A hypothetical gaseous element having molecular formula $M_{x}$ is completely changed to another gaseous allotrope having molecular formula $M_{y}$ at a constant temperature and pressure. In this act volume of the gas is contracted by 12mL to a volume of 8mL. The simplest possible molecular formula of two allotropes are:

M_{2}

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M_{3}

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M_{4}

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M_{5}

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Solution

The correct options are
A $M_{2}$
D $M_{5}$

(A, D)

$V_{2} = 8 m L (g i v e n)$

$V_{1}$ = 8 + 12 = 20mL

At constant T and P,

$V α n$

$\frac{V_{1}}{V_{2}} = \frac{n_{1}}{n_{2}} = \frac{M_{2}}{M_{1}}$

$\frac{20}{8} = \frac{M_{2}}{M_{1}}$

$\Rightarrow \frac{M_{2}}{M_{1}} = \frac{5}{2}$

Thus,the molar masses of two allotropes are in the ratio of 2 : 5. This works only with options A and D.

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The correct options are A M2 D M5 (A, D) V2=8mL(given) V1 = 8 + 12 = 20mL At constant T and P, Vαn V1V2=n1n2=M2M1 208=M2M1 ⇒M2M1=52 Thus,the molar masses of two allotropes are in the ratio of 2 : 5. This works only with options A and D.