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.





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Answer 1

Answer :-

Molecular formula of the compound is X₂Y₄ .

Explanation :-

We have :-

→ Empirical formula = XY₂

→ Vapour density (V.D.) = 50

→ Atomic weight of "X" = 10

→ Atomic weight of "Y" = 20

______________________________

Firstly, let's calculate the empirical formula mass of the compound .

= 10 + (20 × 2)

= 10 + 40

= 50

Now, we have to calculate molecular mass of the compound. For this, we can use the relationship between molecular mass and vapour density .

⇒ Molecular mass = 2 × V.D.

⇒ Molecular mass = 2 × 50

⇒ Molecular mass = 100

______________________________

n = Molecular mass/Emp. formula mass

⇒ n = 100/50

⇒ n = 2

Finally, we can calculate the molecular formula by :-

Molecular formula = n × Emp. formula

⇒ Molecular formula = 2(XY₂)

⇒ Molecular formula = X₂Y₄

Answer 2

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.

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

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

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