$\mathrm{P}_{\mathrm{A}}$ and $\mathrm{P}_{\mathrm{B}}$ are the vapour pressure of pure liquid components,…

$\mathrm{P}_{\mathrm{A}}$ and $\mathrm{P}_{\mathrm{B}}$ are the vapour pressure of pure liquid components, $\mathrm{A}$ and $\mathrm{B}$, respectively of an ideal binary solution. If $X_{A}$ represents the mole fraction of component $\mathrm{A}$, the total pressure of the solution will be.
  1. $\mathrm{P}_{\mathrm{A}}+\mathrm{X}_{\mathrm{A}}\left(\mathrm{P}_{\mathrm{B}}-\mathrm{P}_{\mathrm{A}}ight)$
  2. $\mathrm{P}_{\mathrm{A}}+\mathrm{X}_{\mathrm{A}}\left(\mathrm{P}_{\mathrm{A}}-\mathrm{P}_{\mathrm{B}}ight)$
  3. $\mathrm{P}_{\mathrm{B}}+\mathrm{X}_{\mathrm{A}}\left(\mathrm{P}_{\mathrm{B}}-\mathrm{P}_{\mathrm{A}}ight)$
  4. $\mathrm{P}_{\mathrm{B}}+\mathrm{X}_{\mathrm{A}}\left(\mathrm{P}_{\mathrm{A}}-\mathrm{P}_{\mathrm{B}}ight)$

Solution

$\mathrm{P}=\mathrm{P}_{\mathrm{A}} \mathrm{X}_{\mathrm{A}}+\mathrm{P}_{\mathrm{B}} \mathrm{X}_{\mathrm{B}}$
$=\mathrm{P}_{\mathrm{A}} \mathrm{X}_{\mathrm{A}}+\mathrm{P}_{\mathrm{B}}\left(1-\mathrm{X}_{\mathrm{A}}ight)$
$\Rightarrow \quad \mathrm{P}_{\mathrm{A}} \mathrm{X}_{\mathrm{A}}+\mathrm{P}_{\mathrm{B}}-\mathrm{P}_{\mathrm{B}} \mathrm{X}_{\mathrm{A}}$
$\Rightarrow \quad \mathrm{P}_{\mathrm{B}}+\mathrm{X}_{\mathrm{A}}\left(\mathrm{P}_{\mathrm{A}}-\mathrm{P}_{\mathrm{B}}ight)$ .

Asked in: JEE-TOPICTESTS-CHEMISTRY

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