Formula for determining the atomic mass of an element from natural abundance and mass of the isotopes of the elements is:
[tex]Atomic mass of element = Percent abundance of isotope I\times atomic mass of isotope I+Percent abundance of isotope II\times atomic mass of isotope II[/tex] -(1)
Atomic mass of [tex]^{35}Cl = 34.9689 amu[/tex]
Atomic mass of [tex]^{37}Cl = 36.9659 amu[/tex]
We know that atomic mass of [tex]Cl = 35.453 amu[/tex]
Let's consider that X is the percentage of [tex]^{35}Cl[/tex]
then (100-X) is the percentage of [tex]^{37}Cl[/tex]
Substituting the values in formula 1,
[tex](X\times 34.9689)+((100-X)\times 36.9659) = 100\times 35.453[/tex]
[tex]34.9689X+3696.59-36.9659X=3545.3[/tex]
[tex]36.9659X-34.9689X-=3696.59-3545.3[/tex]
[tex]1.997X=151.29[/tex]
[tex]X= 75.75864[/tex] %.
Therefore, the percentage of [tex]^{35}Cl[/tex] = 75.75864 %
and the percentage of [tex]^{37}Cl[/tex] = 24.24136 %.
