Question

A pure sample of the solvent phenol has a freezing point of $ {{40}}{{.85^\circ C}} $ . A $ {{0}}{{.414}} $ molal solution of isopropyl alcohol in phenol was observed to have a freezing point of $ {{38}}{{.02^\circ C}} $ . What is the freezing point depression of this solution?

Answer 1

Hint: In the above question, the freezing point of phenol is given. A $ {{0}}{{.414}} $ molal solution of isopropyl alcohol is added whose freezing point is also given. We have to find out the freezing point of depression. Freezing point depression results in decrease in freezing point of solvent when some solute is added. We shall use the formula given below.

Formula used:
 $ {{\Delta }}{{{T}}_{{f}}}{{ = }}{{{K}}_{{f}}}{{bi}} $
where $ {{\Delta }}{{{T}}_{{f}}} $ = freezing point depression
 $ {{{K}}_{{f}}} $ = cryoscopic constant
b= molality
i= van’t Hoff factor.

Complete step by step solution:
Freezing-point depression can be defined as the decrease of the freezing point of a solvent on the addition of a non-volatile solute. For example, salt in water, alcohol in water.
Now, let us calculate freezing point depression using the formula $ {{\Delta }}{{{T}}_{{f}}}{{ = }}{{{K}}_{{f}}}{{bi}} $
Here $ {{{K}}_{{f}}} $ is a cryoscopic constant which is dependent on properties of solvent but not on solute. So, $ {{{K}}_{{f}}} $ of phenol is $ {{7}}{{.27KMola}}{{{l}}^{{{ - 1}}}} $
b is molality of the solute which is given as $ 0.414 $ molal.
i is the van’t Hoff factor which indicates the number of ions formed when the alcohol dissociates. Since, alcohol does not dissociate to form ions hence, i=1. So, by substituting the values we get:
 $ {{\Delta }}{{{T}}_{{f}}}{{ = }}{{{K}}_{{f}}}{{bi = 7}}{{.27 \times 0}}{{.414 \times 1 = 3}}{{.009}} $ K.
Hence, freezing point depression is $ {{3}}{{.01}} $ K.

Note:
Freezing point depression has many practical uses. The radiator fluid in an automobile is a mixture of water and ethylene glycol. The freezing-point depression prevents radiators from freezing in winter.
Freezing-point depression is used by some organisms that live in extreme cold. Such creatures have evolved means through which they can produce a high concentration of various compounds such as sorbitol and glycerol.