Question

Calculate the mass of sodium chloride that must be added per kilogram of ice so that it melts at –5°C.
The degree of salt dissociation in this solution is 90%.

Answer 1

Given :

ΔTf = 5°C

α = 90% = 0.9

To Find :

Mass of NaCl, i.e., w

Calculation :

- We know that for dissociation of NaCl, n = 2, M.wt. = 58.5 gm and

α = (i - 1) / (n - 1)

⇒ 0.9 = (i - 1) / (2 - 1)

⇒ i = 0.9 + 1 = 1.9

- Molality, m = No.of moles / weight in kg

⇒ m = w / M.wt.  ( as W = 1 kg)

⇒ m = w / 58.5

- We know that Kf = 1.86

So, ΔTf = i × Kf × m

⇒ 5 = 1.9 × 1.86 × w / 58.5

⇒ 5 × 58.5= 3.534 × w

⇒ w = 292.5 / 3.534

⇒ w = 82.767 gm

⇒ w ≈ 83 gm

- So, 83 gm of NaCl is required per kilogram.