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How would you find the percent abundance of 2 isotopes of an element, given the atomic weight and mass number of each isotope?

1 Answer

Nov 11, 2015

See explanation.

Explanation:

The average atomic mass of elements is calculated by:

$M a s s_{a v r g .} = \sum (isotope mass) \cdot (percent abundance)$ $Mass_(avrg.)=sum("isotope mass")*("percent abundance")$

For example, suppose we want to find the percent abundance of chlorine isotopes $^{35} C l$ $""^35Cl$ and $^{37} C l$ $""^37Cl$ given that the average atomic mass of chlorine is $35.45 a . m . u .$ $35.45 "a.m.u.$ .

Assume that the percent abundance of $^{35} C l$ $""^35Cl$ is $x$ $x$ , therefore, the percent abundance of $^{37} C l$ $""^37Cl$ is $1 - x$ $1-x$ .

Thus, $35.45 = (35 \times x) + (37 \times (1 - x)) \Rightarrow 35.45 = 37 - 2 x$ $35.45=(35xxx)+(37xx(1-x)) => 35.45 = 37 -2x$ .

Solve for $x$ $x$ , $x = 0.775$ $x=0.775$

Therefore, the percent abundance of $^{35} C l$ $""^35Cl$ is $77.5 %$ $77.5%$ and the percent abundance of $^{37} C l$ $""^37Cl$ is $22.5 %$ $22.5%$

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