Question

Ishan’s automobile radiator is filled with 1.0 kg of water. How many grams of ethylene glycol (Molar mass = 62 g mol⁻¹) must Ishan add to get the freezing point of the solution lowered to −2.8°C. K_f for water is 1.86 K kg mol⁻¹.

Answer 1

Given: Amount of water = 1.0 kg

Molar mass of ethylene glycol = 62 g mol⁻¹

K_f for water = 1.86 K kg mol⁻¹

Lowering of freezing point of the solution = −2.8°C

Mass of solute (w) = ?

ΔT_f = 0 − (−2.8) = 2.8°C 

Molality, m = `(("Weight of solute")/("Molecular mass of solute"/"Mass of solvent (g)")) xx 1000` 

`m = (w//62)/1000 xx 1000`

= `w/62`

Now, ΔT_f = K_f × m

`2.8 = 1.86 xx w/62`

⇒ `w = (62 xx 2.8)/1.86`

= 93.3 ≈ 93 g