Question

C2H6O2 is infinitely miscible (soluble) in water. Ethylene Glycol is a noneletrolyte that is used as antifreeze. What is the lowest possible melting point for engine coolant that is 21.7% (by mass) ethylene glycol ?

Kf for H2O is 1.86 degrees c/m

Answer 1

Step-by-step explanation:

As it is assumed that we are given 100 g of solution.

Therefore, mass of ethylene glycol is as follows.

`(21.7)/(100) * 100`

= 21.7 g

Now, number of moles of ethylene glycol is calculated as follows.

No. moles of ethylene glycol =
`\frac{mass}{\text{molar mass}}`

=
`(21.7 g)/(62.07 g/mol)`

= 0.349 mol

Hence, mass of water = (100 - 21.7) g = 78.3 g

= 0.783 kg (a 1 kg = 100 g)

As, molality is number of moles present in kg of solvent.

So, Molality =
`\frac{\text{no. of moles of ethylene glycol}}{\text{mass of water in kg}}`

=
`(0.349 mol)/(0.783)`

= 0.445 m

Melting point depression (
`\Delta T_(f)`) =
`K_(f) * molality`

=
`1.86 ^(o)C/m * 0.445 m`

=
`0.828^(o)C`

Therefore, melting point of solution will be calculated as follows.

Melting point of solution = Melting point of water -
`\Delta T_(f)`

=
`(0.00 - 0.828)^(o)C`

=
`-0.828^(o)C`

Thus, we can conclude that the lowest possible melting point for given engine coolant is
`-0.828^(o)C`.