Question

XY2 is the empirical formula of a compound which has a vapour density of 50 and the atomic weight of X and Y are 10 and 20 respectively. Find its molecular formula.​

Answer 1

Information provided with us:

$\sf {XY_2}$ is the emperical formula of a compound

Vapour density is 50

Atomic weight of X and Y is 10 and 20

What we have to find out:

We have to calculate and find out the molecular formula

Required formulas inorder to solve:

$\underline{ \boxed{ \sf{Vapour \: density \: = \: \dfrac{molecular \: mass}{2} }}}$

i.e.,

$\red{\underline{ \boxed {\sf{molecular \: mass \: = \: 2 \times vapour \: density}}}}$

n:-

$\red{\underline{ \boxed {\sf{n \: = \: \frac{molecular \: weight}{emperical \: formula \: weight} }}}}$

Molecular formula:-

$\red{\underline{ \boxed{\sf{Molecular \: formula \: = \:emperical \: formula \: \times \: n }}}}$

Our calculations gets started:

$\red\bigstar$Finding out emperical formula mass,

Emperical formula mass is something in which we can determine the sum of atomic masses of different elements which is present in the emperical formula.

$: \longmapsto \: \tt{Emperical \: formula \: mass \: = \:10 + 20 \times 2 }$

$: \longmapsto \: \tt{Emperical \: formula \: mass \: = \:10 + 40 }$

$: \longmapsto \: \boxed{ \tt{Emperical \: formula \: mass \: = \:50 }}$

$\underline{\bf{ Therefore\: emperical \: formula \: mass \: is \: 50 }}$

$\red\bigstar$Finding out molecular mass$\red\bigstar$

Substituting the values in the formula of molecular mass,

$: \longmapsto \: \tt{Molecular \: mass \: = \: 2 \times 50}$

$: \longmapsto \: \boxed{\tt{Molecular \: mass \: = \: 100}}$

$\underline{\bf{ Therefore\: molecular \: mass \: is \: 100 }}$

$\red\bigstar$Finding out n$\red\bigstar$

Substituting the values in its formula,

$: \longmapsto \: \tt{n \: = \: \dfrac{100}{50} }$

$: \longmapsto \: \tt{n \: = \: \cancel\dfrac{100}{50} }$

$: \longmapsto \: \boxed{ \tt{n \: = \: 2 }}$

$\underline{\bf{ Therefore\: n \: is \: 2 }}$

$\red\bigstar$Finding out molecular formula$\red\bigstar$

Inorder to find out we have to do these steps:

First find out empirical weight

Divide its molecular weight by number (n)

Multiply that emperical formula by this number and you will get the molecular formula.

Substituting the values in the formula of molecular formula,

Here, n is 2.

$: \implies \: \sf{Molecular \: Formula \: = \: 2 \: × \: (XY_2) }$

$: \implies \: \sf{Molecular \: Formula \: = \: X_2Y_4 }$

$\underline{\bf {Hence, \: molecular \: formula \: is \: X_2Y_4 }}$