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प्रश्न
Obtain the relationship between freezing point depression of a solution containing nonvolatile-nonelectrolyte solute and its molar mass.
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उत्तर
1. The freezing point depression (ΔTf) is directly proportional to the molality of solution.
Thus, ΔTf = Kf m ….(1)
2. Suppose we prepare a solution by dissolving W2 g of solute in W1 g of solvent.
Moles of solute in W1 g of solvent = `"W"_2/"M"_2`
where, M2 is the molar mass of solute.
Mass of solvent = W1 g = `("W"_1 g)/(100 "g"//"kg") = "W"_1/1000` kg
3. The molality is expressed as,
m = `"Moles of solute"/"Mass of solvent in kg"`
m = `("W"_2//"M"_2 "mol")/("W"_1//1000 "kg")`
m = `(1000 "W"_2)/("M"_2 "W"_1) "mol kg"^-1` ....(2)
4. Substituting equation (2) in equation (1), we get,
`triangle "T"_"f" = (1000 "K"_"f" "W"_2)/("M"_2 "W"_1)`
Hence,
`"M"_2 = (1000 "K"_"f" "W"_2)/(triangle "T"_"f" "W"_1)`
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