Bubble point

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]

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:

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

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. 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

See also

• Phase diagram
• Azeotrope
• Dew point