Pressure deviation, denoted as ∆p, refers to the difference between the experimentally measured pressure of a system and the pressure calculated based on a theoretical model or equation of state. This difference is typically analyzed as a function of the system's composition, such as the mole fraction of a component in a liquid mixture.
Understanding Pressure Deviation
Pressure deviation helps assess the accuracy of thermodynamic models in predicting the behavior of real systems. Ideal solutions follow Raoult's Law perfectly, but real solutions often exhibit deviations due to intermolecular interactions. These deviations manifest as differences between the actual pressure and the ideal pressure predicted by Raoult's Law.
Components Contributing to Pressure Deviation
Several factors contribute to pressure deviation in real systems:
- Non-Ideal Mixing: Real mixtures deviate from ideal behavior due to differences in intermolecular forces between the components. These forces can be attractive or repulsive, leading to positive or negative deviations.
- Volume Changes on Mixing: Ideal mixtures assume no volume change upon mixing. However, in reality, the volume may either increase or decrease.
- Heat of Mixing: Ideal mixtures assume no heat is evolved or absorbed during mixing. Real mixtures may exhibit exothermic or endothermic behavior, reflecting differences in intermolecular interactions.
Calculation and Significance
The pressure deviation (∆p) is calculated as follows:
∆p = Pexperimental - Pcalculated
Where:
- Pexperimental is the experimentally measured total pressure of the system.
- Pcalculated is the total pressure calculated using an equation of state (like Raoult's Law for ideal solutions or modified versions for non-ideal solutions).
A significant pressure deviation indicates that the theoretical model being used is not accurately representing the real system. This might prompt the use of more sophisticated models that account for non-ideal behavior, such as activity coefficient models (e.g., NRTL, UNIQUAC).
Example: Benzene (1) + 2-Propanol (2) System
For a system of benzene (1) + 2-propanol (2), the pressure deviation (∆p) would be calculated for various liquid compositions (x1, the mole fraction of benzene). The resulting ∆p values, plotted against x1, would reveal the extent to which the system deviates from ideal behavior. Large deviations might suggest strong interactions between benzene and 2-propanol molecules that aren't accounted for in a simple model.
Types of Pressure Deviation
- Positive Deviation: Occurs when the experimental pressure is higher than the calculated pressure. This suggests weaker intermolecular forces in the mixture compared to the pure components.
- Negative Deviation: Occurs when the experimental pressure is lower than the calculated pressure. This suggests stronger intermolecular forces in the mixture compared to the pure components.
Conclusion
In summary, pressure deviation is a crucial parameter for understanding and quantifying non-ideal behavior in mixtures, especially in vapor-liquid equilibrium studies. It helps in selecting appropriate thermodynamic models for accurate predictions of system properties.
