Question

If $x_{1}$ and $x_{2}$ represent the mole fractions of a component A in the vapour phase and liquid mixture respectively and $p_{A}^{o}$ and $p_{B}^{o}$ represent vapour pressure of pure A and B, then total vapour pressure of liquid mixture is

• A. $\frac{p_{A}^{o} x_{1}}{x_{2}}$
• B. $\frac{p_{A}^{o} x_{2}}{x_{1}}$
• C. $\frac{p_{B}^{o} x_{1}}{x_{2}}$
• D. $\frac{p_{B}^{o} x_{2}}{x_{1}}$

Answer 1

Answer: (B)

According to Dalton's law of partial pressures of gases,
$\frac{p_{A}}{p_{T o t a l}}=x_{1}$
$p_{A}=x_{1}p_{t o t a l}$ ...(i)
and according to Raoult's law
$p_{A}=p_{A}^{o}x_{2}$ ...(ii)
Now by equating (i) and (ii), we get
$p_{T o t a l}x_{1}=p_{A}^{o}x_{2}$
$p_{T o t a l}=\frac{p_{A}^{o} x_{2}}{x_{1}}$