Mass of element P = 1.44 g
Further explanation
Proust stated the Comparative Law that compounds are formed from elements with the same Mass Comparison so that the compound has a fixed composition of elements
In the same compound, although from different sources and formed by different processes, it will still have the same composition/comparison
MW Q₂P₃ = 2.27 + 3.16=102 g/mol
Mass Q₂P₃ (MW=102 g/mol) :
![\tt mass~Q_2P_3=(MW~Q_2P_3)/(2.Ar~Q)* mass Q\\\\mass~Q_2P_3=(102)/(2* 27)* 1.62\\\\mass~Q_2P_3=3.06~g](https://img.qammunity.org/2021/formulas/chemistry/high-school/ketlzk1ao6jw67p3pmvmbqkmsjc9scnpvz.png)
Mass P (Ar=16) :
![\tt mass~P=(3.Ar~P)/(MW~Q_2P_3)* mass~Q_2P_3\\\\mass~P=(3.16)/(102)* 3.06\\\\mass~P=1.44~g](https://img.qammunity.org/2021/formulas/chemistry/high-school/x7dm7y1n2ssiczthagyfl1b87ruaz4azlp.png)
or you can solve it with mol :
Reaction
3P + 2Q ⇒ Q₂P₃
mol Q :
![\tt (1.62)/(27)=0.06](https://img.qammunity.org/2021/formulas/chemistry/high-school/gscql3wyce5f3o69b339inyob3xici4cww.png)
mol P :
![\tt (3)/(2)* 0.06=0.09](https://img.qammunity.org/2021/formulas/chemistry/high-school/kn504ouffvnlh74m56hq1113l3frjr1phv.png)
mass P :
![\tt 0.09* 16=\boxed{\bold{1.44~g}}](https://img.qammunity.org/2021/formulas/chemistry/high-school/kns6efmjntwxn40uozvru74mp5o7mt3xbd.png)