Question

4. On the night of the sinking of the Titanic, the ocean water was around 1°C, roughly the temperature at which oceanic water freezes. Given that the freezing point depression is 2°C, approximately how many grams of sodium chloride are there in 1 kg of ocean water, considering the ocean consists of primarily sodium ions, chloride ions and water? a)15.8 b)18.4 c) 23.9 d) 27.1 e) 31.5

Answer 1

Depression in freezing point, $\Delta T_{f} = i K_{f} m$

where, i = van't Hoff factor = 2 for NaCl

   $\Delta T_{f}$ = depression in freezing point = 2^oC

m= molality , K_f = molal depression constant = 1.86 ^oC m

Thus, m =    $\Delta T_{f} / i K_{_{f}}$   = 2^oC / (2 x 1.86 ^oC m) = 0.5376 m

we know that, m = mass of solute /(molar mass of solute ) x ( kg of solvent)

or mass of solute = m x (molar mass of solute ) x ( kg of solvent) =(0.5376 x 58.5 x 1) gm = 31.449 $\approx$ 31.5 gm