Question

$P_A$ and $P_B$ are the vapour pressures of pure liquid components, $A$ and $B$, respectively of an ideal binary solution. If $x_A$ represents the mole fraction of component $A$, the total pressure of the solution will be:
[1 mark]

• A. $P_A+x_A(P_B-P_A)$
• B. $P_A+x_A(P_A-P_B)$
• C. $P_B+x_A(P_B-P_A)$
• D. $P_B+x_A(P_A-P_B)$

Answer 1

The correct option is D $P_B+x_A(P_A-P_B)$

According to Raoult's law,
$P_{\text{Total}}=x_A{P}_A+x_B{P}_B$
Where, $x_A$ and $x_B$ are the mole fractions of components $A$ and $B$ in solution.
For binary solutions,
$x_A+x_B=1,\Rightarrow x_B=1-x_A$
Putting value of $x_B$
$P=x_A{P}_A+(1-x_A)P_B=x_A{P}_A+P_B-x_A{P}_B$
$=P_B+x_A(P_A-P_B)$