Chlorine has two naturally stable isotopes: 35cl (34.968853 amu) and 37cl (36.965903 amu). the natural abundance of each isotope varies in different regions of the universe. in the gribble region of space, the molar mass for a sample of chlorine is 36.36575 g/mol. using only these three values, determine the relative percent abundance of 35cl.

35Cl ⇒ 34.968853 amu  has an abundance of 30.05%

Explanation:

The molar mass of chlorine, (which is the average of all its naturally stable isotope masses), is 36.36575 amu.

There are 2 naturally stable isotopes, this means together they have an abundance of 100%

The isotopes are:

35Cl ⇒ 34.968853 amu  has an abundance of X %

37Cl ⇒ 36.965903 amu  has an abundance of Y %

X + Y = 100%   OR X = 100% - Y

36.36575 = 34.968853X + 36.965903Y  

36.36575 = 34.968853(1-Y) + 36.936.96590365903Y

36.36575 = 34.968853 -34.968853Y + 36.965903Y

1.396897 = 1.99705Y

Y = 0.699 = 69.95%

X = 100-69.9 = 30.05%

To control, we can plug in the following equation:

34.968853 * 0.3005 + 36.965903 * 0.6995 = 36.3658

This means

37Cl ⇒ 36.965903 amu  has an abundance of 69.95 %

35Cl ⇒ 34.968853 amu  has an abundance of 30.05%

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