How to Calculate Freezing Point

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Assuming standard pressure of one atmosphere, freezing point is the temperature at which a liquid condenses into a solid. Some gases, such as carbon dioxide, can become solids without going through a liquid phase via a process called sublimation. All liquids and gases, with the exception of helium, have characteristic freezing points that scientists have discovered through experimentation, not calculation. However, a general formula known as Blagden's Law allows you to calculate how the addition of a solute will lower the freezing point of a solvent in direct proportion to the concentration of the solution.

    Look up the mass of one mole of the solute. A mole is a specific number of particles -- ions, atoms or molecules -- in a substance. That specific number is Avogadro's constant, 6.02 x 10^23. You can look up the mass of one mole of the solute on the Internet or in a chemistry textbook. For example, the mass of one mole of sodium chloride, or table salt, is 58.44 grams/mole.

    Research the properties of the solvent. For example, you can look up H20, or water, on various websites and find that its freezing point is zero degrees Celsius. Water has another property, called its cryoscopic content ("Kf") equal to 1.86 in units of (degrees Celsius x kilogram / mole). The Kf of a solvent describes how much its freezing point will fall upon the addition of a solute.

    Determine the molality ("m") of the solution, which is defined as the number of moles of solute per kilogram of solvent. For example, if you add 58.44 grams of sodium chloride to one kilogram of water -- which is also one liter of water -- you have a salt water solution with a molality of one mole of salt / one kilogram of water, or one mole/kilogram.

    Look up the van't Hoff factor ("i") for the solute. This is the ratio of moles of the solute before and after it is dissolved. For example, one mole of sodium chloride dissociates in water to form a mole each of sodium and chlorine ions. Therefore, table salt has a van't Hoff factor of two.

    Calculate the depression of the freezing point using the formula Tf = (i x Kf x m), where Tf is the how much the freezing point drops in degrees Celsius. In our example, Tf = (2 x 1.86 x 1), or 3.72 degrees C, dropping the freezing point of water from zero to negative 3.72 degrees C.

    Tips

    • The drop in freezing point depends only on the solvent, not the solute. This is true for dilute solutions, but very concentrated solutions require a complex calculation to determine freezing point depression.

    Warnings

    • Don't confuse molality with the term "molarity," which is the number of moles of solute divided by the volume of the solution.

References

About the Author

Based in Greenville SC, Eric Bank has been writing business-related articles since 1985. He holds an M.B.A. from New York University and an M.S. in finance from DePaul University. You can see samples of his work at ericbank.com.

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