The vaporu pressures of chloroform `(CHCl_(3))` , dichloromethane `(CH_(2)Cl_(2))` at 298 K are 200 mm Hg and 415 mm Hg respectivley. An ideal solutions in prepared by mixing 59.75 g of `CHCl_(3) ` and 21 . 25 g of `CH_(2) Cl_(2)` , the mole fractions of chloroform and dichloromethane in vapour phase respectively are

Options

A. 0 . 509, 0.491
B. 0.491, 0.509
C. 0.201, 0.799
D. 0.799, 0.201

Answer

B

Explanation

Given,
Mass of `CHCl_(3) = 59.75 g`
Molar mass of `CHCl_(3) = 12 xx 1+ 1xx 1 + 35 . 5 xx 3 `
` = 119.5 g mol^(-1)`
`:.` Moles of `CHCl_(3) = (59.75g)/(119.5 g mol^(-1)) = 0 . 5 mol`
Given, mass of `CH_(2)Cl_(2) = 21.25 g`
Molar mass of `CH_(2) Cl_(2) = 12xx 1 + 2 xx 1 35 . 5 xx 2 `
`= 85 g mol^(-1)`
`:.` Moles of `CH_(2) Cl_(2) = (21 . 25 g)/( 85 g mol^(-1))`
= 0 . 25 mol
Total moles = 0 . 5 + 0.25 = 0 . 75 mol
`X _(CH_(2) Cl_(2) = (0.25)/(0.75) =0 . 33 `
`X_(CHCl_(3)= 1 - 0.33 =0 63 `
`:. p_("total") = p_(I)^(@) + (p_(2)^(@) - p_(1)^(@))x_(2)`
` = 200 + (415 - 200) xx 0 . 33`
`:. p_("total") = 270 .95 m m Hg `
Now, ` p_(CH_(2)Cl_(2))=0 . 33 xx 415 m m Hg `
`p_(CHCl_(3) = 0 . 67 xx 200 = 134 m m Hg `
`:.` (mole fraction in vapour phase)
`y_(i) = p_(i) //p_("total")`
`:. y_(CH_(2) Cl_(2))=(136.95 m m Hg)/(270 . 95 m m Hg) = 0 . 505`
and `y_(CHCl_(3))=(134 m m Hg)/(270 . 95 m m Hg) = 0 . 494`