Certain properties of a solution differ from those of a pure solvent due to interactions that take place between the solute and solvent molecules. The properties that exhibit such changes are called the colligative properties and include vapor-pressure lowering, boiling-point elevation, freezing-point depression, and changes in osmotic pressure. These properties are dependent only upon the number of particles dissolved in the solvent, not on the identity of the particles. A particle, in this instance, is defined as an ion or a molecule. This experiment focuses on the property of freezing-point depression.

When a particular solute is dissolved in a solvent, the following expression holds true:

ΔT = T_f° - T_f = K_fm

The terms T_f° and T_f refer to the freezing-point temperatures of the pure solvent and the solution, respectively. The term "m" indicates the molality of the solution, which is defined as the number of moles of solute per 1,000 g of solvent. This quantity is used, rather than molarity, because it is not temperature dependent. The constant, K_f, is referred to as the freezing-point-depression constantand is dependent only upon the solvent. The change in temperature is also dependent upon the number of solute particles in solution - the more particles present, the larger the change in temperature. For this reason, the previous equation is sometimes written as:

T_f° - T_f = K_fim

where i = the number of solute particles produced per formula unit that dissolves. In a solution containing an electrolyte, each ion is considered to be a particle.

This experiment uses cyclohexane, an organic compound that is a liquid at room temperature, as the solvent. The unknown compound is a non-ionic organic molecule; therefore, i is equal to 1. The molecular weight of this unknown compound can be determined by observing the freezing point of a solution of the compound in cyclohexane and comparing it to the freezing point of pure cyclohexane.

The compound cyclohexane has a melting point (or freezing point) of about 6 °C. A series of temperatures of pure cyclohexane are obtained as it cools down from room temperature through its freezing point in an ice bath. These temperatures are then plotted as a function of time. Similarly, temperatures of a solution of the unknown compound dissolved in cyclohexane are obtained as it cools down to the freezing point, which are also plotted. The plots should look similar to the plots in Figure 1. The T_f° and T_f values can be extrapolated, as shown. In Figure 1b, the temperature does not remain entirely constant as the solution freezes. The freezing point of the solution is the point at which it first begins to freeze and is indicated graphically by a change in the slope of the temperature-time curve.

The molality, m, of a solution can be expressed in terms of the molar mass of the solute:

Substituting this expression into the equation for freezing-point depression (where i = 1), obtains:

Rearranging to solve for molar mass, obtains:

The molecular weight (in amu) of a substance has the same numerical value as its molar mass.

The unknown substance is one of the following compounds:

• Biphenyl (C₁₂H₁₀)
• 2-Bromochlorobenzene (C₆H₄BrCl)
• Naphthalene (C₁₀H₈)
• Anthracene (C₁₄H₁₀)
• 1,4-Dibromobenzene (C₆H₄Br₂)

Figure 1. Figure 1a is a plot of temperature as a function of time for the determination of T_f° for the pure solvent. Figure 1b is a plot of temperature as a function of time for the determination of T_f for the solution.

The mass of cyclohexane that was dispensed can be calculated. The density of cyclohexane is 0.779 g/mL.

The values for T_f° and T_f can be determined from the plots.

The molar mass, and thus the molecular weight, of the unknown compound can also be calculated. For cyclohexane, K_f = 20.2 °C kg/mole of solute.

molar mass = 134 g/mol

molecular weight = 134 amu

The molecular weights of the possible compounds are:

• 154.21 amu for Biphenyl
• 191.46 amu for 2-Bromochlorobenzene
• 128.17 amu for Naphthalene
• 178.23 amu for Anthracene
• 235.90 amu for 1,4-Dibromobenzene

The value determined experimentally for the molecular weight of the unknown compound is closest to the literature value for naphthalene.

The percent error can be calculated.

% error = 4.55%

Perhaps the most visible application of the phenomenon of freezing-point depression occurs during the winter months, when roads and sidewalks become icy, and salt is used to treat the slippery surfaces. When the salt mixes with the ice, the freezing point of the water is depressed so the ice melts at a lower temperature. Because the degree of the freezing point depression is dependent on the number of particles in solution, salts that release three ions per formula unit, such as calcium chloride (CaCl₂), are often utilized for this purpose. Ice cream makers also make use of the freezing-point depression that occurs when salt and ice are mixed. The freezing point of cream is well below 0 °C, especially when it is combined with sugar and other ingredients used to make ice cream. For this reason, ice and rock salt are combined in the outer container of an ice cream maker in order to achieve a temperature low enough to freeze the mixture enclosed in the inner container.

Chemists exploit the phenomenon of freezing-point depression in the analysis of solid organic compounds. The purity of a solid product from a chemical synthesis is often determined by measuring the melting point (theoretically, the same as the freezing point) of the material. If an impurity is present in the compound, the observed melting point is lower than expected. This occurs because, as the solid starts to melt, the impurity acts as a solute that is dissolved in the liquid form of the compound; thus, the melting, or freezing, point of the compound is depressed.

The pharmaceutical industry uses large amounts of organic solvents for reactions that lead to the synthesis of therapeutic agents. These solvents create substantial volumes of liquid waste that are hazardous to the environment. Occasionally, it is possible to take advantage of the freezing-point depression phenomenon to eliminate the need for a solvent in a synthesis. When solid reactants involved in a reaction are crushed together, the melting (or freezing) points of the two compounds are lowered. If the two compounds each have a very low melting point, the pair actually become liquids at room temperature when they are ground together, which allows the molecules to interact with each other so the reaction can occur. These solvent-free processes are an example of "green" chemistry, which refers to chemical procedures that reduce or eliminate the use and generation of hazardous substances.