Question

A common antifreeze for car radiators is ethylene glycol, CH2(OH )CH2(OH ). How many millilite~s of this substance would you add to 6.5 L of water 1n the radiator if the coldest day in winter is - 20°C? Would you keep this substance in the radiator in the summer to prevent the water from boiling? (The density and boiling point of ethylene glycol are 1.11 g cm^-3 and 470 K repsectively.)

Answer 1

Explanation:

It is given that volume of water is 6.5 L. Therefore, mass of water present in 1 kg/L will be calculated as follows.

                  $6.5 L \times 1 kg/L$ = 6.5 kg

As 1000 grams are present in 1 kg. So, 6.5 kg equals 6500 grams.

$K_{f}$ of water is 1.86 K kg/mol. And, $\Delta T = -20^{0}C$

Let the weight of glycol is x.

It is known that $\Delta T_{f} = K_{f} \times molality$

Molar mass of ethylene glycol is 62 g/mol.

Hence, putting values in the above formula as follows.

                $\Delta T_{f} = K_{f} \times molality$

                  20 = $1.86 K kg/mol \times \frac{x \times 1000}{62 \times 6500}$

                    x = 4333 g

As density equals mass present in per unit volume. Therefre, calculate the density as follows.

                 Density = $\frac{mass}{volume}$

                 volume = $\frac{mass}{density}$

                               = $\frac{4333 g}{1.11 g cm^{-3}}$

                               = 3903.60 $cm^{-3}$

                               = 3903 mL

The presence of solute will help in elevating the boiling point of solvent. Hence, theoretically it is possible to keep this substance in car radiator also in summer.

Whereas it is not necessary to add this glycol to water in summers as temperature does not reach the boiling point of water which is 373 K.