# Ebullioscopic constant

In thermodynamics, the ebullioscopic constant, ${\displaystyle K_{\mathrm {b} }}$, allows one to relate 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 Vant Hoff factor. It is determined by whether the solute particles in the solution associate or dissociate. If all the particles of the solute trimerise (three associate into one) the Vant hoff factor will be 1/3. If they dissociate into two particles (For example, NaCl as solute which breaks into Na+ and Cl), ${\displaystyle i=2}$.

${\displaystyle K_{\mathrm {b} }=RT_{\mathrm {b} }^{2}\cdot M/\Delta h_{\text{vap}}}$[2]
${\displaystyle R}$ - ideal gas constant
${\displaystyle T_{\mathrm {b} }}$ - boiling point of liquid.
${\displaystyle M}$ - molar mass of solvent.
${\displaystyle \Delta h_{\text{vap}}}$- specific 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 Greek 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]

Chemical ${\displaystyle K_{\mathrm {b} }}$ (in K*kg/mol)
Acetic acid 3.08
Benzene 2.53
Camphor 5.95
Carbon disulfide 2.34
Carbon tetrachloride 5.03
Chloroform 3.63
Cyclohexane 2.79
Diethyl ether 2.02
Ethanol 1.07
Water 0.512