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A 10% solution (by mass) of sucrose in w...

A 10% solution (by mass) of sucrose in water has a freezing point of 269.15 K. Calculate the freezing point of 10% glucose in water if the freezing point of pure water is 273.15 K. [Given : Molar mass of sucrose = 342 g `"mol"^(-1)`, Molar mass of glucose = 180 g `"mol"^(-1)` ]

Text Solution

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Molality of Glucose = `10/180 xx 1000/90`
Molality of Sucrose ` = 10/342 xx 1000/90`
` Delta T_f`(Sucrose) = 273.15 - 269.15 = 4 K
Applying the relation : `Delta T_f = K_f xx ` molality
`Delta T_f`(Glucose) ` = K_f xx `molality (Glucose) ...(1)
` Delta T_f` (Sucrose) ` = K_f xx `molality (Sucrose) ..(2)
Dividing (1) by (2), we get
` (Delta T_f ("Glucose"))/(Delta T_f ("Sucrose") ) = ("Molality (Glucose)")/("Molality (Sucrose)")`
Substituting the values, we have
`(Delta T_f ("Glucose"))/(4) = (10 xx 1000)/(180 xx 90)xx(342 xx 90)/(10 xx 1000) = 342/180`
` Delta T_f ("Glucose") = 342/180 xx 4 = 7.6`
Freezing point of Glucose solution = 273.15 - 7.6 = 265.55 K.
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