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  4. The density of phosphorus vapour at 310° C and 775 mm Hg is 2.64 g/l. Molecular formula of phosphorus is:

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Q. The density of phosphorus vapour at $ 310{}^\circ C $ and 775 mm Hg is 2.64 g/l. Molecular formula of phosphorus is:

JIPMERJIPMER 1997

Solution:

Vapour density of phosphorus at $ 310{}^\circ C $ and 775 mm Hg is 2.64 g/l. i.e., $ {{P}_{1}}=775\,mm=\frac{775}{760}atm $ $ {{T}_{1}}=310+273=583\,K $ $ d=\frac{w}{V}=2.64\,\text{g/l} $ According to gas-equation: $ PV=nRT=\frac{w}{m}RT $ or $ m=\frac{w}{V}\cdot \frac{RT}{P} $ or $ m=\frac{2.64\times 0.0821\times 583}{775\text{/}760} $ Atomic weight of phosphorus is 31. Hence number of atoms bonded together to form one molecule will be $ =\frac{124}{31}=4. $ Hence, molecular formula of phosphorus $ ={{P}_{4}}. $