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Question

The total vapour pressure of a 4 mole % solution of ammonia in water at 293 K is 50.0 torr; the vapour pressure of pure water is 17.0 torr at this temperature. Applying Henry's and Raoult's laws, the total vapour pressure for a 5 mole % solution is (in torr).

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Solution

The given data is
Powater=17.0 torr;
Ptotal(4 mole % solution) = PNH3+Pwater =50.0 torr
xNH3 = 0.04 and ;xwater= 0.96
Now according to Raoult's law;
Pwater=xwater P0water
= 0.96 ×17.0 torr = 16.32 torr, Pammonia=33.68 torr
Now Henry's law constant for ammonia is
KH(NH3)=PNH3xNH3 =842 torr
Hence, for 5 mole % solution, we have PNH3 =KH (NH3) xNH3
= (842 torr) (0.05) = 42.1 torr
Pwater=xwater P0water = (17 torr) (0.95) =16.15 torr
Thus, Ptotal (5 mole % solution) = PNH3+ Pwater = 42.1 + 16.15= 58.25 torr


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