Question

Use the data given in the following table to calculate the molar mass of naturally occurring argon isotopes:

Isotope	Isotopic molar mass	Abundance
$ {}^{36}Ar $	$ 35.96755gmo{l^{ - 1}} $	$ 0.337\% $
$ {}^{38}Ar $	$ 37.96272gmo{l^{ - 1}} $	$ 0.063\% $
$ {}^{40}Ar $	$ 39.9624gmo{l^{ - 1}} $	$ 99.6\% $

Answer 1

Hint: Atomic mass is the total mass of protons and neutrons. An atomic number is the number of protons in the nucleus of an atom. Isotopes: Those elements which have the same atomic number but different atomic mass. For example: $ C - 12 $ and $ C - 13 $ . They both have the same atomic number i.e. $ 6 $ but different atomic mass i.e. in $ C - 12 $ mass is $ 12 $ and in $ C - 13 $ mass is $ 13 $ .

Complete step by step solution:
First of all let us talk about isotopes and isobars.
Atomic mass: It is defined as the total number of protons and neutrons present in the nucleus of an atom. It is represented by symbol A.
Atomic number: It is defined as the number of protons in the nucleus of an atom. It is represented by symbol Z.
Isotopes: Those elements which have the same atomic number but different atomic mass. For example: $ C - 12 $ and $ C - 13 $ . They both have the same atomic number i.e. $ 6 $ but different atomic mass i.e. in $ C - 12 $ mass is $ 12 $ and in $ C - 13 $ mass is $ 13 $ .
Isobars: Those elements which have the same atomic mass but different atomic numbers. For example: argon and calcium. The atomic number of argon is $ 18 $ and that of calcium is $ 20 $ but the atomic mass of both the elements is the same i.e. $ 40 $ .
Here we are given with the isotopes of argon. And the atomic masses of these isotopes are $ 36,38 $ and $ 40 $ .
Now the molar mass of the element is calculated by the sum of the product of atomic mass of the isotopes to its abundance divided by $ 100 $ .
So molar mass of argon will be $ \dfrac{{{}^{36}Ar \times abundance + {}^{38}Ar \times abundance + {}^{40}Ar \times abundance}}{{100}} $ .
Molar mass $ \dfrac{{36 \times 0.337 + 38 \times 0.063 + 40 \times 99.60}}{{100}} = 39.98gmo{l^{ - 1}} $ ,
Hence, the molar mass of naturally occurring argon isotopes is $ 39.98gmo{l^{ - 1}} $ .

Note:
Vapour density is defined as the density of a gas or substance relative to hydrogen at the same temperature and pressure i.e. mass of substance in a certain volume divided by the mass of hydrogen gas at the same volume.