Boiling-Point Elevation

Introduction

A liquid boils when its equilibrium vapour pressure reaches the external pressure. Adding a nonvolatile solute lowers the solvent's vapour pressure at a given temperature, so a higher temperature is usually required to reach that same external pressure. This increase is boiling-point elevation. For a dilute ideal nonelectrolyte solution, its size is proportional to solute molality through a solvent-specific constant.

Core explanation

Define ΔTb = Tb,solution − Tb,pure at the same external pressure. For a dilute nonelectrolyte, ΔTb = Kb m, where m is moles of solute per kilogram of solvent and Kb has units °C kg mol⁻¹ or K kg mol⁻¹. A temperature difference has the same numerical size in Celsius degrees and kelvin. The actual boiling point is Tb,solution = Tb,pure + ΔTb. Do not subtract the elevation or confuse ΔTb with the final temperature.

For water at about one atmosphere, Tb,pure = 100.0 °C and Kb ≈ 0.512 °C kg mol⁻¹. A 0.500 m ideal nonelectrolyte solution gives ΔTb = 0.512 × 0.500 = 0.256 °C and a predicted boiling temperature near 100.256 °C. The result is a model estimate, not a promise that a household pot with solute will boil at exactly this temperature. Atmospheric pressure, solute behaviour and concentration affect the real reading.

The mechanism can be described with two vapour-pressure curves. At a chosen temperature, the solution's solvent vapour pressure lies below that of pure solvent. To meet the same horizontal external-pressure line, the solution curve must be followed to a higher temperature. This explanation does not require solute molecules themselves to evaporate; indeed the simple equation assumes the solute is effectively nonvolatile. It also does not mean a higher boiling temperature is caused by extra heat capacity alone.

The unit molality is essential because Kb is calibrated to moles per kilogram solvent. If 0.100 mol solute is dissolved in 0.250 kg solvent, m = 0.400 m, not 0.100 m. If the question gives grams of solute, convert to moles with molar mass first. If it gives mass of solution , subtract solute mass to obtain solvent kilograms. Inserting molarity in mol L⁻¹ directly into ΔTb = Kb m changes the denominator and generally gives a wrong result.

For an electrolyte, an introductory particle correction writes ΔTb ≈ iKb mformula. Here i is the effective van 't Hoff factor, which can differ from the ideal ion count at finite concentrations. A nonelectrolyte with no association has i near one. The formula requires dilute conditions and a solute that remains dissolved over the temperature range. If the solute decomposes, precipitates or volatilises appreciably, the simple relation is unreliable.

Boiling-point elevation can be used to infer molar mass when the solute mass, solvent mass and measured ΔTb are known. Solve for m = ΔTb/Kb, multiply by kilograms solvent to get solute moles, then divide solute grams by those moles. This is an inference with assumptions: a measured temperature shift may be affected by pressure calibration or nonideal solution behaviour. A detailed experimental report would also state uncertainty rather than quote an overprecise molecular mass.

Step-by-step reasoning

1. Identify pure-solvent boiling temperature and Kb at the given external pressure context. 2. Convert solute mass to moles and solvent mass to kilograms. 3. Calculate molality, adding an effective particle factor only if the problem calls for it. 4. Find positive ΔTb = Kb m for a nonelectrolyte, then add it to Tb,pure. 5. Check dilute, nonvolatile and unchanged-solute assumptions.

Visual explanation

Draw vapour pressure vertically and temperature horizontally. Place the pure-solvent curve above the solution curve at the same T. A horizontal line at external pressure intersects the pure curve first and the solution curve at a higher T. Label the horizontal temperature gap ΔTb. Beside it write Kb × mol solute/kg solvent.

Real-world analogy

If a cyclist begins below a hilltop target, they must travel farther uphill to reach the same height. A solution begins with lower vapour pressure at a given temperature, so it needs a higher temperature to reach the fixed external boiling pressure. The analogy captures the curve shift, not the molecular reason for it.

Real-world example

A laboratory measures boiling-point elevation to estimate the molar mass of an unknown nonvolatile nonelectrolyte. It weighs solute and solvent, measures a small temperature difference at controlled pressure and uses the solvent's Kb. The method needs careful temperature measurement because a dilute aqueous solution can raise boiling by only a fraction of a degree.

Why?

Why does the formula use solvent mass rather than total solution volume? Kb is defined for a particle amount per kilogram of solvent in the dilute relation. Solvent mass stays well defined as temperature changes, whereas solution volume expands and contracts.

Common misconception

“Adding any amount of salt makes water boil dramatically hotter.” Dilute colligative shifts are often small. A concentrated electrolyte can have a larger effect, but the simple ideal equation and integer ion factors may then become inaccurate.

Worked example

Dissolve 9.00 g of a nonvolatile nonelectrolyte of molar mass 90.0 g mol⁻¹ in 0.500 kg water. Solute amount is 0.100 mol and m = 0.100/0.500 = 0.200 mol kg⁻¹. With Kb = 0.512 °C kg mol⁻¹, ΔTb = 0.1024 °C. At 1 atm, predicted boiling point is 100.0 + 0.1024 ≈ 100.10 °C at suitable precision. The final rounding should reflect both the constant and experimental inputs.

Quick check

1. Is ΔTb added to or subtracted from the pure-solvent boiling point? Answer: Added. A dilute solution with nonvolatile solute has a higher predicted boiling point.

Exam focus

Write ΔTb = Tb,solution − Tb,pure = Kb m, show molality in mol kg⁻¹ and preserve pressure conditions. Use i only when appropriate and avoid treating molarity as molality.

Advanced insight

The proportional law is the dilute limit of a solvent chemical-potential calculation. At larger solute concentrations, solution activity changes nonlinearly, and the temperature shift cannot be assumed proportional to analytical molality. For precision work, boiling-point elevation is therefore interpreted with activity data or empirical calibration.

Summary

Nonvolatile solute lowers solvent vapour pressure, so a higher temperature is needed to boil at the same external pressure. In the dilute nonelectrolyte model, ΔTb = Kb m. Kb belongs to the solvent, m uses kilograms solvent, and the positive shift is added to the pure boiling point.

Practice questions

1. Find ΔTb for 0.50 m ideal nonelectrolyte in water, Kb = 0.512 °C kg mol⁻¹. Answer: 0.512 × 0.50 = 0.256 °C. 2. What is the molality of 0.20 mol solute in 0.400 kg solvent? Answer: 0.20/0.400 = 0.500 mol kg⁻¹. 3. Why is a tabulated Kb for water unsuitable for an ethanol solvent calculation? Answer: Kb is a solvent-specific constant; ethanol needs its own value.