Question

The density of h2 gas in a rigid container is 0.135 g/l at a given temperature. what is the pressure of hydrogen in the flask if it is heated to 201 °c?

Answer 1

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