Library / Solution chemistry, equilibria and kinetics / SCH-50
Solution chemistry, equilibria and kinetics
Boiling-point elevation
Raising of the boiling point of a dilute solution of a non-volatile solute at fixed pressure, from the molality b, the solvent’s ebullioscopic constant Kb and the effective particle factor i.
- Ref
- SCH-50
- Rev
- v1
- Field
- Solution chemistry, equilibria and kinetics
- Result
- ΔTb [K]
A non-volatile solute raises the boiling point of the solvent at fixed pressure by ΔTb = i Kb b, with b the molality, Kb the ebullioscopic constant (0.512 K·kg/mol for water) and i the effective particle factor. Add it to the pure-solvent boiling point. The elevation is smaller than the depression of the freezing point because Kb is smaller than Kf. It holds for dilute solutions of a solute that does not itself evaporate.
Raising of the boiling point of a dilute solution of a non-volatile solute at fixed pressure, from the molality b, the solvent’s ebullioscopic constant Kb and the effective particle factor i. Add the result to the pure-solvent boiling point.
Calculator
- Boiling point if the solvent boils at 373.15 K373.3 K
- Molality that gives a 1 K elevation, 1/(i Kb)1.953 mol/kg
- Elevation per 0.1 mol/kg of solute0.0512 K
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- A solution at 0.25 mol/kg boils 0.128 K above the pure solvent, at about 373.28 K for water at 1 atm.
- The effect is small: raising the boiling point of water by 1 K needs 1.95 mol/kg of particles at this i, which is why cooking water barely changes its boiling temperature when salted.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (K) | Local step | Change in result |
|---|---|---|---|---|---|---|
| b Solute molality | 0.001 to 5 mol/kg | 5.12e-4 | 2.56 | 2.559 | +10% | +10 % |
| Kb Ebullioscopic constant of the solvent | 0.1 to 10 K·kg/mol | 0.025 | 2.5 | 2.475 | +10% | +10 % |
| i Effective particle factor | 1 to 5 | 0.128 | 0.64 | 0.512 | +10% | +10 % |
Sweep of Solute molality
| Solute molality (mol/kg) | Boiling-point elevation (K) |
|---|---|
| 0.001 | 5.12e-4 |
| 0.0029 | 0.001485 |
| 0.008409 | 0.004305 |
| 0.02438 | 0.01248 |
| 0.07071 | 0.0362 |
| 0.205 | 0.105 |
| 0.5946 | 0.3044 |
| 1.724 | 0.8828 |
| 5 | 2.56 |
Sweep one variable
Variables and how each one contributes
Boiling-point elevation
What the equation gives you. Everything else feeds it.
Effective particle factor
The effective particle factor. Raises the elevation in direct proportion. Raising it by 10 % (to 1.1) moves the result by +10 %, from 0.128 to 0.1408 K.
Ebullioscopic constant of the solvent
The ebullioscopic constant of the solvent, in K·kg/mol. Raises the elevation in direct proportion. Raising it by 10 % (to 0.5632) moves the result by +10 %, from 0.128 to 0.1408 K.
Solute molality
The solute molality, in mol/kg. Raises the elevation in direct proportion. Raising it by 10 % (to 0.275) moves the result by +10 %, from 0.128 to 0.1408 K.
Worked example with the values above
- Particle molality: i b = 1 × 0.25 = 0.25 mol/kg.
- Multiply by Kb = 0.512 K·kg/mol.
- ΔTb = 0.128 K.
Assumptions and limits
- Dilute or ideal solutions with a non-volatile solute, unless a second volatile component is stated.
- Constant temperature (or constant pressure for boiling-point elevation) and a membrane that passes only the solvent for osmosis.
Common mistakes
- Using molarity in place of molality.
- Forgetting the factor i for an electrolyte.
- Subtracting the elevation from the boiling point, instead of adding it.
Statistics and uncertainty
Colligative formulas assume ideal behaviour, which holds only for dilute solutions. The effective particle factor i of an electrolyte is below its ideal value, by 5 % to 30 % even at 0.1 mol/kg.
Where it is used
- Estimating antifreeze, de-icing and desalination behaviour.
- Finding molar masses and reading simple phase diagrams.
Maths you need
- Raoult’s law: partial pressure = mole fraction × pure vapour pressure
- Colligative properties: properties that depend on particle number
- Molality: moles of solute per kilogram of solvent