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Ethylene glyed (EG),CH(2)(OH)CH(2)(OH), ...

Ethylene glyed `(EG),CH_(2)(OH)CH_(2)(OH)`, is a common automobile antifreeze. It is water solube and fairly nonvolatile `(bp 197^(@)C)`. The freezing point of a solution containing `651 g` of this substance in `2505 g` of water is

A

`-7.79^(@)C`

B

`7.79^(@)C`

C

`9.77^(@)C`

D

`-9.77^(@)C`

Text Solution

Verified by Experts

The correct Answer is:
1
Use `DeltaT_(f)=K_(f)m` to solve the problem. Molality (m) is the number of moles of ethylene glycol in `1000g (or 1 kg)` of water.
`n_(EG)=(mass_(EG))/(molar mass_(EG))`
`=(651 g EG)/(62 g mol^(-1)EG)`
`=10.5 mol`
`Molality(m)=n_(EG)/g_(solvent)xx(1000 g)/(kg)`
`=(10.5 mol)/(2505 g)xx(1000 g)/(kg)`
`=4.19 mol Kg^(-1)`
`DeltaT_(f)=K_(f)m`
`=(1.86^(@)C//m)(4.19 m)`
`=7.79^(@)C`
Since pure water freezes at `0^(@)C`, the solution will freeze at `-7.79^(@)C`
Note that we also keep this substance in our car rediator during the summer because
`DeltaT_(b)=K_(b)m`
`=(1.86^(@)C//m)(4.19 m)`
`=2.2^(@)C`
i.e., it would be preferable to leave the antifreeze in car radiator in summer to prevent the solution from boiling because the solution will boil at `102.2^(@)C`.
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