QJEEAdv18Ch0d6f: JEE Advanced 2018 Chemistry - Class 12 JEEAdv18Ch0d6f Solution: Liquids A and B form ideal solution over the entire range of…

Question

Verified Solution • 2025–26 Session moderate

Liquids A and B form ideal solution over the entire range of composition. At temperature

T,

equimolar binary solution of liquids

A

and

B

has vapor pressure

45

Torr.

At the same temperature, a new solution of

A

and

B

having mole fractions

{X_A}

and

{X_B}

, respectively, has vapour pressure of

22.5

Torr.

The value of

{x_A}/{x_B}

in the new solution is ___________.

(given that the vapor pressure of pure liquid

A

is

20

Torr

at temperature

T

)

Accepted Answer

We know,

${p_{Total}} = p_A^o \times {\chi _A} + p_B^o \times {\chi _B}$

and for equimolar solutions ${\chi _A} = {\chi _B} = 1/2$

Given, ${p_{total}} = 45$ torr for equimolar solution and $p_A^o = 20$ torr

So, $45 = p_A^o \times {1 \over 2} + p_B^o \times {1 \over 2} = {1 \over 2}(p_A^o + p_B^o)$

or $p_A^o + p_B^o = 90$ torr ....... (i)

But we know $p_A^o = 20$ torr

So, $p_B^o = 90 - 20 = 70$ torr (From Eq. (i))

Now, for the new solution from the same formula

${p_{total}} = 22.5$ torr

$22.5 = 20{\chi _A} + 70(1 - {\chi _A})$ (As ${\chi _A} + {\chi _B} = 1$ )

or $22.5 = 70 - 50{\chi _A}$

So, ${\chi _A} = {{70 - 22.5} \over {50}} = 0.95$

Thus, ${\chi _B} = 1 - 0.95 = 0.05$ (as $\chi$ _A + $\chi$ _B = 1)

Hence, the ratio

${{{\chi _A}} \over {{\chi _B}}} = {{0.95} \over {0.05}} = 19$

Step-by-Step Verified Solution