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

(a) 0.575 m;

(b) 0.527 m

Step-by-step 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 = (\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 = (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 = (1.96^oC)/(2\cdot 1.86^oC/m) = 0.527 m`