If the ratio by mass of magnesium and sulphur is $3:4$ in Magnesium sulphide, then what is the ratio of the number of magnesium and sulphur atoms?

Step 1: Calculate the mass of magnesium and sulphur in Magnesium sulphide:

1. The chemical formula of Magnesium sulphide is $\mathrm{MgS}$.
2. The ratio of atoms of magnesium and sulphur is $1:1$.
3. If ratio by mass of magnesium and sulphur is $3:4$,
4. Then, the mass of magnesium is $3\mathrm{g}$ and the mass of sulphur is $4\mathrm{g}$.

Step 2: Calculate the number of atoms in $3\mathrm{g}$ of magnesium:

We know that one mole of any substance contains a mass equal to its atomic mass.

One mole of magnesium $\left(\mathrm{Mg}\right)$ = $24\mathrm{g}$

From Avagadro's number, we know

$24\mathrm{g}$ of $\left(\mathrm{Mg}\right)$ = $\left(6.022\times {10}^{23}\right)$ atoms of $\left(\mathrm{Mg}\right)$

$3\mathrm{g}$ of $\left(\mathrm{Mg}\right)$ = $\frac{3\mathrm{g}\times \left(6.022\times {10}^{23}\right)}{24\mathrm{g}}$ = $\frac{6.022\times {10}^{23}}{8}$ atoms of $\left(\mathrm{Mg}\right)$

Step 3: Calculate the number of atoms in $4\mathrm{g}$ of sulphur:

We know that one mole of any substance contains a mass equal to its atomic mass.

One mole of sulphur $\left(\mathrm{S}\right)$ = $32\mathrm{g}$

From Avagadro's number, we know

$32\mathrm{g}$ of $\left(\mathrm{S}\right)$ = $\left(6.022\times {10}^{23}\right)$ atoms of $\left(\mathrm{S}\right)$

$4\mathrm{g}$ of $\left(\mathrm{S}\right)$ = $\frac{4\mathrm{g}\times \left(6.022\times {10}^{23}\right)}{32\mathrm{g}}$ = $\frac{6.022\times {10}^{23}}{8}$ atoms of $\left(\mathrm{S}\right)$

Step 4: Calculate the ratio of the number of magnesium and sulphur atoms:

From the above calculation, we know that there are

$\frac{6.022\times {10}^{23}}{8}$ atoms of $\left(\mathrm{Mg}\right)$ and $\frac{6.022\times {10}^{23}}{8}$atoms of $\left(\mathrm{S}\right)$

Hence, the ratio of the number of atoms of magnesium and sulphur is $\left[\frac{6.022\times {10}^{23}}{8}\right]:\left[\frac{6.022\times {10}^{23}}{8}\right]$ = $1:1$