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Question
The degree of dissociation of Ca(NO3)2 in a dilute aqueous solution containing 7 g of the salt per 100 g of water at 100°C is 70%. If the vapour pressure of water at 100°C is 760 mm. The vapour pressure of the solution is ______ mm.
Options
538.97
675.56
746.10
823.12
Solution
The degree of dissociation of Ca(NO3)2 in a dilute aqueous solution containing 7 g of the salt per 100 g of water at 100°C is 70%. If the vapour pressure of water at 100°C is 760 mm. The vapour pressure of the solution is 746.10 mm.
Explanation:
The molar mass of calcium nitrate is 164 g/mol.
7 g of calcium nitrate = `7/164` = 0.0427
The molar mass of water is 18 g/mol.
100 g of water = `100/18` = 5.56 moles
The mole fraction of calcium nitrate = X = `0.0427/(0.0427 + 5.56)` = 0.00762
The degree of dissociation α = 70% = 0.7
The van't Hoff factor i = [1 + (n − 1)α]
i = [1 + (3 − 1) × 0.7]
i = 2.4
The relative lowering of the vapour pressure
`("P"^0 - "P")/("P"^0)` = iX
`(760 - "P")/760` = 2.4 × 0.00762
`(760 - "P")/760` = 0.018
760 − P = 0.018 × 760
760 − P = 13.9
P = 746.10 mm
