#### How do you measure the mass of the gas?

Question

At 273 K and under pressure of 100 atm the compressibility factor of oxygen 0.97. Calculate the mass of oxygen necessary to fill a gas cylinder of 108.5 lit capacities under the given conditions.

Answer

T = 273 K, Z = 0.97 and P = 100 atm.

Compressibility factor, Z = PV/RT where V is molar volume.

The molar volume of oxygen

V_{m} = ZRT/P

= (0.97 × 0.082 × 273 K)/(100)

= 2.17 lit mol^{-1}

The mass of this molar volume will be equal to the molar mass of oxygen, which is 2.17 lit of oxygen equal to 32 gm.

Thus the mass of oxygen required to fill the gas cylinder 108.5 lit under the given condition

= 1600 gm

= 1.6 Kg

Question

Calculate the weight of oxygen necessary to fill up a cylinder of 5-liter capacity at 0^{0} C and 100-atmosphere pressure when the compressibility factor 0.96.

Answer

Number of moles (n) = g/M gm mol^{-1} and Z = compressibility factor.

PV = Z × nRT or, n = PV/ZRT

∴ g/M = PV/ZRT or, g = PVM/ZRT

∴ Weight of oxygen = PVM/ZRT

= 744 gm

#### Write the units of van der Waals constants a and b?

For n mole real gas, Van der Waals equation of state

Unit of a = atm lit^{2} mol^{-2}

CGS unit of a = dyne cm^{-2} cm^{6} mol^{-2} = dyne cm^{4} mol^{-4}

SI unit of a = Newton m^{-2} m^{6} mol^{-2} = Newton m^{4} mol^{-2}

SI unit of b = m^{3} mol^{-1}

CGS unit of b = cm^{3} mol^{-1}

The dimension of a = [M L^{5} T^{-2} mol^{-1}]

Dimension of b = [L3 mol^{-1}]

Question

What is the Boyle temperature of nitrogen gas if a = 1.4 atm lit² mol⁻² and b=0.04 lit mol⁻¹?

Answer

Boyle temperature, TB = a/Rb.

∴ Boyle temperature for nitrogen gas

= 1.4/(0.082 × 0.04) K

= 427 K