Question

Consider the following partially labelled figure for an ideal binary solution of benzene and toluene and answer the following questions:
The composition of the liquid for which the vapour contains equal number of benzene and toluene molecules is about:

• A. $X_{\text{toluene}}=0.75$
• B. $X_{\text{toluene}}=0.50$
• C. $X_{\text{toluene}}=0.40$
• D. $X_{\text{toluene}}=0.90$

Answer 1

The correct option is A $X_{\text{toluene}}=0.75$

We know the $P_B^0=100mmHg$ and $P_T^0=30mmHg$
Let's say for mole fraction of benzene equal to $x_b$, partial pressure of both benzene and toluene are equal
$P_B^0{x}_b=P_T^0(1-x_b)$
$100\left(x_b\right)=30(1-x_b)$
$\therefore x_b=0.23$
Hence $x_t=1-0.23=0.77$ so approximately 0.75