The vapor pressures of the components, A and B, in a binary solution have been modeled and found to obey PA = XAPA* exp(XB²) PB = XBPB* exp (X₁²) where XA and XB are the mole fractions, and PA* and PB* are the vapor pressures of each pure substance. (a) If PA* = 0.175 bar and PB* = 0.126 bar, compute the total vapor pressure (in bars) of the mixture when XB = 0.68. (b) Assuming that the vapor is an ideal gas, what are the mole fractions of each component in the vapor phase?

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**Vapor Pressure in Binary Solutions**

The vapor pressures of the components, \( A \) and \( B \), in a binary solution have been modeled and found to obey the following equations:

\[
P_A = \chi_A P_A^* \exp(\chi_B^2)
\]
\[
P_B = \chi_B P_B^* \exp(\chi_A^2)
\]

where \( \chi_A \) and \( \chi_B \) are the mole fractions, and \( P_A^* \) and \( P_B^* \) are the vapor pressures of each pure substance.

### Problems

**(a)** If \( P_A^* = 0.175 \, \text{bar} \) and \( P_B^* = 0.126 \, \text{bar} \), compute the total vapor pressure (in bars) of the mixture when \( \chi_B = 0.68 \).

**(b)** Assuming that the vapor is an ideal gas, what are the mole fractions of each component in the vapor phase?
Transcribed Image Text:**Vapor Pressure in Binary Solutions** The vapor pressures of the components, \( A \) and \( B \), in a binary solution have been modeled and found to obey the following equations: \[ P_A = \chi_A P_A^* \exp(\chi_B^2) \] \[ P_B = \chi_B P_B^* \exp(\chi_A^2) \] where \( \chi_A \) and \( \chi_B \) are the mole fractions, and \( P_A^* \) and \( P_B^* \) are the vapor pressures of each pure substance. ### Problems **(a)** If \( P_A^* = 0.175 \, \text{bar} \) and \( P_B^* = 0.126 \, \text{bar} \), compute the total vapor pressure (in bars) of the mixture when \( \chi_B = 0.68 \). **(b)** Assuming that the vapor is an ideal gas, what are the mole fractions of each component in the vapor phase?
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