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aqa a level chemistry questions need help

A sample of chromium containing the isotopes 50Cr, 52Cr and 53Cr has a
relative atomic mass of 52.1
The sample contains 86.1% of the 52Cr isotope.
Calculate the percentage abundance of each of the other two isotopes

can someone help, how do they get to the answers of 12.6% and 1.3%? thanks

Reply 1

alishbaxox

Original post by somone456

Hi I’ve worked it out and this is where you get the 12.6 and 1.3 from so have a look below( the attached pic below)
If you have any qs about the working out pls ask 🙂

(edited 2 years ago)

C6C1F1E5-3A0F-4C40-8A90-0688DC98A888.jpg390.2KB

Reply 2

bingbongdingbong

Hey there,

The way of working this questions out is quite simple.
So basically, to make things easier to deal with, we will convert the 86.1% to 0.861.
So, if 52Cr = 0.861, and 50Cr = 𝑥, that means that the % abundance of 53Cr must = 1 - 0.861 - 𝑥.

Then, write the normal numerator of the RAM equation (because we are finding the percentage abundances), substituting the expressions
----> (0.861x52) + 50𝑥 + [53 x (1 - 0.861 - 𝑥)]
----> 44.772 + 50𝑥 + [53 x (0.139 - 𝑥)]
----> don't forget to expand the brackets!
--> 44.772 + 50𝑥 + 7.367 - 53𝑥
and then we do some fun algebra, adding the 𝑥s and numbers together, and of course, making it equal to 52.1
52.139 + - 3𝑥 = 52.1

now, we rearrange it to: 52.139 - 52.1 = 3𝑥
and then solve it to find 𝑥!!
---> 0.039/3 = 0.013.
therefore, 𝑥 = 0.013.
This means that, if we substitute 0.013 in the expressions for the isotopes we made before, and convert to percentages,
50Cr = 1.3%
53Cr = 12.6%