Question

A sample of sea water taken from the Atlantic ocean freezes at -2.14 degree Celsius and a sample taken from the Arctic ocean freezes at -1.96 degree Celsius. What is the molality of salt in each seawater sample? (Assume the only solute in each sample is sodium chloride)

Answer 1

Answer:

(a) 0.575 m;

(b) 0.527 m

Explanation:

Let's use the freezing point depression law in each of these cases.

(a) According to the law:

$\Delta T_f = iK_fb$

Rearrange the equation for molality, b:

$b = \frac{\Delta T_f}{iK_f}$

NaCl is an ionic substance, 1 mole of it dissociates into 2 moles of ions, sodium ion and chloride ion, this means the van 't Hoff factor i = 2.

$\Delta T_f = T_o - T_n$

Here:

$T_o = 0.00^oC$ is the initial freezing point of water,

$T_n = -2.14^oC$ is the final freezing point of water.

For water:

$K_f = 1.86^oC/m$

Applying the equation

$b = \frac{2.14^oC}{2\cdot 1.86^oC/m} = 0.575 m$

(b) Applying the same equation for the same salt and the same conditions, except a new freezing point, we would expect to obtain:

$b = \frac{1.96^oC}{2\cdot 1.86^oC/m} = 0.527 m$