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31 g of ethylene glycol (C(2)H(6)O(2)) i...

31 g of ethylene glycol `(C_(2)H_(6)O_(2))` is mixed with 500 g of solvent (`K_(f)` of the solvent is 2 K `kg mol^(-1)`). What is the freezing point of the solution (in K) ? (Freezing point of solvent = 273 K)

A

272

B

271

C

270

D

274

Text Solution

Verified by Experts

The correct Answer is:
B
Given, `W_(B)` = mass os solute (ethylene glycol) = 31 g
`W_(A)` = mass of solvent = 500 g
`M_(B)` = Ethylene glycol `(C_(2)H_(6)O_(2))`
`= (2 xx 12 + 6 + 2 xx 16) = 62 g`
`K_(f) = 2 K kg mol^(-1)`
`Delta T_(f) = K_(f) (W_(B))/(M_(B)) xx (1000)/(W_(A))`
`Delta T_(f) = (2 xx 31 xx 1000)/(62 xx 500) = 2K`
`because Delta T_(f) = T_(f)^(@) - T_(f)`
`T_(f) = T_(f)^(@) - 2`
(`because` Depression in freezing point = 2K)
`therefore T_(f) = 273 - 2 = 271 K`
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