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## Summary

In thermodynamics, the bubble point is the temperature (at a given pressure) where the first bubble of vapor is formed when heating a liquid consisting of two or more components. Given that vapor will probably have a different composition than the liquid, the bubble point (along with the dew point) at different compositions are useful data when designing distillation systems. Mole fraction vs. temperature diagram for a two-component system, showing the bubble point and dew point curves.

For a single component the bubble point and the dew point are the same and are referred to as the boiling point.

## Calculating the bubble point

At the bubble point, the following relationship holds:

$\sum _{i=1}^{N_{c}}y_{i}=\sum _{i=1}^{N_{c}}K_{i}x_{i}=1$

where

$K_{i}\equiv {\frac {y_{ie}}{x_{ie}}}$ .

K is the distribution coefficient or K factor, defined as the ratio of mole fraction in the vapor phase ${\big (}y_{ie}{\big )}$  to the mole fraction in the liquid phase ${\big (}x_{ie}{\big )}$  at equilibrium.
When Raoult's law and Dalton's law hold for the mixture, the K factor is defined as the ratio of the vapor pressure to the total pressure of the system:

$K_{i}={\frac {P'_{i}}{P}}$

Given either of $x_{i}$  or $y_{i}$  and either the temperature or pressure of a two-component system, calculations can be performed to determine the unknown information.