Chemistry

Boiling-Point Elevation

Estimate the boiling-point increase caused by a nonvolatile solute.

Δ T_{b} = i K_{b} 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

Dissolved particles lower the solvent’s vapor pressure, so a higher temperature is needed to boil at the same external pressure. The dilute-solution approximation relates this positive temperature shift to molality and the effective number of solute particles.

Variables & Units

Understanding each component

Symbol	Meaning	Units
$Δ T_{b}$	Boiling-point increase relative to the pure solvent	$K$
$i$	Effective van ’t Hoff particle factor	$1$
$K_{b}$	Solvent boiling-point elevation constant	$K kg mo l^{- 1}$
$b$	Solute molality	$mol k g^{- 1}$

Real-World Applications

Where this formula is used in practice

Solution boiling

Estimate a boiling-point shift from solute concentration.

Colligative comparison

Compare equal-molality solutes with different particle factors.

Worked Example

Step-by-step calculation with real numbers

Problem

For a dilute aqueous nonelectrolyte solution, use i = 1, molality 0.200 mol/kg, and K_b = 0.512 K·kg/mol. Find the boiling-point increase.

Given

i = 1

b = 0.200 mol k g^{- 1}

K_{b} = 0.512 K kg mo l^{- 1}

Solution

Δ T_{b} = i K_{b} b

Δ T_{b} = (1) (0.512 K kg mo l^{- 1}) (0.200 mol k g^{- 1})

Δ T_{b} \approx 0.1024 K

Final Answer

Δ T_{b} \approx 0.1024 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

• Assume a sufficiently dilute solution with a nonvolatile solute at fixed external pressure.
• Use a solvent-specific K_b and an appropriate effective particle factor i.

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