A spherical shaped balloon of 12 m diameter contains H2 at 30°C and 1.21 bar. Find the mass of H2 in the balloon using real gas equation.

Question

A spherical shaped balloon of 12 m diameter contains [latex]H _2[/latex] at 30°C and 1.21 bar. Find the mass of [latex]H _2[/latex] in the balloon using real gas equation.

Accepted Answer

Diameter of spherical balloon = 12 m

∴ Volume, [latex]V=4 / 3 \pi imes(6)^3=904.78[/latex] m³

Temperature, T = 30 + 273 = 303 K

Pressure, p = 1.21 bar

Mass of [latex]H _2[/latex] in the balloon, m :

For [latex]H _2[/latex] (from Table 8.3) [latex]p_c=12.97[/latex] bar

[latex]T_c=33.3[/latex] K

Now, [latex]p_r=\frac{p}{p_c}=\frac{1.21}{12.97}=0.093[/latex]

[latex]T_r=\frac{T}{T_c}=\frac{303}{33.3}=9.1[/latex]

From compressibility charge, corresponding to [latex]p_r=0.093 ext { and } T_r=9.1[/latex]

[latex]Z \simeq 1[/latex]

(This indicates that the gas having higher critical pressure and lower critical temperature behaves like an ideal gas at normal pressure and temperature conditions.)

Also, [latex]p V=Z m R T[/latex]

or [latex]m =\frac{p V}{Z R T}=\frac{1.21 imes 10^5 imes 904.78}{1 imes\left(\frac{8314}{2} ight) imes 303}= 8 6 . 9[/latex] kg.

Table 8.3. Critical Constants
Substance	Pressure [latex]\left(p_c ight)[/latex] bar	Temperature [latex]\left(T_c ight)[/latex] K
Air	37.69	132.5
Argon	48.64	151.0
Carbon dioxide	73.86	304.2
Carbon monoxide	34.96	133.0
Helium	2.29	5.3
Hydrogen	12.97	33.3
Nitrogen	33.94	126.2
Oxygen	50.76	154.8
Water	228.59	647.15
Ethane	48.84	305.5
Ethylene	51.17	282.4
Methane	46.41	191.1
Propane	42.55	370.0

Question 8.15: A spherical shaped balloon of 12 m diameter contains H2 at 3...

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