?The following is a rule of thumb: For a binary system in VLE at low pressure, the

Chapter 13, Problem 13.21

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The following is a rule of thumb: For a binary system in VLE at low pressure, the equilibrium vapor-phase mole fraction \(y_{1}\) corresponding to an equimolar liquid mixture is approximately

\(y_{1}=\frac{P_{1}^{\mathrm{sat}}}{P_{1}^{\mathrm{sat}}+P_{2}^{\mathrm{sat}}}\)

where \(P_{i}^{\text {sat }}\) is a pure-species vapor pressure. Clearly, this equation is valid if Raoult’s law applies. Prove that it is also valid for VLE described by Eq. (13.19), with \(\ln \gamma_{1}=A x_{2}^{2} \text { and } \ln \gamma_{2}=A x_{1}^{2}\).

Text Transcription:

y_1

y_1=P_1^sat/P_1^sat+P_2^sat

P_i^sat

ln gamma_1=A x_2^2 and ln gamma_2=A x_1^2

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