# Bubble point

Mole fraction vs. temperature diagram for a two-component system, showing the bubble point and dew point curves.

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.[1][2] 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.[3]

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:

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

where

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

K is the distribution coefficient or K factor, defined as the ratio of mole fraction in the vapor phase ${\displaystyle {\big (}y_{ie}{\big )}}$ to the mole fraction in the liquid phase ${\displaystyle {\big (}x_{ie}{\big )}}$ 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:[1]

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

Given either of ${\displaystyle x_{i}}$ or ${\displaystyle y_{i}}$ and either the temperature or pressure of a two-component system, calculations can be performed to determine the unknown information.[4]

## References

1. ^ a b McCabe, Warren L.; Smith, Julian C.; Harriot, Peter (2005), Unit Operations of Chemical Engineering (seventh ed.), New York: McGraw-Hill, pp. 737–738, ISBN 0-07-284823-5
2. ^ Smith, J. M.; Van Ness, H. C.; Abbott, M. M. (2005), Introduction to Chemical Engineering Thermodynamics (seventh ed.), New York: McGraw-Hill, p. 342, ISBN 0-07-310445-0
3. ^ Perry, R.H.; Green, D.W., eds. (1997). Perry's Chemical Engineers' Handbook (7th ed.). McGraw-hill. ISBN 0-07-049841-5.
4. ^ Smith, J. M.; Van Ness, H. C.; Abbott, M. M. (2005), Introduction to Chemical Engineering Thermodynamics (seventh ed.), New York: McGraw-Hill, p. 351, ISBN 0-07-310445-0