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I have the following equations for weight and atom percent:

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Where m is the mass of each element.

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where A is the atomic weight of each element and m prime is the mass of each element.

And I'm told that you can convert between them with the following equations: enter image description here

My question is how are the two sets of conversion equations derived?

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    $\begingroup$ Take the conversion for atom percent to weight percent, C1 for example, substitute all the C primes for their equivalents from the definition of atom percent, and then simplify the equation. You'll see it's a matter of manipulating the units by rearranging and substituting n = m/A in the different definitions. $\endgroup$
    – J. Ari
    Commented Nov 9, 2022 at 22:09

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