Distillation of a Miscible Mixture
Some liquids will evaporate entirely over time if left in an open container at room temperature. However, this evaporation process can be significantly accelerated if the liquid is heated. As the liquid is heated, the molecules within it gain the energy to escape the liquid phase and transition into the gas phase in the form of bubbles. This phenomenon is called boiling.
Consider a closed container of liquid. Initially, some of this liquid evaporates, but only until the rate of vaporization equals the rate of condensation. After this point is reached, there is no further change in the system, and the liquid and vapor are at equilibrium. Once this has been established, the pressure exerted by the vapor above the liquid is called the vapor pressure. The tendency for a liquid to vaporize is called its volatility. A more volatile liquid has a higher vapor pressure, while a less volatile liquid has a lower vapor pressure.
When an open container of liquid is heated, more of the liquid evaporates. If enough heat is added, bubbles of vapor form in the liquid and the liquid boils. The temperature at which the vapor pressure of the liquid is the same as the atmospheric pressure is known as the boiling point.
For a pure substance, the vapor pressure is simple to determine. What about a mixture of different liquids? If pure liquids form a miscible homogenous solution, each one will contribute to the total vapor pressure as partial pressures. The total gas pressure of a mixture of gases is equal to the sum of the individual pressures each gas would exert in isolation. This rule is known as Dalton’s law. Therefore, to determine the total vapor pressure of the mixture, you must know the vapor pressures of the pure substances and the molar contribution of each liquid to the total mixture, a value known as the mole fraction. This relationship is known as Raoult’s law:
pA = pA* xA
where pA is the vapor pressure of a liquid component in a mixture, pA* is the vapor pressure of the pure liquid in isolation, which can be referenced from the literature, and xA is the mole fraction of the liquid component in the liquid mixture. Mole fractions are calculated by dividing the number of moles of the liquid component over the total number of moles of each component in the liquid mixture.
Dalton's law of partial pressures can be applied once you know the vapor pressure of each individual component.
P = pA + pB
The total pressure (P) is the sum of the vapor pressure of both liquids above the mixture, where pA and pB are the vapor pressures of liquids A and B, respectively, above the mixture.
The temperature at which a pure organic substance is changed from the liquid phase to the gas phase is known as the boiling point. In a mixture of miscible liquids, the solution boils when the total vapor pressure of the solution equals the atmospheric pressure. Thus, a mixture's boiling point occurs at a temperature between the boiling points of the two pure liquids.
As the mixture is heated to its boiling point, some of the molecules escape the liquid phase and enter the gas phase. The temperature at which the first bubbles start to form in a miscible solution that is being heated is the bubble point temperature. In the case of a pure liquid, the bubble point is the same as the boiling point.
The gas phase is rich with the molecules of the more volatile component, or the component with the higher vapor pressure and lower boiling point. The number of molecules that evaporate increases as more heat is applied. Thus, the liquid phase is rich with molecules of the less volatile component, or the component with the lower vapor pressure and higher boiling point. The temperature at which the first liquid drops begin to form during distillation is known as the dew point temperature.
Vapor-Liquid Equilibrium Diagram
A vapor-liquid equilibrium diagram is a plot of the equilibrium temperature of the mole fraction of components of a binary mixture, with a curve drawn for the liquid phase and vapor phase. The x-axis represents the mole fraction of each of the two components in the mixture, and the y-axis is the temperature. These plots are available in the literature for common mixtures and can be used to identify boiling point temperatures of a mixture given the mole fraction of each component. They are also used to determine the composition of each phase in a distillation experiment.
Distillation is a separation technique that takes advantage of the boiling point properties of mixtures. To perform distillation, a miscible mixture of two liquids with a significant difference in boiling points — at least 20 °C — is heated. As the solution heats up and reaches the bubble point of the more volatile component, some molecules of the more volatile component transition into the gas phase and travel upward into the condenser. The condenser is a glass tube with separate inner and outer sections. The vapor travels into the inner section of the condenser, where it is condensed to liquid by the cold water flowing in the outer section of the condenser. This condensed vapor is called the distillate, and it is collected in a graduated cylinder or test tube.
As the distillation progresses, the temperature needed to boil the solution increases as the more volatile component boils off earlier. Thus, the composition of the distillate changes over time. Early on in the distillation, the distillate is rich with the more volatile component; in the middle of the distillation, the distillate contains a mix of the two components; and at the end of the distillation, the distillate is rich with the less volatile component.
The vapor-liquid equilibrium diagram shows the change in both the composition of the liquid in the flask and the distillate over the course of the distillation. There are two curves on the plot; the bottom curve describes the boiling point of the liquid in the flask as it relates to its composition, while the top curve describes the temperature of the vapor as it relates to its composition. By extension, the top curve describes the composition of the distillate.
A published vapor-liquid equilibrium diagram from the literature can be used to identify the composition of the liquid and vapor at a given temperature during the experiment. This can help determine when to end the distillation to separate the two components.
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- Felder, R.M., Rousseau, R.W. (2000). Elementary Principles of Chemical Processes. New York, NY: Wiley and Sons, Inc.