# How to Compute the Freezing Point of a Mixture

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In a mixture of a solid and liquid, or two liquids, the major component represents the solvent, and the minor component represents the solute. The presence of the solute induces the phenomenon of a freezing-point depression in the solvent, where the freezing point of the solvent in the mixture becomes lower than that of the pure solvent. The freezing-point depression is calculated according to delta(T) = Km, where K represents the freezing-point depression constant of the solvent, and m represents the molality of the solution. Molality, in this case, represents the moles of solute particles per kilogram of solvent. Chemists determine the moles of solute particles by dividing the mass of the solute by its molecular weight, as determined by adding together the atomic masses of all of the atoms in its chemical formula.

Identify the solute and solvent in the mixture. By definition, the solute represents the compound present in lesser amount. For example, for a mixture of 10 grams of sodium chloride (salt) dissolved in 100 grams of water, the sodium chloride represents the solute.

Determine the formula weight or molecular weight of the solute by adding together the atomic weights of all of the atoms in the solute’s chemical formula. Sodium chloride contains one sodium atom and one chlorine atom, and the atomic weights from the periodic table of the elements for sodium and chlorine are 22.99 and 35.45, respectively. Its formula weight is therefore (1 x 22.99) + (1 x 35.45), which is 58.44.

Calculate the moles of solute by dividing the grams of solute by its formula weight. Continuing the previous example of sodium chloride, 10 grams/58.44, or 0.171 moles of sodium chloride .

Determine the moles of particles by multiplying the moles of solute by the number of particles created when the solute dissolves. For molecular substances with covalent bonds, such as sugar, each formula represents one molecule or particle in the solution. However, ionic compounds such as sodium chloride produce two or more particles per formula unit. You can identify ionic compounds easily because they always consist of a metal and a nonmetal, whereas molecular compounds such as sugar contain nonmetals only. A compound such as calcium chloride would produce three particles. For the example of 10 grams of sodium chloride (0.171 moles of NaCl) x (2 particles per formula), or 0.342 moles of particles.

Determine the molality of the solution by dividing the moles of particles by the mass of the solvent in kilograms. In the previous example, the prepared solution contained 10 grams of sodium chloride dissolved in 100 grams of water. Because 1 kilogram contains 1000 grams, 100 grams of water represents 0.100 kilograms of water. Use the online conversion tool to convert the mass of solvent to kilograms, if necessary. The particle molality of 10 grams of sodium chloride in 100 grams of water is therefore 0.342 / 0.100, or 3.42 moles per kilogram.

Refer to a table of freezing-point depression constants to determine the freezing-point depression constant, K, of the solvent. The K of water, for example, is 1.86 degrees C per molal.

Calculate the freezing-point depression, delta(T), of the solvent by multiplying its K value by the molality of the solute: delta(T) = Km. Continuing the previous example, delta(T) = 3.42 x 1.86, or 6.36 degrees C.

Determine the freezing point of the mixture by subtracting delta(T) from the freezing point of the pure solvent. Most tables of freezing-point depression constants will also provide the freezing point - sometimes listed as the melting point - of the pure solvent. In the case of water, the freezing point is 0 degrees C. The freezing point of 100 grams of water containing 10 grams of sodium chloride is therefore 0 - 6.36, or -6.36 degrees C.

#### Things You'll Need

• Periodic table of the elements
• Table of freezing-point depression constants