An unknown substance that uses gas at room temperature can be condensed to a solid at –80^(@)C. As a solid, it is found to have cubic unit cell, 5.15 Å on each side, containing four molecules. The density of solid is 0.73 g/cm3. What is the density of the substance as a gas at 27(@)C and at a pressure of 1.00 atmopshere ?

An unknown substance that uses gas at room temperature can be condense

1.	An unknown substance that uses gas at room temperature can be condensed to a solid at –80^(@)C. As a solid, it is found to have cubic unit cell, 5.15 Å on each side, containing four molecules. The density of solid is 0.73 g/cm3. What is the density of the substance as a gas at 27(@)C and at a pressure of 1.00 atmopshere ?
Answer» Solution :For a cubic unit CELL: DENSITY `(rho)=(nM)/(N_(A)a^(3))` Where, n : No. of molecules per unit cell, M = Molar mass NA = Avogadro's constant, a = Edge length of unit cell.`IMPLIES` 0.73 g//cm^(3)=(4xxm)/(6.023xx10^(23)(5.15xx10^(-6)cm)^(3))` M=15 g/mol M Molar mass of a SUBSTANCE is independent of state. `impliesAs a gas ,Density `(rho)=(pM)/(RT)=(1.05xx15)/(0.082xx300)` 0.6097 g/L