Friday, April 26, 2019

periodic table - What is the formula for finding the average atomic mass of an element based on the abundance of its isotopes?


In my class my teacher showed us how to find the average atomic mass of an element with a method, but he didn't really state a formula one could use. I came up with a formula of my own, and from what I observed it works: i1x+i2y100=A,

where A is the atomic mass, i1 is the first isotope's atomic weight, i2 is the second isotope's atomic weight, x and y are the percentages of the isotopes, respectively, and they add up to 100, i.e. x+y=100.


Therefore: i1x+i2(100x)100=A


I'm just wondering, is there an official formula, or is this method it?



Answer



The average relative atomic mass of an element comprised of n isotopes with relative atomic masses Ai and relative fractional abundances pi is given by:


A=p1A1+p2A2++pnAn=ni=1piAi


For example carbon:



IsotopeIsotopic Mass AAbundance pA×pX12X2122C:12.000000 u0.98892=11.867 uX13X2132C:13.003354 u0.01108=00.144 u


Since we have p1A1 and p2A2, we add those together to find A, therefore the chemical relative atomic mass of carbon is A=00.144 u+11.867 u=12.0011 u.


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