic abundances and masses:

Abundance of
`${ }^(30) X=67.83 \%$`

Abundance of
`${ }^(32) X=100 \%-67.83 \%=32.17 \%$`

Mass of
`${ }^(30) X=29.97645 \mathrm{amu}$` (atomic mass units)

Mass of
`${ }^(32) X=31.97381 \mathrm{amu}$`

Calculate the weighted average atomic mass:

The atomic mass is a weighted average of the individual isotope masses, where the weights are the corresponding isotopic abundances. We can use the following formula:

Average atomic mass = (abundance of isotope 1 × mass of isotope 1) + (abundance of isotope 2 × mass of isotope 2) + ...

In this case, the formula becomes:

Average atomic mass = (0.6783 × 29.97645 amu) + (0.3217 × 31.97381 amu)

Calculating this, we get:

Average atomic mass ≈ 30.6193 amu

Round to 4 significant figures:

Since we were given the abundances to 4 significant figures, the final answer should also be reported to 4 significant figures. Therefore, the rounded atomic mass of element X is:

Average atomic mass ≈ 30.62 amu