The normal boiling point of diethyl ether is 34.5 degrees C. A solution containing a nonvolatile solute dissolved in diethyl ether has a vapor pressure of 675 torr at 34.5 degrees C. What is the mole fraction of diethyl ether in the solution?
Solution-
Total pressure of the system ( room temperature pressure)= 760 mmHg
Since normal boiling point of ether is 34.5 oC.
The vapour pressure of diethyl ether must equal to that of the total pressure.
Hence Vapour pressure of diethyl ether = 760 mmHg
Now when a non-volatile solute is now added, the vapour pressure of ether has went down
Vapour pressure of ether after addition of non volatile solute
Here now we apply roults law
YiPt=P = Xi Psat
here P= partial pressure of the solution
Xi = the mole fraction in liquid state
Psat is the vapour pressure of the pure solvent.
From the question
P = 675 Torr, Psat = 760 Torr
substituting this in the above equation,
675 = Xi*760
Xi =0.89
Therefore, mole fraction of diethyl = 0.89
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