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

4 atoms of phosphorus are there in one phosphorus molecule.

Step-by-step 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* 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'* M'=d'RT'`...(2)

Dividing (1) and (2):

`(P* M)/(P'* M')=(dRT)/(d'RT')`

`M=(2.7 g/L* 1 atm * 28 g/mol* R* 553.15 K)/(0.62 g/L* 1 atm* R* 553.15 K)`

M = 121.93 g/mol

Atomic mass of 1 phosphorus atom = 31 g/mol

Number of phosphorus atom in phosphorus gas:

`(121.93 g/mol)/(31 g/mol)=3.933 \approx 4`

4 atoms of phosphorus are there in one phosphorus molecule.