(Solved): Problem 1: Calculate the compressibility factor for the gas shown in the table below at 13.94MP ...

Expert Answer

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Answer:- To calculate the compressibility factor for the given gas mixture, we can use the Peng-Robinson equation of state. The compressibility factor (Z) is calculated using the following equation:

  

Where:
P = Pressure (in Pa)
V = Molar volume (in m³/mol)
R = Ideal gas constant   
T = Temperature (in K)

To calculate the molar volume (V), we can use the following equation:

  
Where:
  
Zc = Critical compressibility factor
B = Constant

Where:
Vc = Critical molar volume
Zc = Critical compressibility factor
B = Constant

First, we need to determine the critical properties (Pc, Tc, and Zc) and acentric factor (?) for each component in the mixture. Here are the values for the given components:

Component - Molar Fraction (x) - Pc (MPa) - Tc (K) - Zc - ?
N? - 0.0046 - 3.39 - 126.2 - 0.291 - 0.037
CO? - 0.0030 - 7.38 - 304.2 - 0.273 - 0.225
H?S - 0.1438 - 8.77 - 373.2 - 0.274 - 0.098
C? - 0.8414 - 4.95 - 190.6 - 0.282 - 0.008
C? - 0.0059 - 4.88 - 305.4 - 0.275 - 0.098
C? - 0.0008 - 4.25 - 369.8 - 0.277 - 0.152
iC? - 0.0003 - 3.79 - 408.1 - 0.284 - 0.183
nC? - 0.0002 - 3.77 - 425.2 - 0.283 - 0.193


The compressibility factor (Z) is a dimensionless parameter that describes the deviation of a gas from ideal behavior. A value of Z close to 1 indicates that the gas behaves ideally, while values significantly different from 1 indicate deviations from ideal behavior.

In the calculation, we used the Peng-Robinson equation of state to estimate the compressibility factor. This equation takes into account the critical properties (Pc, Tc, and Zc) and acentric factor (?) of each component in the gas mixture.

First, we determined the critical properties and acentric factors for the given components: N?, CO?, H?S, C?, C?, C?, iC?, and nC?. These properties are essential for characterizing the behavior of each component.