A level chemistry help please

Ok so I was doing this question:

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.

So I looked at the mark scheme and it showed:
52.1= [50x (13.9-x)] + (52x86.1) + (53x)

Now the thing I’m confused with is that it could have been either 53x or 50x, but here they have chosen 53x; does this mean the largest number is x?
Hopefully that makes sense and thank you in advance for your help.

Reply 1

UtterlyUseless69

Original post by Gracie212

It works regardless of whether you choose x to be the abundance of 50Cr or 53Cr - provided you set the abundance of the other to be 100 - x - 86.1 = 13.9 - x (in this case).

As long as you find a value of x and can plug it back into 13.9 - x to find the other abundance, you’re good.

I just think the examiners were too lazy to write the calculation out twice, so they just gave one example and left it at that.

(edited 1 month ago)

Reply 2

Gracie212

Thank you so muchhhh!!!

Reply 3

awchemtutor

Ar 52.1 closer to 53. Hence, I'll 53 goes with the x.

Reply 4

TypicalNerd

Original post by awchemtutor

Ar 52.1 closer to 53. Hence, I'll 53 goes with the x.

As explained by UtterlyUseless69, it really doesn’t matter which abundance you call x in this question as you need to calculate both unknown abundances anyway. No convention exists about defining percentage abundances algebraically when comparing them to the Ar of the element.

That said, had the question specifically asked for you to calculate the abundance of just one of the two isotopes, you would have been better off defining the abundance of the isotope the question wants you to find as x, as the calculation would just spit out the answer you need without having to do an extra step to find it. So if the question had asked for you to just calculate the abundance of 50Cr (and to not bother with the abundance of 53Cr), then it would be better to call the abundance of 50Cr x.