The correct option is B 15
Given:
p∘Ap∘B=13
where,
p∘A⇒Pure vapour pressure of Ap∘B⇒Pure vapour pressure of B
YAYB=43
where,
YA⇒Mole fraction of A in vapour phaseYB⇒Mole fraction of B in vapour phase
From Dalton's law,
pA=PT×YA
where,
PT⇒Total pressure of the liquid mixturepA⇒Partial vapour pressure of AYA⇒Mole fraction of A in vapour phase
From Raoult's law,
pA=p∘A×XA
where,
pA⇒Vapour pressure of AXA⇒Mole fraction of A in liquidp∘A⇒Pure vapour pressure of A
Thus,
YA=pAPT⇒p∘AXAPT....eqn (i)
Similarly,
YB=p∘BXBPT.....eqn (ii)
Dividing equation (i) and (ii), we get,
YAYB=p∘Ap∘B×XAXB⇒43=13×XA(1−XA)4=XA(1−XA)XA=45XB=1−45XB=15