The vapour pressures of two pure liquids `A` and `B` that form an ideal solution are `300` and 800 torr, respectively, at tempertature `T`.A mixture of the vapours 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 condensate.
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.
e. Composition of the last bubble.

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`

Explanation

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