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  4. Benzene and napthalene form ideal solution over the entire range of composition. The vapour pressure of pure benzene and naphthalene at 300 K are 50.71 mm of Hg and 32.06 mm of Hg respectively. What will be the mole fraction of benzene in vapour phase if 80 g of benzene is mixed with 100 g of naphthalene?

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Q. Benzene and napthalene form ideal solution over the entire range of composition. The vapour pressure of pure benzene and naphthalene at 300 K are 50.71 mm of Hg and 32.06 mm of Hg respectively. What will be the mole fraction of benzene in vapour phase if 80 g of benzene is mixed with 100 g of naphthalene?

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Solution:

$\frac{P ^\circ _{A} X_{A}}{P ^\circ _{B} X_{B}}=\frac{X_{A}^{'}}{X_{B}^{'}}$
$\frac{50.71\left(\frac{80}{78}\right)}{32.06\left(\frac{100}{128}\right)}=\frac{\mathrm{X}_{\mathrm{A}}^{\prime}}{1-\mathrm{X}_{\mathrm{A}}{ }^{\prime}}$
$X_{A}^{'}=0.675$