GeoWiki.png
ChemWiki: The Dynamic Chemistry E-textbook > Physical Chemistry > Physical Properties of Matter > Solutions and Mixtures > Colligative Properties > Freezing Point Depression

Freezing Point Depression

Table of Contents

Nonelectrolytes are substances with no ions, only molecules. Strong electrolytes, on the other hand, are composed mostly of ionic compounds, and essentially all soluble ionic compounds form electrolytes. Therefore, if we can establish that the substance that we are working with is uniform and is not ionic, it is safe to assume that we are working with a nonelectrolyte, and we may attempt to solve this problem using our formulas. This will most likely be the case for all problems you encounter related to freezing point depression and boiling point elevation in this course, but it is a good idea to keep an eye out for ions. It is worth mentioning that these equations work for both volatile and nonvolatile solutions. This means that for the sake of determining freezing point depression or boiling point elevation, the vapor pressure does not effect the change in temperature. Also remember that a pure solvent is a solution that has had nothing extra added to it or dissolved in it. We will be comparing the properties of that pure solvent with its new properties when added to a solution.

Introduction

The universe is always spontaneously undergoing disorder. Matter will always go to its most stable state and thus result in increasing disorder. Similarly, adding solutes to an ideal solution results in a positive ΔS, an increase in entropy. Because of this, the newly altered solution’s chemical and physical properties will also change. The properties that undergo changes due to the addition of solutes to a solvent are known as colligative properties. These properties are dependent on the amount of solutes added, not on their identity. Two examples of colligative properties are boiling point and freezing point: due to the addition of solutes, the boiling point tends to increase and freezing point tends to decrease.

The freezing point and boiling point of a pure solvent can be changed when added to a solution. When this occurs, the freezing point of the pure solvent may become lower, and the boiling point may become higher. The extent to which these changes occur can be found using the formulas:

\(\Delta{T}_f = -K_f \times m\)

\(\Delta{b}_f = -K_b \times m\)

where m is the solute molality, and the K values are proportionality constants.

If solving for the proportionality constant is not the ultimate goal of the problem, these values will most likely be given. Some common values for \(K_f\) and \(K_b\), respectively, are:

  • Water: 1.86, .512
  • Acetic acid: 3.90, 3.07
  • Benzene: 5.12, 2.53
  • Phenol: 7.27, 3.56

Molality is defined as the number of moles of solute per kilogram solvent. Be careful not to use the mass of the entire solution. Often, the problem will give you the change in temperature and the proportionality constant, and you must find the molality first in order to get your final answer.

The solute, in order for it to exert any change on colligative properties, must fulfill two conditions. First, it must not contribute in the vapor pressure of the solution and second, it must remain suspended in the solution even during phase changes. Because the solvent is no longer pure with the addition of solutes, we can say that the chemical potential of the solvent is lower. Chemical potential is the molar Gibb's energy that one mole of solvent is able to contribute to a mixture. The higher the chemical potential of a solvent is, the more it is able to drive the reaction forward. Consequently, solvents with higher chemical potentials will also have higher vapor pressures.

Entropy.JPG

Boiling point is reached when the chemical potential of the pure solvent, a liquid, reaches that of the chemical potential of pure vapor. Because of the decrease of the chemical potential of mixed solvents and solutes, we observe this intersection at higher temperatures. In other words, the boiling point of the impure solvent will be at a higher temperature than that of the pure liquid solvent. Thus, boiling point elevation occurs. The increase in temperature is quantified using ΔTb = KbbB where Kb is known as the ebullioscopic constant and bB is the molality of the solute.

Freezing point is reached when the chemical potential of the pure liquid solvent reaches that of the pure solid solvent. Again, since we are dealing with mixtures with decreased chemical potential, we expect the freezing point to change. Unlike the boiling point, the chemical potential of the impure solvent requires a colder temperature for it to reach the chemical potential of the solid pure solvent. Therefore, we observe a freezing point depression. We measure the change in the freezing point temperature using ΔTf =KfbB where Kf is known as the cryoscopic constant and bB is again the molality of the solute.

colligative properties.JPG

Example  

2.00 g of some unknown compound reduces the freezing point of 75.00 g of benzene from 5.53 to 4.90 \(^{\circ}C\). What is the molar mass of the compound?

Solution: First we must compute the molality of the benzene solution, which will allow us to find the number of moles of solute dissolved.

\(m = \dfrac{\Delta{T}_f}{-K_f}\) 

\(m = \dfrac{(4.90 - 5.53)^{\circ}C}{-5.12^{\circ}C / m}\) 

\(= 0.123 m\)

\(Amount \; Solute = 0.07500 \; kg \; benzene \times \dfrac{0.123 \; m}{1 \; kg \; benzene}\)

\(= 0.00923 \; m \; solute\)

We can now find the molecular weight of the unknown compound:

\(Molecular \; Weight = \dfrac{2.00 \; g \; unknown}{0.00923 \; mol}\)

\(= 216.80 \; g/mol\)

The freezing point depression is especially vital to aquatic life. Since saltwater will freeze at colder temperatures, organisms can survive in these bodies of water.


References:

  1. Atkins, Peter and de Paula, Julio. Physical Chemistry for the Life Sciences. New York, N.Y.: W. H. Freeman Company, 2006. (124-136).

Contributors

  • Lorigail Echipare (UCD), Zachary Harju (UCD)

You must to post a comment.
Last Modified
09:34, 2 Oct 2013

Page Rating

Was this article helpful?

Tags

Module Vet Level:
Module Target Level:

Creative Commons License UC Davis GeoWiki by University of California, Davis is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License. Permissions beyond the scope of this license may be available at copyright@ucdavis.edu. Terms of Use