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

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.