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Say I have this problem, for example:

How many atoms are in 39.6g of pure tungsten?

So what I would know here is that first off the molar mass of tungsten is $183.84\,\text g/\text{mol}$. While I understand this, what I don't understand is how I would get the number of atoms in this sample from here. Intuitively it's obvious that (rounding calculations to 2 decimal places)$$\text{Number of atoms in }1\text{ g of tungsten}:\dfrac{1\text{ mol}}{183.84}\\=\dfrac{6.02\times10^{23}}{183.84}\text{ atoms}=3.27\times10^{21}\text{ atoms}$$and therefore the number of atoms in 39.6g of tungsten is equal to$$3.27\times10^{21}\times39.6=129.492\times10^{21}\\=1.29492\times10^2\times10^{21}=1.29\times10^{23}\text{ atoms}$$But my question is this:

Why does this method work? Intuitively it seems that the number of atoms in a given mass of a pure substance is calculated as$$(\text{atomic mass})^{-1}\times\text g\times1\text{ mol}$$however it doesn't exactly make sense as to why I would be taking the reciprocal of $\text{atomic mass}\times\text{mol}^{-1}$ if I'm not taking the reciprocal of $\text g$ along with that.

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    $\begingroup$ I don't really understand your problem here... Since the atomic mass is in $\text{grams} \times \text{mol}^{-1}$, its reciprocal is indeed in $\mathrm{mol}\times \mathrm{grams}^{-1}$, so a multiplication by a mass gives an amount of moles, i.e. a number of atoms at the end. Maybe I missed the point of your question? $\endgroup$
    – Thomas Prévost
    Commented Oct 16 at 19:49
  • $\begingroup$ $$N = \frac{m[\pu{g}]}{M[\pu{g mol-1}]} \cdot N_\text{A}[\pu{mol-1}]$$ $\endgroup$
    – Poutnik
    Commented Oct 16 at 20:34

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It isn't complicated if you think about the principles

Imagine for the purposes of argument that eggs all weigh 50g.

You have a collection of eggs that weigh 600g in a box. You can calculate the number or eggs you have by dividing the total weight of the eggs by the weight of an individual egg. 600g/50g = 12. You have a dozen eggs.

The math for the number of atoms is exactly the same except that the convenient unit for counting atoms is moles not dozens.

Don't get confused by the math, the intuition is simple.

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