I'm not sure I understand the problem. I interpret this problem as unmixed. If that is true, then you want
Pa = Xa*Poa = Xa*500
Pb = Xb*Pob = Xb*200 and since Pa = Pb, then
Xa*500 = Xb*200
Xa + Xb = 1 and solve for Xa and Xb. I get something like 143 mm Hg but that is approximate. Let me know if this is not the correct interpretation.
2 liquids a and b have vapour pressure of 500 mm hg and 200 mm hg .calculate mole fraction of a at which 2 liquids have equal partial pressure
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I also think so
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