Equation of State for Nitrous Oxide

 

Pressure of gaseous nitrous oxide can be calculated by:

Ideal gas law by Boyle & Gay Lussac [1-3]:

where    p — gas pressure, Pa

             R — universal gas constant, R= 8.314472 J/mol/K

             T — gas temperature, K

             molar volume, m³/mol

             µ — molar mass, kg/mol

             ρ — gas density, kg/m³  

 

The van der Waals equation [1-3]:

where    a, b — gas constants for the equation

             a = 0.2060842 Pa m⁶ mol^-2

             b = 3.2458×10^-5 m³ mol^-1

 

The Berthelot equation [1,3]:

 

where    a, b — gas constants for the equation

             a = 87.198 Pa K m⁶ mol^-2

             b = 3.2458×10^-5 m³ mol^-1

 

The Dieterici equation [1,3]:

where    a, b — gas constants for the equation

             a = 0.500275 Pa m⁶ mol^-2

             b = 4.86×10^-5 m³ mol^-1

 

The Benedict-Webb-Rubin (BWR) equation of state [2,3] within temperature range from -30 to 150°C, for densities up to 900kg/m³, and maximum pressure of 200bar:

where    A₀, B₀, C₀, a, b, c, α, γ — gas constants for the equation

             A₀ = 0.313 kg m⁵ s^-2 mol^-2

             B₀ = 5.1953×10^-5 m³ mol^-1

             C₀ = 1.289×10⁴ kg m⁵ K² s^-2 mol^-2

             a = 1.109 ×10^-5 kg m⁸ s^-2 mol^-3

             b = 3.775×10^-9 m⁶ mol^-2

             c = 1.398 kg m⁸ K² s^-2 mol^-3

             α = 9.377×10^-14 m⁹ mol^-3

             γ = 5.301×10^-9 m⁶ mol^-2

 

The Harmens-Knapp equation [3]:

where    b, c — gas constants for the equation

              Pa m⁶ mol^-2

             b = 2.78292×10^-5 m³ mol^-1

             c = 1.922537

             T_c — critical point temperature, K

 

The Peng-Robinson equation of state [4]:

where    a, b — gas constants for the equation

             a = 0.417602925 Pa m⁶ mol^-2

             b = 2.76046×10^-5 m³ mol^-1

              

             T_c — critical point temperature, K

 

Figure 1 shows comparison of pressure-temperature data obtained by the above equations of state to the data by the National Institute of Standards and Technology (NIST).

Figure 1. P-T saturation data comparison

 

Although for low temperatures all data are in good agreement for Boyle & Gay Lussac, van der Waals, and Berthelot equations the discrepancy arises with increasing temperature.  Table 1 suggests that Dieterici, Benedict-Webb-Rubin, Harmens-Knapp, and Peng-Robinson equations of state give satisfactory correlation with NIST data for vapor pressure of saturated nitrous oxide. 

 

Table 1. The R-squared value for selected equations

Equation of State	R2
Boyle & Gay Lussac	0.911566
van der Waals	0.95507
Berthelot	0.993837
Dieterici	0.999837
Benedict-Webb-Rubin	0.999976
Harmens-Knapp	0.9999913
Peng-Robinson	0.9999837

 

Although Benedict-Webb-Rubin and Harmens-Knapp equations of state give satisfactory correlation with NIST data for vapor pressure of saturated nitrous oxide their prediction of critical point is rather poor (Table 2).

 

Table 2. Critical point parameters

Parameter	NIST	Benedict-Webb-Rubin	Harmens-Knapp
Pressure, bar	72.54	74.039	72.54
Temperature, K	309.584	310.968	309.576
Density, kg/m3	452.5	423.9	401.1

 

References

1. Dilip Kondepudi, Ilya Prigogine, Modern Thermodynamics, John Wiley & Sons, 1998, ISBN: 0-471-97393-9

2. Hsieh, Jui Sheng, Engineering Thermodynamics, Prentice-Hall Inc., Englewood Cliffs, New Jersey 07632, 1993. ISBN: 0-13-275702-8

3. Stanley M. Walas, Phase Equilibria in Chemical Engineering, Butterworth Publishers, 1985. ISBN: 0-409-95162-5

4. M. Aznar, and A. Silva Telles, A Data Bank of Parameters for the Attractive Coefficient of the Peng-Robinson Equation of State, Braz. J. Chem. Eng. vol. 14 no. 1 São Paulo Mar. 1997, ISSN 0104-6632

 

 

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