Question #294927

One component of an ideal binary solution has a pure component vapor pressure equal to one-fourth the total pressure of the vapor mixture. The component constitutes 20 mole % of liquid phase. What is its mole fraction in the vapor phase?

1
Expert's answer
2022-02-08T21:04:02-0500

Using Raoult's law and Dalton law


xi=yipTOTALpix_i=\frac{y_i\>p_{TOTAL}}{p_i^*}


Where xi=x_i= Mole fraction of ii component in solution

yi=y_i= Mole fraction of component ii in gas phase

pTOTAL=p_{TOTAL}= Total vapor pressure

pi=p_i^*= Equilibrium vapor pressure of the pure component ii


20100=yipTOTAL14pTOTAL\frac{20}{100}=\frac{y_i\>p_{TOTAL}}{\frac{1}{4}\>p_{TOTAL}}


yi=14×15y_i=\frac{1}{4}×\frac{1}{5}


=120=\frac{1}{20}




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