Antimony has two naturally occuring isotopes, 121 Sb and 123 Sb . 121 Sb has an atomic mass of 120.9038 u , and 123 Sb has an atomic mass of 122.9042 u . Antimony has an average atomic mass of 121.7601 u . What is the percent natural abundance of each isotope?

[tex]Average\ atomic\ mass=(\frac {\%\ of\ the\ first\ isotope}{100}\times {Mass\ of\ the\ first\ isotope})+(\frac {\%\ of\ the\ second\ isotope}{100}\times {Mass\ of\ the\ second\ isotope})[/tex]

Given that:

Since the element has only 2 isotopes, so the let the percentage of first be x and the second is 100 -x.

For first isotope, 121 Sb :

% = x %

Mass = 120.9038 u

For second isotope, 123 Sb:

% = 100 - x

Mass = 122.9042 u

Given, Average Mass = 121.7601 u

Thus,

[tex]121.7601=\frac{x}{100}\times 120.9038+\frac{100-x}{100}\times 122.9042[/tex]

[tex]120.9038x+122.9042\left(100-x\right)=12176.01[/tex]

Solving for x, we get that:

x = 57.2 %

Thus, percentage abundance of 121 Sb is = 57.2 %

percentage abundance of 123 Sb is = 100 - 57.2 % = 42.8 %

CintiaSalazar CintiaSalazar · Answer 2 · 2022-01-28T12:15:37+01:00

Considering the definition of atomic mass, isotopes and atomic mass of an element,

Definition of atomic mass A

First of all, the atomic mass (A) is obtained by adding the number of protons and neutrons in a given nucleus of a chemical element.

Definition of isotopes

The same chemical element can be made up of different atoms, that is, their atomic numbers are the same, but the number of neutrons is different. These atoms are called isotopes of the element.

Atomic mass of an element

On the other hand, the atomic mass of an element is the weighted average mass of its natural isotopes. In other words, the atomic masses of chemical elements are usually calculated as the weighted average of the masses of the different isotopes of each element, taking into account the relative abundance of each of them.

Percent natural abundance of each isotope of antimony

In this case, 121 Sb and 123 Sb are the naturally isotopes of antimony. 121 Sb has an atomic mass of 120.9038 u , and 123 Sb has an atomic mass of 122.9042 u.

Being the average atomic mass of antomony 121.7601 u, the average mass of antimony can be calculated as:

average mass of antimony= percent natural abundance of 121 Sb× atomic mass of 121 Sb + percent natural abundance of 123 Sb× atomic mass of 123 Sb

Being percent natural abundance of 123 Sb= 1 - percent natural abundance of 121 Sb, and substituting the corresponding values, you get:

121.7601 u= percent natural abundance of 121 Sb× 120.9038 u + (1 - percent natural abundance of 121 Sb)× 122.9042 u

Solving:

121.7601 u= percent natural abundance of 121 Sb× 120.9038 u + 1× 122.9042 u - percent natural abundance of 121 Sb× 122.9042 u

121.7601 u= percent natural abundance of 121 Sb× (-2.0004 u) + 122.9042 u

121.7601 u - 122.9042 u= percent natural abundance of 121 Sb× (-2.0004 u)

-1.1441= percent natural abundance of 121 Sb× (-2.0004 u)

-1.1441÷ (-2.0004 u) = percent natural abundance of 121 Sb

0.5719 ×100 % = percent natural abundance of 121 Sb

57.19% = percent natural abundance of 121 Sb

So:

percent natural abundance of 123 Sb= 1 - percent natural abundance of 121 Sb

percent natural abundance of 123 Sb= 1 - 0.5719

percent natural abundance of 123 Sb= 0.4281

percent natural abundance of 123 Sb= 0.4281× 100

percent natural abundance of 123 Sb= 42.81%

Finally, the percent natural abundance of 121 Sb is 57.19% and the percent natural abundance of 123 Sb is 42.81%

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