Volatility, relative volatility, boiling point

I. Volatility: Volatility is the ratio of the vapor pressure of a certain component in the gas phase to its molar fraction in the liquid phase in equilibrium with it, denoted by the symbol . For a two-component mixture consisting of A and B, we have: va = pa/Xa, vb = pb/Xb. Here, va and vb represent the volatilities of components A and B respectively ； pa, pb —— the partial pressures of components A and B in the gas phase at vapor-liquid equilibrium ； Xa, Xb —— the molar fractions of components A and B in the liquid phase at vapor-liquid equilibrium. In an ideal solution, the volatility of each component is numerically equal to its saturated vapor pressure. II. Relative Volatility: Relative volatility is the ratio of the volatilities of two components in a solution, denoted by the symbol α. The magnitude of the relative volatility α value indicates that the concentration ratio of the two components in the gas phase is a multiple of the concentration ratio in the liquid phase. Therefore, the α value can serve as an indicator of the ease with which a mixture can be separated by distillation. If α is greater than 1 and y > x, it indicates that the solution can be separated using distillation; the higher α is, the easier it is to separate component A ； If α=1, it indicates that the gas-phase components of the mixture are equal to those of the liquid phase ； Then ordinary distillation methods will be unable to separate this mixture ； α1. III. Average relative volatility αm: For a distillation column, since the x and y compositions as well as the temperatures vary in different sections of the column, α also changes. Therefore, for the entire distillation column, the average value of the relative volatility is generally used to represent it, denoted by the symbol αm. IV. Boiling point: The temperature at which, under a certain pressure, the saturated vapor pressure of a substance is equal to that pressure.

Not bad. Come and learn a bit, haha!

The separation principle behind distillation is the difference in volatility of various components under the same operating conditions. The greater the difference in volatility between the components, the easier it is for them to separate when a second phase is formed. The gas-liquid phase equilibrium relationship is the theoretical basis for analyzing the principles of distillation and calculating distillation equipment. I. Phase rule: In equation (7-1), F represents the degree of freedom, that is, the number of independent variables in the system ； ——Number of independent components ； ——Number of phases. In the formula, the number 2 indicates that in the external environment, only temperature and pressure are the two factors that affect the equilibrium state of the system. Since the degree of freedom for a two-component gas-liquid phase equilibrium system is 2, the equilibrium relationship can be expressed as a function of t-x(y) or x-y, or through a phase diagram, when operating at a constant pressure. II. Phase equilibrium relations for ideal systems (I) Definition of ideal systems (1) The liquid phase is an ideal solution, and the equilibrium relations obey Raoult’s law. (2) The gas phase is an ideal gas, obeying the ideal gas law and Dalton’s law of partial pressures. (II) Raoult’s law (7-2), (7-2a). In these equations, — represents the saturated vapor pressure of component i at the same temperature, in Pa ； x —— the molar fraction of component i. (III) Calculation of equilibrium composition: When the solution boils, the total pressure above the solution is given by equation (7-3). Then, equation (7-4) applies. If the gas phase is considered an ideal gas that obeys Dalton’s law of partial pressures, then equation (7-5) holds. Equation (7-5) represents the gas-liquid equilibrium equation for a two-component ideal solution; once the temperature and pressure of the system are known, the compositions of the gas and liquid phases at equilibrium can be determined using this equation. III. Phase diagram of gas-liquid equilibrium for two-component ideal solutions (I) Temperature-composition (t-x-y) phase diagram. Figure 7-1 shows the t-x-y phase diagram of benzene-toluene mixture. As illustrated in Figure (7-1), the following brief explanations are provided: (1) The endpoints of the curve represent the boiling points of the pure components; the left endpoint corresponds to the boiling point of the pure light component, while the right endpoint corresponds to the boiling point of the pure heavy component. (2) The curve above represents the saturated steam line, also known as the dew point line; the area above this line corresponds to the superheated steam region ； The curve below represents the saturated liquid line, also known as the bubble point line; the area below this line denotes the subcooled liquid region. (3) The region between the two curves is the gas-liquid coexistence zone, and the equilibrium relationship is represented by the horizontal line segment between the two curves. Clearly, only in the gas-liquid coexistence zone can a certain separation effect be achieved. (4) The boiling point of the mixture is not a fixed value, but changes depending on its composition. With the same composition, the bubble point (the temperature at which the first bubble appears) is not equal to the dew point (the temperature at which the first drop of liquid forms). (II) The x-y phase diagram can be drawn by reading several equilibrium data points from the t-x-y phase diagram. (As shown in Figure 7-2) Figure 7-2: x-y phase diagram of benzene-toluene mixture. The following is a brief explanation: (1) Any point D on the curve represents equilibrium between a liquid phase with composition x and a gas phase with composition y; it also indicates that point D has a definite state, and this curve is known as the equilibrium curve. (2) The diagonal lines in the figure are the lines where x=y, and they are provided for reference when consulting the chart. (3) When y > x, the equilibrium line lies above the diagonal; the farther the equilibrium line is from the diagonal, the easier it is to separate the solution. (4) When the total pressure changes little, the effect of external pressure on the equilibrium line can be ignored, but the t-x-y diagram changes significantly with pressure. IV. Volatility ν and Relative Volatility α (1) Volatility ν For a pure liquid, its volatility refers to its saturated vapor pressure at a certain temperature; whereas the volatility of components in a mixture can be expressed as: (7—6) (7—6a) Note: (1) For an ideal solution: , and similarly: . (2) Since volatility ν varies with temperature, making it inconvenient to use, the concept of relative volatility is adopted. (II) Relative volatility α (7–7) When the operating pressure is not high, the gas phase obeys Dalton’s law of partial pressures; thus, equation (7–8) holds. Equation (7-8) is known as the gas-liquid equilibrium relationship for ideal binary solutions, and it is widely used. Note: (1) Since , it changes in the same direction as temperature, therefore the value changes little and can be treated as a constant. (2) The magnitude of α can indicate the degree of separation. When α>1, that is, when y>x, distillation can be used for separation. Moreover, the larger α is, the further the equilibrium line deviates from the diagonal, making separation easier. (3) When α=1, it cannot be separated by ordinary distillation methods, but can be treated using special distillation techniques. (4) When the normal boiling point of a pure liquid is low, it indicates that its vapor pressure is high at the same temperature; therefore, the ease of volatilization of the two components in an ideal solution can also be indicated by their boiling points. The greater the difference in boiling points, the greater α is as well. V. Non-ideal solutions: The non-ideality of solutions arises from the fact that the forces between different molecules are not equal to those between identical molecules, that is. This is manifested in the deviation of its equilibrium vapor pressure from Raoult’s law, which can be positive or negative, with positive deviations being more common. (1) Positive deviation system: When <, the repulsive forces prevail; molecules can more easily leave the liquid surface and enter the gas phase. As a result, the bubble point is lower than that of an ideal solution. During mixing, the volume change ΔV > 0, and phenomena such as a constant boiling point, partial miscibility, or complete immiscibility may occur. For example, the ethanol-water system is a positive deviation system, and its phase diagram is shown in Figure 7-3. Figure 7-3 Phase diagram of the ethanol-water system at atmospheric pressure (II) Negative deviation systems: At such times, it is difficult for molecules to leave the liquid phase and enter the gas phase; therefore, the bubble point is higher than that of an ideal solution. During mixing, ΔV