The density of phosphorus vapor at 310 degrees celcius and 775 mmHg is 2.64g/L. what is the molecular formula of the phosphorus under these conditions?

The molecular formula of the phosphorus is P4

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