Raoult's Law

on . Posted in Fluid Dynamics

Raoult's Law is a principle in physical chemistry that describes the vapor pressure behavior of ideal solutions.  It states that the partial vapor pressure of each component in an ideal mixture is directly proportional to its mole fraction in the mixture.  This law is particularly applicable when the components of the mixture are similar and have similar intermolecular forces.  It assumes that the interactions between unlike molecules (A-B interactions) are similar to the interactions between like molecules (A-A and B-B interactions).

Raoult's Law Index

Raoult's law is a useful approximation for dilute solutions and for systems where the components exhibit similar behavior.  However, it's important to note that deviations from Raoult's law can occur in real solutions, especially when there are significant differences in the intermolecular forces between the components.  These deviations are often observed in non ideal solutions, and they can result from factors such as molecular size differences, polarity variations, and the presence of hydrogen bonding.  In such cases, more complex models, like the Van't Hoff factor or activity coefficients, may be used to describe the vapor pressure behavior more accurately.

Raoult's Law Formula

$$p_i \;=\; x_i \; p^* _i$$     (Raoult's Law)

$$x_i \;=\; p_i \;/\; p^* _i$$

$$p^* _i \;=\; p_i \;/\; x_i$$

Symbol English Metric
$$p_i$$ = vapor pressure - $$Pa$$
$$x_i$$ = mole fraction of component i in the mixture $$dimensionless$$ $$dimensionless$$
$$p^* _i$$ = vapor pressure of pure component i $$dimensionless$$ $$dimensionless$$

Raoult's Law for Vapor Pressure Formula

$$p_A \;=\; x_A \; p^* _A + x_B \; p^* _B$$     (Raoult's Law for Vapor Pressor)

$$x_A \;=\; x_A \;p^* _A + x_B \;p^* _B$$

$$p^* _A \;=\; x_A \;p^* _A + x_B \;p^* _B$$

$$x_B \;=\; x_A \;p^* _A + x_B \;p^* _B$$

$$p^* _B \;=\; x_A \;p^* _A + x_B \;p^* _B$$

Symbol English Metric
$$p_A$$ = partial vapor pressure of component A in the mixture - $$Pa$$
$$p_B$$ = partial vapor pressure of component B in the mixture - $$Pa$$
$$x_A$$ = the mole fraction of component A $$dimensionless$$ $$dimensionless$$
$$x_B$$ = the mole fraction of component B $$dimensionless$$ $$dimensionless$$
$$p^* _A$$ = the vapor pressures of pure A $$dimensionless$$ $$dimensionless$$
$$p^* _B$$ = the vapor pressures of pure B $$dimensionless$$ $$dimensionless$$