`P` and `Q` are two elements which from `P_(2)Q_(3),PQ_(2)` molecules. If `0.15 "moles of" P_(2)Q_(3)` and `PQ_(2)` weighs `15.9 g` and `9.3 g`, respectively, what are atomic weighs of `P` and `Q`?

Explanation

Let the atomic mass of the element `P=a`
Let the atomic mass of element `Q = b`
`:.` Molecular mass of `P_(2)Q_(3) = 2a + 3b`
Molecular mass of `PQ_(2) = a+2b`
According to available data,
Molar mass of `P_(2)Q_(3)=((15.9g)xx(1gmol))/((0.15gmol))=106g`
Molar mass of `PQ_(2)=((9.3g)xx(1gmol))/((0.15g mol))=62g`
On comparing, we get
`2a+3b=106`
`a+2b=62`
Multiply eqn (ii) by 2 and subtract eqn. (i) from it.
`2a+4b-2a-3b=124-105orb=18`
Substituting the value of b in eqn (i),
`2a+3xx18=106or a=(106-54)/(2)=16`
`:.` Atomic mass of element P = 26
Atomic mass of element Q = 18.