Question

$p_A$ and $p_B$ are the vapour pressure of pure liquid components, A and B respectively of an ideal binary solution. If ${\chi }_A$ represents the mole fraction of component A, the total pressure of the solution will be

• A. $p_B+{\chi }_A(p_A-p_B)$
• B. $p_A+{\chi }_A(p_A-p_B)$
• C. $p_B+{\chi }_A(p_B-p_A)$
• D. $p_A+{\chi }_A(p_B-p_A)$

Answer 1

The correct option is A $p_B+{\chi }_A(p_A-p_B)$

By Raoult's Law :
$P_T=p_A{\chi }_1+p_B{\chi }_2......eqn\left(1\right)$
where
$P_T$ is the total pressure of the solution.
$p_A$ is the vapour pressure of pure component A
$p_B$ is the vapour pressure of pure component B
${\chi }_A$ is the mole fraction of component A in liquid phase.
${\chi }_B$ is the mole fraction of component B in liquid phase.

For binary solution,
${\chi }_A+{\chi }_B=1$
${\chi }_b=1-{\chi }_A$

$\therefore$
$P_T=p_A{\chi }_A+(1-{\chi }_A)p_B$
$P_T=p_A{\chi }_A+p_B-{\chi }_A{p}_B$
$P_T=p_B+{\chi }_A(p_A-p_B)$

Hence, option (d) is correct.