Algebra/chemistry

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mezzogoch

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Apr 18, 2007
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:?: Frustrated:Thought I knew how to solve this but alas NOT!
The Problem:
The Made-up element Pk exist in nature as two isotopes:151PK has a mass of 150.9196amu, and 153Pk has a mass of 152.9209amu. The ave. atomic mass of PK is 151.960amu. Calculate the relative abundance(%) of each of the two Pk isotopes.
The only hint I got from my chem instructor was that I need to solve for two unknowns(no kidding)I'm only an algebra 92 student and this was my best attempt.
%151Pk=x x(150.9196)+(100%-x)(152.9209)=151.960(100%)
%153Pk=(100%-x)
AvePK=100%
He "My instructor" told me today that I "just don't have the algebra chops to solve this yet" Meanwhile this is the kind of stuff I'm faced whith in Chem. right now!
When someone with more "algebra chops"than me replies please show work and reasoning. I'm not just fishin for an answer,I really want to know how to do this. Thanks
 
Let's say the 151PK isotope has an abundance of x%.

Then the 153PK isotope has an abundance of (100 - x)%.

Now assume you took one hundred atoms of this element. Then the average mass of one Pk atom is:

Average mass = [x * 150.9196 + (100 - x)*152.9209]/100

The above step is probably the most difficult (knowing the formula).

We're given that the average mass is 151.960:

15196 = 150.9196x + 15292.09 - 152.9209x

So it's a matter of solving the above equation (not two unknowns).

So x is about 48.014%, making the 151Pk isotope have an abundance of 48.014%, and the
other isotope having an abundance of 51.986%.
 
Morson; Thanks soooooooo much,got to get to class but would like to dicuss this further later.
 
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