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 $\left(P\right)$ of the solution will be:

• A. $p_A+x_A(p_B-p_A)$
• B. $p_A+x_A(p_B-p_A)$
• 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 $p_B+x_A(p_A-p_B)$

Accordung to Raoult's law,
$P=x_A{p}_A+x_B{p}_B...\left(i\right)$
For binary solution,
$x_A+x_B=1$
$x_B=1-x_A...\left(ii\right)$
Putting the values of $x_B$ from equation $\left(ii\right)$ into equation $\left(i\right)$, we get
$P=x_A{p}_A(1-x_A)p_B=x_A{p}_A+p_B-x_A{p}_B$
$P=p_B+x_A(p_A-p_B)$