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Question

Cyclohexane and ethanol at a particular temperature have vapour pressures of 280 mm Hg and 168 mm Hg respectively. If the mole fraction of cyclohexane in the solution mixture is 0.32 and the mixture is found to have a total vapour pressure of 250 mm Hg.
Which of the following is correct?

A
The solution mixture obeys Raoult's law
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B
The solution mixture shows positive deviation from Raoult's law.
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C
The solution mixture shows negative deviation from Raoult's law.
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D
Solvent-solute interaction is more than the solvent-solvent and the solute-solute interactions.
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Solution

The correct option is B The solution mixture shows positive deviation from Raoult's law.
Given,
Pure vapour pressure of cyclohexane, pA=280 mm HgPure vapour pressure of ethanol, pA=168 mm Hg

Mole fraction of cyclohexane, XA=0.32Mole fraction of ethanol, XB=10.32=0.68

By Raoult's law
Total vapour pressure of solution,
PT=XA.pA+XB.pB
PT=280×0.32+168×0.68
=203.84 mm Hg
For the solution to be an ideal one, the vapour pressure should be 203.84 mm as calculated from Raoult's law but the given value of vapour pressure is 250 mm, so the solution is not ideal. It violates the Raoult's law. Hence, it is an non-Ideal solution.
In given solution mixture,
PT>XA.pA+XB.pB
250 mm Hg>203.84 mm Hg
Thus, the given mixture shows positive deviation from the Raoult's law.
Cyclohexane-Ethanol interaction is less than the Ethanol-Ethanol and the Cyclohexane-Cyclohexane interaction.

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