Mole Fraction and Atom Fraction [closed]








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I'm probably overthinking this but would appreciate a peer check.


Mole fraction of element $i$ in compound: $\frac{\mathcal{M}\_i}{\mathcal{M}}$


I used script M so as not to confuse with molar mass (often denoted as capital M).


Atom fraction of element $i$ in compound: $\frac{N\_i}{N}$


Now, if Avogadro's number is atoms/mol then isn't the mole fraction equal to the atom fraction?


$$
\frac{N\_i}{N}\frac{[\text{atom}]}{[\text{atom}]} \cdot \frac{N\_a}{N\_a}\frac{[\text{atom}/\text{mol}]}{[\text{atom}/\text{mol}]} = \frac{\mathcal{M}\_i}{\mathcal{M}} \frac{[\text{mol}]}{[\text{mol}]}\\
\frac{N\_a}{N\_a}=1\\
\frac{N\_i}{N}=\frac{\mathcal{M}\_i}{\mathcal{M}}
$$




The fallacy lies in the assumption that mole fraction and the number fraction are always the same.


For example, take $\ce{Na2SO4}$


what is the atom fraction of Na: 2/(2+1+4) = 2/7


What about the mole fraction of Na? It 2$N\_A$/$N\_A$(2+1+4)= 2/7


However, this "simple" formula of yours breaks down in the case of mixtures even if we mix them in 1:1 mol ratio. Calculate the mol fraction of Na ions in a mixture using your formula for $\ce{NaCl}$ and $\ce{Na2SO4}$ and see that you will not get the right answer.


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