The saturation pressure of component \(i\) = (1,2) is calculated using the Antoine equation:
$$
P_i^{sat} = 10^{(A_i - \frac{B_i}{T'+C_i})}
$$
where \(A_i\), \(B_i\), and \(C_i\) are Antoine constants, \(T'\) is temperature (°C), and \(P_i^{sat}\) is in bar.
The two-parameter Margules model is used to calculate the activity coefficients for a non-ideal liquid mixture of beneze 1 and ethanol 2. This model fits the excess Gibbs free energy:
$$
\frac{G^E}{RT} = x_Bx_E(A_{21}x_B + A_{12}x_E),
$$
where \(G^E\) is excess Gibbs energy, \(R\) is the ideal gas constant, \(T\) is temperature (K), \(x_B\) and \(x_E\) are the liquid mole fractions of benzene and ethanol (\(x_B + x_E = 1\)), and \(A_{21}\) and \(A_{12}\) are the Margule parameters.
The activity coefficients \(\gamma_1\), \(\gamma_2\) are given by:
ln\((\gamma_1) = x_E^2(A_{12} + 2(A_{21}-A_{12})x_B)\),
ln\((\gamma_2) = x_B^2(A_{21} + 2(A_{12}-A_{21})x_E)\),
The modified Raoult's law is used to calculate the bubble-point and dew-point pressures using the \(K\) factors:
$$
K_i = \frac{y_i}{x_i} = \frac{\gamma_iP_i^{sat}}{P},
$$
where \(y_i\) is the vapor mole fraction and \(y_B\) + \(y_E\) = 1, and \(P\) is the total pressure (bar).
Bubble-point pressure calculation:
$$
P = x_B\gamma_1P_1^{sat} + x_E\gamma_2P_2^{sat}.
$$
Dew-point pressure calculation:
$$
P = (\frac{B}{\gamma_1P_1^{sat}} + \frac{y_E}{\gamma_2P_2^{sat}})^{-1}.
$$
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