Boiling-point elevation

Boiling-point elevation describes the phenomenon that the boiling point of a liquid (a solvent) will be higher when another compound is added, meaning that a solution has a higher boiling point than a pure solvent. This happens whenever a non-volatile solute, such as a salt, is added to a pure solvent, such as water. The boiling point can be measured accurately using an ebullioscope.

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The equation for calculations at dilute concentration

The extent of boiling-point elevation can be calculated by applying Clausius–Clapeyron relation and Raoult's law together with the assumption of the non-volatility of the solute. The result is that in dilute ideal solutions, the extent of boiling-point elevation is directly proportional to the molal concentration (amount of substance per mass) of the solution according to the equation:^[1]

ΔT_b = K_b · b_B

where the boiling point elevation, is defined as T_{b (solution)} - T_{b (pure solvent)}.

K_b, the ebullioscopic constant, which is dependent on the properties of the solvent. It can be calculated as K_b = RT_b²M/ΔH_v, where R is the gas constant, and T_b is the boiling temperature of the pure solvent [in K], M is the molar mass of the solvent, and ΔH_v is the heat of vaporization per mole of the solvent.
b_B is the molality of the solution, calculated by taking dissociation into account since the boiling point elevation is a colligative property, dependent on the number of particles in solution. This is most easily done by using the van 't Hoff factor i as b_B = b_solute · i. The factor i accounts for the number of individual particles (typically ions) formed by a compound in solution. Examples:
- i = 1 for sugar in water
- i = 1.9 for sodium chloride in water, due to the near full dissociation of NaCl into Na⁺ and Cl⁻ (often simplified as 2)
- i = 2.3 for calcium chloride in water, due to nearly full dissociation of CaCl₂ into Ca²⁺ and 2Cl⁻ (often simplified as 3)

Non integer i factors result from ion pairs in solution, which lower the effective number of particles in the solution.

Equation after including the van 't Hoff factor

ΔT_b = K_b · b_solute · i

At high concentrations, the above formula is less precise due to nonideality of the solution. If the solute is also volatile, one of the key assumptions used in deriving the formula is not true, since it derived for solutions of non-volatile solutes in a volatile solvent. In the case of volatile solutes it is more relevant to talk of a mixture of volatile compounds and the effect of the solute on the boiling point must be determined from the phase diagram of the mixture. In such cases, the mixture can sometimes have a boiling point that is lower than either of the pure components; a mixture with a minimum boiling point is a type of azeotrope.

Ebullioscopic constants

Values of the ebullioscopic constants K_b for selected solvents:^[2]

Compound	Boiling point in °C	Ebullioscopic constant K_b in units of [(°C·kg)/mol] or [°C/molal]
Acetic acid	118.1	3.07
Benzene	80.1	2.53
Carbon disulfide	46.2	2.37
Carbon tetrachloride	76.8	4.95
Naphthalene	217.9	5.8
Phenol	181.75	3.04
Water	100	0.512

Uses

Together with the formula above, the boiling-point elevation can in principle be used to measure the degree of dissociation or the molar mass of the solute. This kind of measurement is called ebullioscopy (Greek "boiling-viewing"). However, since superheating is difficult to avoid, precise ΔT_b measurements are difficult to carry out,^[1] which was partly overcome by the invention of the Beckmann thermometer. Furthermore, the cryoscopic constant that determines freezing-point depression is larger than the ebullioscopic constant, and since the freezing point is often easier to measure with precision, it is more common to use cryoscopy.

Among many urban legends related to the effect of ebullioscopic increase, one of them leads to adding salt when cooking pasta only after water has started boiling. The misconception is that since the water boils at a higher temperature, food will cook faster. However, at the approximate concentration of salt in water for cooking (10 g of salt per 1 kg of water, or 1 teaspoon per quart), the ebullioscopic increase is approximately 0.17 °C (0.31 °F), which will arguably make no practical difference for cooking, although salt may add to flavors.

References

^ ^a ^b Cite error: The named reference Atkins was invoked but never defined (see the help page).
^ P. W. Atkins, Physical Chemistry, 4th Ed., p. C17 (Table 7.2)

[Atkins-1] Cite error: The named reference Atkins was invoked but never defined (see the help page).

[2] P. W. Atkins, Physical Chemistry, 4th Ed., p. C17 (Table 7.2)

[1]

[2]

v t e Chemical solutions
Solution	Ideal solution Aqueous solution Solid solution Buffer solution Flory–Huggins Mixture Suspension Colloid Phase diagram Phase separation Eutectic point Alloy Saturation Supersaturation Serial dilution Dilution (equation) Apparent molar property Miscibility gap
Concentration and related quantities	Molar concentration Mass concentration Number concentration Volume concentration Normality Molality Mole fraction Mass fraction Isotopic abundance Mixing ratio Ternary plot Total dissolved solids
Solubility	Solubility equilibrium Solvation Solvation shell Enthalpy of solution Lattice energy Raoult's law Henry's law Solubility table (data) Solubility chart Miscibility
Solvent	(Category) Acid dissociation constant Protic solvent Polar aprotic solvent Inorganic nonaqueous solvent Solvation List of boiling and freezing information of solvents Partition coefficient Polarity Hydrophobe Hydrophile Lipophilic Amphiphile Lyonium ion Lyate ion

The equation for calculations at dilute concentration

Ebullioscopic constants

Uses

See also

References