Question

Average atomic mass of magnesium is 24.31 amu. This magnesium is composed of 79 mole% of ${}^{24}Mg$ and remaining 21 mole% of ${}^{25}Mg$ and ${}^{26}Mg$. Calculate mole% of ${}^{26}Mg$.
(A) 10
(B) 11
(C) 15
(D) 16

Answer 1

Hint: An average atomic mass plays an important role while solving such problems. We need to know the basics of this concept to solve this illustration. Also, only one option can be correct while we solve this question.
The average atomic mass of an element is the sum of product of the masses of its isotopes to its abundance in nature. Its unit is generally expressed as amu (Dalton).

Complete answer:
Let us know the basic concept of average atomic mass;
-The atomic mass of any element is empirical and is based on the number of protons in its nucleus purely.
-The elements in the modern periodic table can exist in their isotopic form in actual nature where the elements have the same atomic number but different atomic mass. Such elements reside on the same position in the periodic table where the most abundant form of isotope is placed.
-Isotope of an element have the same atomic number but the number of neutrons vary in their nucleus thus, atomic masses are different.
Now, moving towards the illustration;
Given data,
Average atomic mass of magnesium = 24.31 amu
Mole % of ${}^{24}Mg$ = 79
Mole % of ${}^{25}Mg$ and ${}^{26}Mg$ = 21
Now, let x be the mole % of ${}^{26}Mg$. Thus, mole % of ${}^{25}Mg$ will be (21 - x).
Solving in accordance with the average atomic mass of magnesium;
Average atomic mass = 24.31 = ${\displaystyle \frac{79}{100}}\times 24+{\displaystyle \frac{x}{100}}\times 26+{\displaystyle \frac{21-x}{100}}\times 25$
Thus, $x=10$
Therefore, mole % of ${}^{26}Mg$ is 10.

Hence, option (A) is correct.

Note:
General concept of average atomic mass helps us reach the answer. Here, there is no interference of units as everything is in the form of percentages. But care must be taken while solving the problem.