Question

For an ideal binary liquid solution with $P _{ A }^{0}> P _{ B }^{ o },$ which relation between $X_{A}$ (mole fraction of $A$ in liquid phase $)$ and $Y_{A}$ (mole fraction of A in vapour phase) is correct?

• A. $Y_{A}=Y_{B}$
• B. $\frac{Y_{A}}{Y_{B}}=\frac{X_{A}}{X_{B}}$
• C. $\frac{Y_{A}}{Y_{B}}>\frac{X_{A}}{X_{B}}$
• D. $\frac{Y_{A}}{Y_{B}}<\frac{X_{A}}{X_{B}}$

Answer 1

Answer: (C)

$P _{ A }= P _{ A }^{0} X _{ A }$ (Raoult's law)

$P _{ A }= P _{\text {total }} Y _{ A }$ (Daltons law)

$\therefore P _{ A }^{0} X _{ A }= P _{\text {total }} Y _{ A }$

$P_{A}^{0}=\frac{P_{\text {total }} Y_{A}}{X_{A}} \ldots \ldots$(1)

(2) Similarly, $P _{ B }^{0}=\frac{ P _{\text {total }} Y _{ B }}{ X _{ B }} \ldots \ldots$(2)

Now, $P_A^0 > P_B^0$

$\therefore P_{\text {Total }} \frac{Y_{A}}{X_{A}}>P_{\text {Total }} \frac{Y_{B}}{X_{B}}$

$\frac{Y_{A}}{X_{A}}>\frac{Y_{B}}{X_{B}}$