Density of sulphur vapour at 600°c and 700mm pressure is 3.29g/L .calculate molecular mass and molecular formula?

To determine the molecular mass and molecular formula of sulfur vapor, we will use the ideal gas equation and the concept of vapor density.

Given Data:
Temperature (T) = 600°C = (600 + 273) K = 873 K
Pressure (P) = 700 mm Hg
Converting to atm:
1 atm = 760 mm Hg
So, P = 700/760 atm = 0.921 atm
Density (d) = 3.29 g/L
Gas constant (R) = 0.0821 L·atm·mol⁻¹·K⁻¹
Step 1: Use the Ideal Gas Equation to Find Molecular Mass
We use the ideal gas law in the form:

M = (dRT) / P

Substituting the given values:

M = (3.29 × 0.0821 × 873) / 0.921
M = (235.97) / 0.921
M ≈ 256 g/mol

Step 2: Determine the Molecular Formula
The atomic mass of sulfur (S) is 32 g/mol.
To find the molecular formula, we divide the molecular mass by the atomic mass:

Number of sulfur atoms = 256 / 32 = 8

Thus, the molecular formula of sulfur vapor at this temperature is S₈.

Final Answer:
Molecular Mass = 256 g/mol
Molecular Formula = S₈