Equilibrium ideal liquid solution

EQUILIBRIUM BETWEEN A PURE SOLID AND AN IDEAL LIQUID SOLUTION... 

EQUILIBRIUM BETWEEN A PURE SOLID AND AN IDEAL LIQUID SOLUTION 329 is a function of both pressure and mole fraction. Thus,... 

In Chapter 13 we discussed briefly the solid-liquid equilibrium diagram of a feldspar. Feldspar is an ideal, solid solution of albite (NaAlSiaOg) and anorthite (CaAlSi20g) in the solid state as well as an ideal, liquid solution of the same components in the molten state. The relationships that we have developed in this chapter permit us to interpret the feldspar phase diagram (Figure 13.4) in a quantitative way. 

We define the standard state of a liquid as ay = 1 and for gases as an ideal gas pressure of 1 bar, Pj = I- For ideal liquid solutions (activity coefficients of unity), we write ay = Cy so at chemical equilibrium... 

Ideal Liquid Solutions, Two limiting laws of solution thermodynamics that are widely employed are Henry s law and Raoult s law, which represent vapor—liquid partitioning behavior in the concentration extremes. These laws are used frequendy in equilibrium problems and apply to a variety of real systems (10). 

In Sec. 10.5 we treated dew- and bubble-point calculations for multicomponent systems that obey Raoult s law [Eq. (10.16)], an equation valid for low-pressure VLE when an ideal-liquid solution is in equilibrium with an ideal gas. Calculations for the general case are carried out in exactly the same way as for Raoult s law,... 

A gas-liquid system in which the vapor-liquid equilibrium relationship for every volatile species is either Raoult s law or Henry s law is said to exhibit ideal solution behavior. An ideal liquid solution is a mixture of liquids that exhibits ideal solution behavior at equilibrium. 

The pressure at which the first vapor forms when a liquid is decompressed at a constant temperature is the bubble-point pressure of the liquid at the given temperature. Equation 6.4-4 can be used to determine such a pressure for an ideal liquid solution at a specific temperature, and the mole fractions in the vapor in equilibrium with the liquid can then be determined as... 

As discussed in Chapter 4, the vapor-liquid equilibrium between an ideal gas and an ideal liquid solution is governed by Raoult s law ... 

The reaction mixture is an ideal liquid solution (constant density) at all temperatures. (a) Assuming that AH° is constant, plot a curve of the equilibrium conversion vs temperature from 0 to 100°C. (b) If the forward-rate constant is... 

The above characterization of ideal solutions does not require the fluid to behave as an ideal gas. In fact, certain liquid mixtures behave as ideal solutions, but they obviously do not obey the ideal gas law. In a mixture forming a vapor phase and a liquid phase at equilibrium with each other, either one of the phases, or both phases, may approach ideal solution behavior. Ideal solution behavior is approached at low pressures and usually with mixtures of chemically similar components. Referring to Equation 1.24, if the vapor phase is assumed to behave as an ideal gas, 0/ = 1, and the left-hand side of the equation reduces to T , where P is the total pressure. Moreover, for ideal liquid solutions,... 

If two or more liquid species form an ideal liquid solution with an equilibrium vapor mixture, the partial pressure p,- of each component in the vapor is proportional to its mole fraction in the liquid x,. The proportionality constant is the vapor pressure Pf of the pure species at the system temperature, and the relationship is named Raoult s law in honor of the French scientist who developed it. 

As a generalization of the behavior of real solutions the ideal solution follows Raoult s law over the entire range of concentration. Taking this definition of an ideal liquid solution and combining it with the general equilibrium condition leads to the analytical expression of the chemical potential of the solvent in an ideal solution. If the solution is in equilibrium with vapor, the requirement of the second law is that the chemical potential of the solvent have the same value in the solution as in the vapor, or... 

A gaseous mixture of two substances under a total pressure of 0.8 atm is in equilibrium with an ideal liquid solution. The mole fraction of substance A is 0.5 in the vapor phase and 0.2 in the liquid phase. What are the vapor pressures of the two pure liquids ... 

We next consider expressions for the fugacities of the vapor in equiUbrium with the ideal liquid solution. At equilibrium between liquid and vapor... 

When an ideal liquid solution containing two volatile components is in equilibrium with its vapor, the more volatile component will he relatively richer in the vapor. This fact forms the basis of distillation, a technique used to separate (or partially separate) mixtures containing volatile components. Distillation is the procedure by which a moonshiner obtains whiskey using a still and by which petrochemical plants achieve the separation of crude petroleum into gasoline, diesel fuel, lubricating oil, and so forth ( FIGURE 13.22). Distillation is also used routinely on a small scale in the laboratory. 

The van t Hoff equation for the temperature of equilibrium between an ideal liquid solution of mole fractional and pure crystalline component 1, T is... 

When the gas mixture in equilibrium with an ideal liquid solution also follows the ideal-gas law, the partial pressure p of a solute gas A equals the product of its vapor pressure p at the same temperature and its mole fraction in the solution x. This is Raoult s law,... 

An ideal liquid solution has two volatile components. In the vapor in equilibrium with the solution, the mole fractions of the components are (a) both 0.50 (b) equal, but not necessarily 0.50 (c) not very... 

This illustrates the statement made earlier that the most convenient choice of standard state may depend on the problem. For gas-phase problems involving A, it is convenient to choose the standard state for A as an ideal gas at 1 atm pressure. But, where the vapor of A is in equilibrium with a solution, it is sometimes convenient to choose the standard state as the pure liquid. Since /a is the same for the pure liquid and the vapor in equilibrium... 

Equation 1 implies that solubility is independent of solvent type, and is only a function of the equilibrium temperature and characteristic properties of the solid phase. In real systems the effect of non-ideality in the liquid phase can significantly impact the solubility. This effect can be correlated using an activity coefficient (y) to account for the non-ideal liquid phase interactions between the dissolved solute and solvent molecules. Eq. 1. then becomes [7,8] ... 

Equation (1) may be applied to the equilibrium between vapor and liquid of a pure substance (X = vapor pressure) or to the equilibrium between an ideal dilute solution and the pure phase of a solute X = solubility) or to the equilibrium of a chemical reaction (X = equilibrium constant). 

The aqueous solubility of a gaseous compound is commonly reported for 1 bar (or 1 atm = 1.013 bar) partial pressure of the pure compound. One of the few exceptions is the solubility of 02 which is generally given for equilibrium with the gas at 0.21 bar, since this value is appropriate for the earth s atmosphere at sea level. As discussed in Chapter 3, the partial pressure of a compound in the gas phase (ideal gas) at equilibrium above a liquid solution is identical to the fugacity of the compound in the solution (see Fig. 3.9d). Therefore equating fugacity expressions for a compound in both the gas phase and an equilibrated aqueous solution phase, we have ... 

Assuming ideal gas behavior, the equilibrium partial pressure, ph of a compound above a liquid solution or liquid mixture is a direct measure of the fugacity, fu, of that compound in the liquid phase (see Fig. 3.9 and Eq. 3-33). 

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