Question

What is the lowest freezing temperature for a saltwater solution? The solubility of sodium chloride (NaCl) is 280g per 1000g of water at 0°C. kf of H2O = 1.86°C/m.

Answer 1

M(NaCl) = 58.44 g/mol

n(NaCl) $= \frac{280}{58.44} = 4.79 \;mol$

Molality $m = \frac{4.79}{1 \; kg} = 4.79 \;m$

Dissociation of NaCl is

NaCl → Na⁺ + Cl^-

i = 2 (one mole of Na⁺ and one mole of Cl^-)

$ΔT_f = i \times k_f \times m \\ = 2 \times 1.86 \times 4.79 \\ = 17.82 \; °C \\ ΔT_f = T_f^0 -T_f(sol) \\ T_f(sol) = T_f^0 -ΔT_f \\ = 0 -17.82 \\ = -17.82 \; °C$

Answer: -17.82 °C