34.05 mL of phosphorus vapour weighs 0.0625 g at 546°C and 0.1 bar pressure. What is the molar mass of phosphorus?

Given,

p = 0.1 bar

V = 34.05 ml = 34.05 × 0.001 L = 34.05 × 0.001dm³

R = 0.083 bar dm³/K mol

T = 546°C = (546 + 273) K = 819 K

The number of moles (n) can be calculated using the ideal gas equation as:

PV = nRT

Where, P - Pressure of gas

V - Volume of gas

n - Number of moles of gas

R- Gas constant

T -Temperature of gas

⇒

n = 5.01×10^-5 mol

Therefore, molar mass of phosphorus = mass/moles

⇒

⇒ M = 1247.5 g/mol

Hence, the molar mass of phosphorus is 1247.5 g/mol.