Chemistry

Freezing-Point Depression

Estimate how dissolved particles lower a solvent’s freezing point.

Δ T_{f} = i K_{f} b

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Source & review

Difficulty

Beginner

Read time

3 min

Prerequisites

Basic algebra and molar quantities

Review statusNeeds review

Source

OpenStax, Chemistry 2e, §11.4

Adapted from Teng-Jui Lin’s CHEM 145 equation sheet. The linked textbook reference was used to check the equation and its physical context. Pending editorial review.

Adapted from Teng-Jui Lin, Equation Sheets, under CC BY 4.0.

FormuLab adapted notation and chemical symbols, added variable meanings, units, applicability conditions, and an original worked example.

Definition

Understanding the core concept

A dissolved solute can lower the freezing temperature of its solvent. The temperature shift here is the positive magnitude of that decrease; subtract it from the pure solvent’s freezing point to find the solution’s freezing point.

Variables & Units

Understanding each component

Symbol	Meaning	Units
$Δ T_{f}$	Positive freezing-point decrease	$K$
$i$	Effective van ’t Hoff particle factor	$1$
$K_{f}$	Solvent freezing-point depression constant	$K kg mo l^{- 1}$
$b$	Solute molality	$mol k g^{- 1}$

Real-World Applications

Where this formula is used in practice

Freezing shifts

Estimate the temperature decrease for a dilute solution.

Particle concentration

Relate a measured freezing shift to effective dissolved-particle molality.

Worked Example

Step-by-step calculation with real numbers

Problem

An aqueous solution has molality 0.100 mol/kg and effective i = 1.80. Taking K_f = 1.86 K·kg/mol, estimate the freezing-point decrease.

Given

i = 1.80

b = 0.100 mol k g^{- 1}

K_{f} = 1.86 K kg mo l^{- 1}

Solution

Δ T_{f} = i K_{f} b

Δ T_{f} = (1.80) (1.86 K kg mo l^{- 1}) (0.100 mol k g^{- 1})

Δ T_{f} \approx 0.3348 K

Final Answer

Δ T_{f} \approx 0.3348 K

Formula Guide

Info

DifficultyBeginner

Read Time3 min

PrerequisitesBasic algebra and molar quantities

Tools

Source & review

StatusNeeds review

Last reviewedPending

Source

OpenStax, Chemistry 2e, §11.4

Adapted from Teng-Jui Lin’s CHEM 145 equation sheet. The linked textbook reference was used to check the equation and its physical context. Pending editorial review.

Adapted from Teng-Jui Lin, Equation Sheets, under CC BY 4.0.

FormuLab adapted notation and chemical symbols, added variable meanings, units, applicability conditions, and an original worked example.

Assumptions

• Use the dilute-solution approximation and a solvent-specific K_f.
• Use an effective i that accounts for dissociation or association in the stated conditions.

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