Teaching Phase Equilibria

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Experimental data from Binary diagram activity C. Due to the nature of the thermodynamic model, activity coefficients are calculated for each single ion. The calculated single ion activity coefficients can be used for binary diagram activity mean ionic activity coefficients.

They do not represent the thermodynamic value of the single ion activity coefficient. According to many researcher, single ion activity coefficients can not be measured experimentally F. If the water activity was plotted as a function of the molality of salt, the result would be an almost straight line. In order to reflect the behavior of salts at high dilutiuon, the water activity is usually expressed as osmotic coefficient.

At high dilution, the water activity is close to 1 and the logarithm to the water activity is close to 0. By dividing the logarithm of the water activity by the number of moles of ions present at these conditions, the osmotic coefficient reflects the concentration dependence of binary diagram activity water activity in much more detail than the water activity itself does.

The differential heat of dilution is the enthalpy change by adding a differential amount of solvent to a solution. The integral heat of dilution to infinite dilution is the enthalpy change by diluting a salt solution from a certain molality to infinite dilution.

The integral heat of dilution to infinite dilution is the negative of he relative enthalpy. The relative enthalpy is the excess enthalpy relative to the unsymmetric standard state. In this standard state, activity coefficients tend to 1 as the concentration is decreased towards infinite dilution.

On the graph binary diagram activity the left, experimental values of the integral heat of dilution of ammonia solutions to infinite dilution are plotted together with values calculated with the Extended UNIQUAC model. The integral heat of solution is the enthalpy change by dissolving crystalline salt to form a solution of molality m. The differential heat of solution is the enthalpy change when a differential amount of salt is dissolved in a solution.

When the solute binary diagram activity a gas, the corresponding binary diagram activity integral heat of absorption and differential heat of absorption are used. The apparent molal heat capacity of a salt is the heat capacity of an aqueous solution of one mol of the salt minus the heat capacity of the corresponding amount of pure water.

The apparent molal binary diagram activity capacity therefore indicates the apparent effect of adding salt to water. In some cases the heat capacity decreases below that of pure water binary diagram activity other cases it increases.

C p is the heat capacity of the solution. Heat of solution The integral heat of solution is the enthalpy change by dissolving crystalline salt to form a solution of molality m. Apparent molal heat capacity The apparent molal heat capacity of a salt is the heat binary diagram activity of an aqueous solution of one mol of the salt minus the heat capacity of the corresponding amount of pure water.

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A complete isothermal phase diagram for a binary system must be constructed. Therefore, no feed composition is required. Only phase equilibria need to be calculated. However, we do not know in advance what type of phase equilibria may occur, and all possibilities must be checked. Vapour - Liquid equilibrium always occurs if the temperature is between the triple point temperature and the critical temperature of any one of the components. The system contains highly polar components, which means that a strongly non-ideal system is expected.

Pressures are low, so an activity coefficient model is acceptable. In this example, the Margules equation is used:. It is also possible to state that the vapour-liquid equilibrium will present an azeotropic behaviour, using the criterion defined in the textbook:.

Some help on nomenclature and tips to use this file can be found here. The calculations are performed as follows:. With all these results, we should draw the phase diagram cf. At this point, it can be noticed that the calculated isothermal phase diagram features a non-physical behaviour: When this kind of phase diagram is found, the reader should immediately consider that in reality the system features a liquid-liquid phase split that the calculation mode cannot make visible.

At the crossing of the two dew lines, it can be stated that the vapour phase is in equilibrium with two distinct liquid phases. This means that at higher pressures, a liquid-liquid phase split exists. In order to better understand this phase diagram, we should perform a stability analysis. This consists in examining the Gibbs energy of the liquid and the vapour phases. The liquid Gibbs energy is the sum of the ideal Gibbs energy of mixing and the excess Gibbs energy determined from the activity model.

The ideal Gibbs energy of mixing gives the lower symmetric curve and the excess Gibbs energy a positive asymmetric one. The sum is asymmetric and negative. The vapour Gibbs energy is written assuming that the vapour phase is ideal due to the low total pressure level. Note that since we have chosen the pure component liquid Gibbs energies for both components to be zero at the mixture pressure and temperature conditions, their vapour Gibbs energies are not zero.

We now need to calculate the Gibbs energy of the vapour in the reference state for both compounds. These values are calculated from the liquid-vapour equilibrium of pure compound:. We can see that assuming a null reference state of the liquid yields a reference state of the vapour related to the vapour pressure. So, the Gibbs energy of the vapour phase should be calculated as:. Now, we should carry on the analysis of the Gibbs energy based on the comparison of the liquid and the vapour curves.

Let us start at low pressure 40kPa. Figure 3a shows the Gibbs energies and figure 3b the Pxy diagram. The Gibbs energy of the vapour phase is lower than the Gibbs energy of the liquid phase and only the vapour phase is stable. For a slightly higher pressure 80 kPa , the Gibbs energy of the liquid phase and of the vapour phase cross figure 4a. For low water concentrations below 0. For high water concentration above 0.

Between these two regions i. It now becomes clear how two vapour- liquid zones appear two tangent plane regions at the same pressure, one at low water concentration between 0. For a pressure equal to kPa the crossing of the two dew lines figure 6a shows that the two tangent planes merge and are equal to the tangent to the Gibbs energy of the vapour phase. It can be stated that the vapour phase is in equilibrium with two distinct liquid phases.

This is the three phase pressure of the system. Finally, for higher pressures e. For a molar fraction of water less than 0. Figure 8 shows at Note that the liquid-liquid region is presented by a vertical slice. This is a result of the assumption that the activity coefficient is independent of pressure. As a first approximation, it is a good solution, but the graph cannot be extended to pressures larger than 1 MPa. Home Chapters Case studies Authors Order the book.

Vapour pressure predictions of methane using different formulas Quality evaluation of molar volume correlations Evaluation of the ideal gas heat capacity equations for n-pentane Quality evaluation of vapourisation enthalpy correlations Comparison of second virial coefficient calculation methods Comparison of critical points and acentric factor from different databases Use of the group contribution methods of Joback and Gani 3. Diesel fuel characterization 3.

Vapour pressures of di-alcohols 3. Find the parameters to fit the vapour pressure of ethyl oleate 3. Separation of n-butane from 1,3 butadiene at Draw the heteroazeotropic isothermal phase diagram of the binary mixture of water and butanol at Isothermal phase diagram using the Flory Huggins activity coefficient model 3.

Use of an equation of state for pure component vapour pressure calculations. Draw the isothermal phase diagram of the binary mixture of water and butanol at The vapour pressures of the pure components are: In this example, the Margules equation is used: See complete results in file xls: Figure 2 Liquid excess, mixture and total Gibbs energy as a function of the composition. Figure 3a Gibbs analysis at 40 kPa.

Figure 3b Phase diagram of the binary with a pressure of 40 kPa. Figure 4a Gibbs analyses at 80 kPa. Figure 4b Phase diagram of the binary with a pressure of 80 kPa. Figure 5a Gibbs analyses at kPa. Figure 5b Phase diagram of the binary with a pressure of kPa. Figure 6a Gibbs analyses at kPa. Figure 6b Phase diagram of the binary with a pressure of kPa. Figure 7 Gibbs analyses at kPa.