Question

The vapour pressure of two pure liquids, A and B that form an ideal solution are 300 and 800 torr respectively, at temperature T. A mixture of the vapour of A and B for which the mole fraction of A is 0.25 is slowly compressed at temperature T, Calculate
(a) the composition of the first drop of the condesate,
(b) the total pressure when this drop is formed,
(c) the composition of the solution whose normal boiling point is T,
(d) the pressure when only the last bubble of vapour remains, and
(e) the composition of the last bubble.

Answer 1

Correct Answer - (a)0.47, (b) 565 torr, (c)`"X"_("A")=0.08," X"_("B")=0.92,` (d)`"X"_("A")^(1)=0.11," X"_("B")^(1)=0.89`
(a) `"P"_("A")="X"_("A")xx"P"_("A")^(0)`
`"P"_("T")="X"_("A")("P"_("A")^(0)-"P"_("B")^(0))+"P"_("B")^(0)`
`564.7="X"_("A")(300-800)+800`
`"X"_("A")=0.47`
(b) `("Y"_("A"))/("P"_("A")^(0))+("Y"_("B"))/("P"_("B")^(0))=1/"P"_("T")`
`0.25/300+0.75/800=1/"P"_("T")`
`"P"_("T")=564.7 " torr"`
(c) At boiling temp vapour pressure=760 torr
`300"X"_("A")+800"X"_("B")=760`
`"X"_("A")(300-800)+800=760`
`"X"_("A")=0.08`
`"X"_("B")=0.92`
(d) When only the last bubble of vapour remains, we can assme that the composition of vapour is now the composition of the codensation
`therefore " X"_("A")=0.25, " X"_("B")=0.75`
` "P"_("T")= "X"_("A")"P"_("A")^(0)+"X"_("B")"P"_("B")^(0)`
`=0.25xx300+0.75xx800`
`=675 "torr"`
(e) Composition of last bubble`="X"_("A")`
`"X"_("A")="Y"_("A")`
`"X"_("A")="P"_("A")/"P"_("T")`
`"X"_("A")=75/675=0.11," X"_("B")=1-0.11=0.89`