Answer:
The molecular formula of the phosphorus is P4
Step-by-step explanation:
Step 1: Data given
Density of phosphorus vapor at 310 °C and 775 mmHg = 2.64g /L
Step 2: Calculate the molecular weight
We assume phosphorus to be an ideal gas
So p*V = n*R*T
⇒ with p = the pressure of phosphorus = 775 mmHg
⇒ with V = the Volume
⇒ with n = the number of moles = mass/molecular weight
⇒ with R = ideal gas constant = 0.08206 L*atm/K*mol
⇒ with T = the absolute temperature
p*V = m/MW *R*T
MW = mRT/PV
⇒ Since the volume is unknown but can be written as density = mass/volume
MW = dRT/P
MW = (2.64g/L * 0.08206 L*atm/K*mol * 583 Kelvin)/1.0197 atm
MW = 123.86 g/mol
Step 3: Calculate molecular formula of phosphorus
The relative atomic mass of phosphorus = 30.97 u
123.86 / 30.97 = 4
The molecular formula of the phosphorus is P4