Question

Calculate the percentage of the naturally occurring isotopes and that accounts \[^{35}Cl\] for the atomic mass of chlorine takes as $35.45$.

Answer 1

Hint: We can calculate the natural abundance (or) percentage of naturally occurring isotopes of chlorine using their atomic mass and the mass number. We can consider the percentage of isotopes of chlorine as x and form an algebraic equation. We have to equate the algebraic equation with atomic mass, and solve the value of x to get the percentage of naturally occurring isotopes.

Complete answer:
We are provided with two naturally occurring isotopes of chlorine. The two naturally occurring isotopes of chlorine are \[^{35}Cl\] and $^{37}Cl$. We have identified the mass number of chlorine-$35$ as $35$ and the mass number of chlorine-$37$ as $37$ .
We are given the atomic mass of chlorine as $35.45$.
Let us consider the percentage of naturally occurring isotopes \[^{35}Cl\] as x and the percentage of naturally occurring isotopes $^{37}Cl$ as $\left( {100 - x} \right)$.
Therefore, the average atomic mass is given as,
$X \times 35\left( {100 - x} \right) \times \dfrac{{37}}{{100}} = 35.45$
Let us now calculate the value of x is given as,
$35x + 3700 - 37x = 3545$
$2x = 155$
$x = 77.5\% $
So, we have calculated the percentage of \[^{35}Cl\] as $77.5\% $.
Let us now calculate the percentage of $^{37}Cl$ is calculated as,
$\% \,of{\,^{37}}Cl = \left( {100 - x} \right)$
$\% \,of{\,^{37}}Cl = \left( {100 - 77.5} \right)$
$\% \,of{\,^{37}}Cl = 22.5\% $
So, we have calculated the percentage of $^{37}Cl$ as $22.5\% $.
The percentage of \[^{35}Cl\] as $77.5\% $.
The percentage of $^{37}Cl$ as $22.5\% $.

Note:
We have to know that the atomic mass of an element is the weight of one atom of that specific element. We can determine the atomic mass of an element by mass spectrometry. We can write that the unit of atomic mass is the atomic mass unit. The atomic mass unit is weight equal one-twelfth of weight of one carbon-$12$ atom.