To calculate the fugacity of each component in a gas mixture, you can use an appropriate equation of state, such as the Van der Waals equation, Redlich-Kwong equation, or Peng-Robinson equation. The fugacity of each component is dependent on the composition of the mixture, temperature, pressure, and the equation of state used.
Here's a general outline of the steps to calculate fugacity for each component using the Peng-Robinson equation of state:
Convert the mole fractions of each component to mole fractions (yi).
Calculate the compressibility factor (Z) using the Peng-Robinson equation of state.
Calculate the fugacity coefficient (φi) for each component using the Peng-Robinson equation of state.
Calculate the fugacity (fi) of each component.
Given:
Mixture composition: 70 mol% N2, 20% O2, 10% CO2
Pressure: 100 bar
Temperature: 150°C (convert to Kelvin: 150°C + 273.15 = 423.15 K)
First, convert the mole fractions to mole fractions:
N2: yi_N2 = 0.70
O2: yi_O2 = 0.20
CO2: yi_CO2 = 0.10
Then, using the Peng-Robinson equation of state, you would calculate Z for the given temperature and pressure. Once you have Z, you can calculate the fugacity coefficient (φi) for each component.
Finally, calculate the fugacity (fi) for each component using the following equation:
[ f_i = \phi_i \cdot P ]
Where:
( f_i ) is the fugacity of component i
( \phi_i ) is the fugacity coefficient of component i
( P ) is the pressure
Perform these calculations for each component, substituting the appropriate values into the Peng-Robinson equation of state and the fugacity equation, to obtain the fugacity of each component in the gas mixture.