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Calculating the Abundance of Isotopes Problem
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Topic: Calculating the Abundance of Isotopes Problem (Read 7144 times)
texascowgirl17
Labrat
Posts: 5
Calculating the Abundance of Isotopes Problem
«
on:
August 15, 2009, 08:58:13 AM »
Any help with the following problem would be greatly appreciated:
Gallium consists of two naturally occuring isotopes with masses of 68.926 and 70.925 amu. The average atomic mass of Ga is 69.72 amu. Calculate the abundance of each isotope.
Answer should be:
69
Ga: 60.3%,
71
Ga: 39.7%
This is how I set up the problem:
Average atomic mass = (mass
69
Ga)(x) + (mass
71
Ga)(y)
Where x and y are the relative abundances of
69
Ga and
71
Ga respectively. So,
69.72 = 68.926(x) + 70.925(y)
I tried solving for one of the variables and then plugging it back in to try to find the other, but I just ended up with 69.72 = 69.72. Which doesn't really help! So I'm guessing there's probably something wrong with my arithmetic. ><"
Thanks for your time! :]
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kingchemist
Global Moderator
Hero Member
Posts: 2426
A Liverpool FC fan
Re: Calculating the Abundance of Isotopes Problem
«
Reply #1 on:
August 15, 2009, 12:51:25 PM »
I think if you let the abundance of 1 isotope = x, then the abundance of the other will be (100 - x).
In this way the problem will have 1 unknown.
So
Average atomic mass = (68.926) (x/100) + (70.925)(100-x/100) = 69.72
68.926x + 7092.5 - 70.925x = 6972
-1.999x = - 120.5
x = 60.280
So abundance of 69 Ga = 60.280%
Please check my calculations
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'Chemistry is not just the study of matter; Chemistry is the study which matters!' - Kingchemist
texascowgirl17
Labrat
Posts: 5
Re: Calculating the Abundance of Isotopes Problem
«
Reply #2 on:
August 17, 2009, 11:21:10 AM »
Thanks again Kingchemist!
I did the math - that worked out perfectly. :]
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