# Bubble point

When heating a liquid consisting of two or more components, the bubble point is the temperature (at a given pressure) where the first bubble of vapor is formed. 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.

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:[1]

$K_i = \frac{P'_i}{P}$

## 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