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Isotope and relative atomic mass question

I have come across this question:

'Chlorine has two naturally occurring isotopes that exist in an almost 75:25 abundance ratio. The average relative atomic mass of chlorine is 35.5.
What are the relative atomic masses of these isotopes? .'

I know the answer, which is 35 and 37, but I don't understand how 35 and 37 were calculated using the ratio and average relative atomic mass.
Help?
(3a+b)/4=35.5
3a+b=142

well they're going to be 2 positive integers that are both quite close to 35.5..
if the abundance ratio was 50:50 then 35 and 36 would do it

so you could just plug in some candidate numbers and use trial/error
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PhysBang
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Original post by Joinedup
(3a+b)/4=35.5
3a+b=142

well they're going to be 2 positive integers that are both quite close to 35.5..
if the abundance ratio was 50:50 then 35 and 36 would do it

so you could just plug in some candidate numbers and use trial/error




Joinedup,

I understand the second part of what you've said and that was my approach, but I didn't understand/recognise the formula you used at the beginner of your comment 3a+b/4=35.5 etc
Original post by PhysBang
Joinedup,

I understand the second part of what you've said and that was my approach, but I didn't understand/recognise the formula you used at the beginner of your comment 3a+b/4=35.5 etc


if it's a 75:25 ratio then one of the isotopes is 3 times more abundant than the other because 75=3*25

so you get a range of possible solutions like (1,139) (2,136) (3,133)... but you're only interested in the ones that are quite close to 35

hope that helped.
Reply 4
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PhysBang
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Original post by Joinedup
if it's a 75:25 ratio then one of the isotopes is 3 times more abundant than the other because 75=3*25

so you get a range of possible solutions like (1,139) (2,136) (3,133)... but you're only interested in the ones that are quite close to 35

hope that helped.


That makes sense and your response did help, thank you!
Reply 5
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alow
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Original post by PhysBang
That makes sense and your response did help, thank you!


Honestly it's a crap question. Usually questions like this specify one of the isotopic masses to make sure the only masses you can calculate are the right ones.
Reply 6
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PhysBang
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Original post by alow
Honestly it's a crap question. Usually questions like this specify one of the isotopic masses to make sure the only masses you can calculate are the right ones.



Well, that is partially reassuring if a question would normally provide one of the masses, although surprising as it's from a physics AS A level book.
Original post by PhysBang
Well, that is partially reassuring if a question would normally provide one of the masses, although surprising as it's from a physics AS A level book.


Yeah I'd hoped it had been originally presented as a multi-choice and you had to eliminate some impossible choices

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