Freezing Point Depression Calculator

About Freezing Point Depression Calculator

Freezing point depression: adding solute lowers the freezing point. Salt on roads uses this principle. For water, Kf = 1.86 °C/m.

How to use this calculator

1. Enter the van 't Hoff factor, which tells how many particles the solute makes in solution.
2. Enter the freezing point depression constant for the solvent, written as \(K_f\).
3. Enter the molality, \(m\), of the solution in \(\text{mol/kg}\).
4. Read the freezing point change, then subtract it from the pure solvent's freezing point if you need the new freezing point.

The formula explained

The calculator uses \(\Delta T_f = iK_fm\) to compute the amount the freezing point is lowered. Here, \(\Delta T_f\) is the freezing point depression, not the final freezing point itself.

• \(\Delta T_f\) = the freezing point depression, in degrees Celsius or Kelvin
• i = the van 't Hoff factor, the number of particles formed per formula unit of solute
• \(K_f\) = the freezing point depression constant of the solvent
• m = the molality of the solution, in \(\text{mol/kg}\)

Step by step method

1. Find \(i\), \(K_f\), and \(m\) for your solution.
2. Multiply \(i\), \(K_f\), and \(m\) to get \(\Delta T_f\).
3. If you want the new freezing point, subtract \(\Delta T_f\) from the pure solvent's freezing point.
4. Check that your molality is in \(\text{mol/kg}\), because using molarity will give the wrong result.

Worked example

Problem. A solution has \(i = 2\), \(K_f = 1.86\,\degree C\cdot\text{kg/mol}\), and \(m = 0.50\,\text{mol/kg}\). Find the freezing point depression.

1. Use the formula \(\Delta T_f = iK_fm\).
2. Substitute the values: \(\Delta T_f = 2 \times 1.86 \times 0.50\).
3. Compute the result: \(\Delta T_f = 1.86\,\degree C\).

Tips and common mistakes

• Molality uses mass of solvent in \(\text{kg}\), not volume, so do not confuse it with molarity.
• For electrolytes like \(\text{NaCl}\), the value of \(i\) may be close to \(2\), but real solutions can differ slightly.

Frequently asked questions