Question

Chlorine has two isotopes of atomic mass units 34.97 and 36.97. The relative abundance of isotope is 0.755 and 0.245 respectively. Find the average atomic mass of chlorine.

Answer 1

Hint: Isotopes are variants of a particular element which only differ in number of neutrons and hence in nucleons. All isotopes of an element have the same number of protons but different numbers of neutrons present in it.


Complete answer:
Before solving the question, let us first know what is average atomic mass.
- Average atomic mass of any element is the sum of the masses of its isotopes where each multiplied by its abundance in nature. The average atomic mass of any element can be found on the periodic table under the element’s symbol.
- When there is mass number then what is the need of average atomic masses? We know most of the elements have isotopes with different mass numbers but atomic numbers are the same. These are present in particular composition in an element for considering isotopic mass and normal element’s mass in their composition ratio; we are calculating average atomic mass.

- Average atomic mass is given by${{\text{f}}_{1}}{{\text{M}}_{1}}+{{\text{f}}_{2}}{{\text{M}}_{2}}+..........+{{\text{f}}_{\text{n}}}{{\text{M}}_{\text{n}}}$where f is the fraction of the natural abundance of the isotope and M is the mass of the isotope.

Step (1)- Let us first write what is given to us; ${{\text{f}}_{1}}$= 0.755, ${{\text{M}}_{1}}$= 34.97, ${{\text{f}}_{2}}$= 0.245 and ${{\text{M}}_{2}}$= 36.97 is given.

Step (2)- Calculate the required values: The value of ${{\text{f}}_{1}}{{\text{M}}_{1}}$ and ${{\text{f}}_{2}}{{\text{M}}_{2}}$will be $\left( 0.755\times 34.97 \right)$and$\left( 0.245\times 36.97 \right)$; which is 26.40 and 9.057 respectively.

Step (3)- Now, add ${{\text{f}}_{1}}{{\text{M}}_{1}}$ and ${{\text{f}}_{2}}{{\text{M}}_{2}}$ to obtain average atomic mass, Average atomic mass is 35.45 (${{\text{f}}_{1}}{{\text{M}}_{1}}+ {{\text{f}}_{2}}{{\text{M}}_{2}}$ is 26.40 + 9.057).
The average atomic mass of Chlorine is 35.45 atomic mass units.

Additional Information:
Uses of chlorine:
- Chlorine is used as a disinfectant as it is used in treatment of drinking water to kill bacteria.
- It is used as an antiseptic.
- Used in the production of paper and its products.
- Used in manufacturing of dyes and plastics.


Note: There is a difference between atomic mass and atomic weight. Do not consider both the terms the same.

ATOMIC WEIGHT	ATOMIC MASS
It is the average weight of an element.	Atomic mass is the mass of a single atom.
Depends on the atomic masses of isotopes and their abundance.	Does not depend on atomic masses of isotopes.
Calculated using percentage abundance of all isotopes of an element.	Mass is calculated as the sum of protons and neutrons.