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: $$ \frac{i_1x + i_2y}{100} = A, $$ where $A$ is the atomic mass, $i_1$ is the first isotope's atomic weight, $i_2$ 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: $$ \frac{i_1x + i_2(100-x)}{100} = A $$
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 $A_i$ and relative fractional abundances $p_i$ is given by:
$$ A = p_1 A_1 + p_2 A_2 + \dots + p_n A_n = \sum\limits_{i=1}^n p_i A_i $$
For example carbon:
\begin{array}{lrrr} \text{Isotope} & \text{Isotopic Mass $A$} & \text{Abundance $p$} & A\times p\\\hline \ce{^{12}C}: & \pu{12.000000 u} & 0.98892 &= \pu{11.867 u}\\ \ce{^{13}C}: & \pu{13.003354 u} & 0.01108 &= \pu{00.144 u} \end{array}
Since we have $p_1A_1$ and $p_2A_2$, we add those together to find $A$, therefore the chemical relative atomic mass of carbon is $$A = \pu{00.144 u} + \pu{11.867 u} = \pu{12.0011 u}.$$
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