Question

At its boiling point (280°C) and at atmospheric pressure, phosphorus gas has a density of 2.7 g L–1 . Under the same conditions, nitrogen gas has a density of 0.62 g L–1 . How many atoms of phosphorus are there in one phosphorus molecule under these conditions?

Answer 1

Answer:

4 atoms of phosphorus are there in one phosphorus molecule.

Explanation:

Density of phosphorus gas,d = 2.7 g/L

Temperature of the gas = T = 280°C = 553.15 K

Molar mass of phosphorus gas = M

Pressure of the gas ,P= 1 atm

$PM=dRT$

$P\times M=dRT$...(1)

Density of nitrogen gas,d' = 0.62 g/L

Temperature of the gas = T'= 280°C = 553.15 K

Molar mass of nitrogen gas = M' = 28 g/mol

Pressure of the gas ,P' = 1 atm

$P'M'=d'RT'$

$P'\times M'=d'RT'$...(2)

Dividing (1) and (2):

$\frac{P\times M}{P'\times M'}=\frac{dRT}{d'RT'}$

$M=\frac{2.7 g/L\times 1 atm \times 28 g/mol\times R\times 553.15 K}{0.62 g/L\times 1 atm\times R\times 553.15 K}$

M = 121.93 g/mol

Atomic mass of 1 phosphorus atom = 31 g/mol

Number of phosphorus atom in phosphorus gas:

$\frac{121.93 g/mol}{31 g/mol}=3.933 \approx 4$

4 atoms of phosphorus are there in one phosphorus molecule.