My Chemistry Tutor

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:⁶⁹Ga: 60.3%, ⁷¹Ga: 39.7%

This is how I set up the problem:

Average atomic mass = (mass ⁶⁹Ga)(x) + (mass ⁷¹Ga)(y)

Where x and y are the relative abundances of ⁶⁹Ga and ⁷¹Ga 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! :]

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
                                   

Thanks again Kingchemist!

I did the math - that worked out perfectly. :]

May I ask a question?

Why did 69.72 (amu of Gallium) was changed to 6972?


thanks! :)