Ethylene bromide `C_(2)H_(4)Br_(2)`, and 1,2 -dibromopropane,`C_(3)H_(6)Br_(2)`,form a series of ideal solutions over the whole range of composition. At `85^(@)C`, the vapour pressure of these two pure liquids are `173` and `127` torr, respectively.
. If `10.0 g` of ethylene bromide is dissolved in `80.0 g` of 1,2-dibromopropane, calculate the partial pressure of each component and teh total pressure of the solution at `85^(@)C`.
b. Calculate the mole fraction of ethylene bromide in the vapour in equilibrium with the above solution.
c. What would be the mole fraction of ethylene bromide in a solution at `85^(@)C` equilibrated with a `50 : 50` mole mixture in the vapour?

Explanation

a. Moles of `C_(2)H_(4)Br_(2)=10//188=0.0532`
Moles of `C_(3)H_(6)Br_(2) = 80//202 = 0.396`
`chi_((C_(2)H_(4)Br_(2)))=(0.0532)/(0.0532+0.396)= 0.118`
`P_((C_(2)H_(4)Br_(2))=p^(@)chi_((C_(2)H_(4)Br_(2)))`
`= 173` torr `xx 0.118 = 20.4` torr
`P_((C_(2)H_(4)Br_(2)))=p^(@)chi_((C_(2)H_(4)Br_(2))) = 127` torr `xx 0.882 = 112` torr
`P_("total") = 20.4+112 = 132.4`
b. `chi_((C_(2)H_(4)Br_(2)))^(vv) = (p_((C_(2)H_(4)Br_(2))))/(p_("total"))=20.4//132.4 = 0.155`
c. `P_(C_(2)H_(4)Br(2)) = P_(C_(3)H_(6)Br(2))`
`173chiP_(C_(2)H_(4)Br(2)) = 127chiP_(C_(3)H_(6)Br(2))`
`=127(1-chi_(C_(3)H_(6)Br(2))`
`173chi = 127 (1 - chi)`
`300chi =127 rArr chi 0.423`.