Question

A liquid mixture of benzene ($B$) and toluene ($T$) contains 1 mole each of $B$ and $T$. If $P_T^o=4.274kN{m}^{-2}$ and $P_B^o=13.734kN{m}^{-2}$.

What is the mole fraction of the last trace of liquid $B$ (write the integer part)?

Answer 1

1 mole each of $B$ and $T$ is present.
The mole fraction of $B$ is $\frac{1}{1+1}=0.5$.
The mole fraction of $T$ is $1-0.5=0.5$.
The partial pressure of $B$ is $P_B=X_B{P}_B^0=0.5\times 13.734kN{m}^{-2}=6.867kN{m}^{-2}$.
The partial pressure of $T$ is $P_T=X_T{P}_T^0=0.5\times 4.274kN{m}^{-2}=2.137kN{m}^{-2}$.
The total pressure is $P=P_B+P_T=6.867kN{m}^{-2}+2.137kN{m}^{-2}=9.004kN{m}^{-2}$.

The mole fraction of B in the last trace of vapor formed is $Y_B=\frac{P_B}{P}=\frac{6.867kN{m}^{-2}}{9.004kN{m}^{-2}}=0.7627$
The mole fraction of T in the last trace of vapor formed is $=1-0.7627=0.2373$