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$p_A$ and $p_B$ are the vapour pressure 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
A
$p_B + x_A(p_A - p_B)$
B
$p_A + x_A(p_B - p_A)$
C
$p_A + x_A(p_A - p_B)$
D
$p_B + x_A(p_B - p_A)$
Detailed Solution
By Raoult's law, $p_{Total} = p_Ax_A + p_Bx_B$
$x_A + x_B = 1$, so $x_B = 1 - x_A$
$p_{Total} = p_Ax_A + p_B(1 - x_A)$
$p_{Total} = p_B + x_A(p_A - p_B)$
$x_A + x_B = 1$, so $x_B = 1 - x_A$
$p_{Total} = p_Ax_A + p_B(1 - x_A)$
$p_{Total} = p_B + x_A(p_A - p_B)$