# Ebullioscopic constant

In thermodynamics, the ebullioscopic constant ${\displaystyle K_{\mathrm {b} }}$ relates molality ${\displaystyle b}$ to boiling point elevation.[1] It is the ratio of the latter to the former:

${\displaystyle \Delta T=i\cdot K_{\mathrm {b} }\cdot b}$

• ${\displaystyle i}$ is the van 't Hoff factor, the number of particles the solute splits into or forms when dissolved.
• ${\displaystyle b}$ is the molality of the solution.

A formula to compute the ebullioscopic constant is:[2]

${\displaystyle K_{\mathrm {b} }=RT_{\mathrm {b} }^{2}\cdot M/\Delta H_{\text{vap}}}$
• ${\displaystyle R}$ is the ideal gas constant.
• ${\displaystyle T_{\mathrm {b} }}$ is boiling point of the solvent.
• ${\displaystyle M}$ is the molar mass of the solvent.
• ${\displaystyle \Delta H_{\text{vap}}}$ is the molar enthalpy of vaporization.

Through the procedure called ebullioscopy, a known constant can be used to calculate an unknown molar mass. The term "ebullioscopy" comes from the Latin language and means "boiling measurement." This is related to cryoscopy, which determines the same value from the cryoscopic constant (of freezing point depression).

This property of elevation of boiling point is a colligative property. It means that the property, in this case ${\displaystyle \Delta T}$, depends on the number of particles dissolved into the solvent and not the nature of those particles.

## Some ${\displaystyle K_{\mathrm {b} }}$ values[3]

Solvent${\displaystyle K_{\mathrm {b} }}$ (in K*kg/mol)
Acetic acid3.08
Benzene2.53
Camphor5.95
Carbon disulfide2.34
Carbon tetrachloride5.03
Chloroform3.63
Cyclohexane2.79
Diethyl ether2.02
Ethanol1.07
Water0.512