Let's assume that H₂ gas has ideal gas behavior.
Then we can use ideal gas formula,
PV = nRT
Where,
P = Pressure of the gas (Pa)
V = Volume of the gas (m³)
n = moles of the gas (mol)
R = Universal gas constant (8.314 J K⁻¹ mol⁻¹)
T = Temperature in Kelvin (K)
But,
n = m/M,
Where m is mass of the gas (kg) and M is molar mass of the gas (kg/mol)
Hence PV= mTR / M
P = mTR / VM = (m/V)TR / M
m/V = d (density (kg/m³)
By rearranging,
P = dRT / M
d = 0.135 g/L = 0.135 kg/m³
T = (273 + 201) K = 474 K
M = 2 g/mol = 2 x 10⁻³ kg/mol
From substitution,
P = 0.135 kg/m³ x 8.314 J K⁻¹ mol⁻¹ x 474 K / 2 x 10⁻³ kg/mol
P = 266006.43 Pa
P = 266 kPa
Hence the pressure of H₂ gas at 201⁰C is 266 kPa
