By Timothy Banas • Updated Mar 24, 2022

While the freezing (0 °C) and boiling (100 °C) points of pure water are common knowledge, adding a solute shifts these temperatures. Salt in water lowers the freezing point and raises the boiling point. This guide shows how to compute the new values for any solution using molality and the appropriate constants.

Determining a Change in Freezing Point

Step 1: Identify the Solvent’s Base Freezing Point

Look up the pure solvent’s freezing point on its material safety data sheet (MSDS). For water, this is 0 °C.

Step 2: Calculate the Molality of the Solution

Molality (m) is defined as the number of moles of solute per kilogram of solvent:

molality = moles of solute ÷ mass of solvent (kg)

Example: Dissolving 0.5 mol of NaCl into 1 L of water (1 kg) gives a molality of 0.5 m.

Step 3: Find the Freezing Point Depression Constant (K_f)

Each solvent has an experimentally determined K_f that quantifies how much its freezing point decreases per unit molality. For water, K_f = 1.86 °C kg mol⁻¹.

Step 4: Apply the Freezing Point Depression Formula

ΔT_f = K_f × m

New freezing point = T₀ – ΔT_f

Using the example: ΔT_f = 1.86 × 0.5 = 0.93 °C
New freezing point = 0 °C – 0.93 °C = –0.93 °C

Determining a Change in Boiling Point

Step 1: Identify the Solvent’s Base Boiling Point

Refer to the MSDS for the pure solvent’s boiling point. For water, this is 100 °C.

Step 2: Calculate the Molality of the Solution

Use the same molality calculation as above. For the example, molality = 0.5 m.

Step 3: Find the Boiling Point Elevation Constant (K_b)

Each solvent has a K_b value that indicates how much its boiling point rises per unit molality. For water, K_b = 0.512 °C kg mol⁻¹.

Step 4: Apply the Boiling Point Elevation Formula

ΔT_b = K_b × m

New boiling point = T₀ + ΔT_b

Using the example: ΔT_b = 0.512 × 0.5 = 0.256 °C
New boiling point = 100 °C + 0.256 °C = 100.256 °C