Help with relative atomic mass of rubidium.

[Msingh_G]

I was doing some summer work given by my chem teacher to help prepare us for chemistry class starting in september. I need help with this question:

 

"Rubidium has only two isotopes in nature: ⁸⁵Rb and ⁸⁷Rb. Calculate the percentage abundance of the isotopes of rubidium given that the relative atomic mass (weighted average) is 85.47."

 

How would you calculate this? 

 

Thank you. 

[mr_awesome]

Ok, so basically you use the formula:

85.47 = (isotope mass x %) + (isotope mass x %)  / 100

 

since we do not know the % value of the isotopes you sub x as the percentage for the first isotope (Rb-85), which means that the second isotope (Rb-87) would have a percentage of 100 - x

therefore: 85.47 = 85 (x) + 87 (100-x)  /100

multiple each side by 100 and simplify.

therefore:
8547 = 85x + 8700 - 87x

8547 = -2x + 8700

-153 = -2x

x = 76.5


Once you work out what x is equal to you, you've basically found the percentage of the first isotope (Rb-85), and because there are only 2 isotopes, to work out the percentage of Rb-87 you do 100 - x.

so Rb-85 = 76.5%
    Rb-87 = 100-76.5  = 23.5%

 

[Emmi]

The above procedure is correct, but the percent abundance numbers are incorrect. I was about to post the solution I had written out but they beat me to it.

 

Instead of assuming 85 and 87 as the mass numbers, use the actual masses, which is 84.9117 for ⁸⁵Rb and 86.9092 for ⁸⁷Rb. You will get 72.06% for ⁸⁵Rb and 27.94% for the other isotope, which is correct according to several internet sources.

Edited July 9, 2014 by Emmi

[Msingh_G]

Thank you for your help!