An ideal gas obeys Dalton s law that is, the total pressure is the sum of the partial pressures of the components. An ideal solution obeys Raoult s law that is, the partial pressure of the ith component in a solution is equal to the mole fraction of that component in the solution times the vapor pressure of pure component i. Use these relationships to relate the mole fraction of component 1 in the equilibrium vapor to its mole fraction in a two-component solution and relate the result to the ideal case of the copolymer composition equation. [Pg.429]

The ideal solution is a model fluid which serves as a standard to which teal solution behavior can be compared. Equation 151, which characterizes the [Pg.496]

Equations for the mixture properties of an ideal solution foUow immediately. [Pg.497]

If the parameters were to become increasingly correlated, the confidence ellipses would approach a 45 line and it would become impossible to determine a unique set of parameters. As discussed by Fabrics and Renon (1975), strong correlation is common for nearly ideal solutions whenever the two adjustable parameters represent energy differences. [Pg.104]

A fairly simple treatment, due to Guggenheim [80], is useful for the case of ideal or nearly ideal solutions. An abbreviated derivation begins with the free energy of a species [Pg.65]

Figure III-9u shows some data for fairly ideal solutions [81] where the solid lines 2, 3, and 6 show the attempt to fit the data with Eq. III-53 line 4 by taking ff as a purely empirical constant and line 5, by the use of the Hildebrand-Scott equation [81]. As a further example of solution behavior, Fig. III-9b shows some data on fused-salt mixtures [83] the dotted lines show the fit to Eq. III-SS. |

Condensed phases of systems of category 1 may exhibit essentially ideal solution behavior, very nonideal behavior, or nearly complete immiscibility. An illustration of some of the complexities of behavior is given in Fig. IV-20, as described in the legend. [Pg.140]

If an ideal solution is formed, then the actual molecular A is just Aav (and Aex = 0). The same result obtains if the components are completely immiscible as illustrated in Fig. IV-21 for a mixture of arachidic acid and a merocyanine dye [116]. These systems are usually distinguished through the mosaic structure seen in microscopic evaluation. [Pg.140]

The entropy of mixing of very similar substances, i.e. the ideal solution law, can be derived from the simplest of statistical considerations. It too is a limiting law, of which the most nearly perfect example is the entropy of mixing of two isotopic species. [Pg.374]

As the time separation 11 -, s approaches w tlie second tenn in this correlation vanishes and the remaining tenn is the equilibrium density-density correlation fomuila for an ideal solution. The second possibility is to consider a non-equilibrium initial state, c(r, t) = (r). The averaged solution is [26] [Pg.704]

At the outset it will be profitable to deal with an ideal solution possessing the following properties (i) there is no heat effect when the components are mixed (ii) there is no change in volume when the solution is formed from its components (iii) the vapour pressure of each component is equal to the vapour pressure of the pure substances multiplied by its mol fraction in the solution. The last-named property is merely an expression of Raoult s law, the vapour pressure of a substance is pro- [Pg.5]

Let us consider a mixture forming an ideal solution, that is, an ideal liquid pair. Applying Raoult s law to the two volatile components A and B, we have [Pg.6]

Solutions in water are designated as aqueous, and the concentration of the solution is expressed in terms of the number of moles of solvent associated with 1 mol of the solute. If no concentration is indicated, the solution is assumed to be dilute. The standard state for a solute in aqueous solution is taken as the hypothetical ideal solution of unit molality (indicated as std. state or ss). In this state [Pg.532]

Boiling points versus composition diagram for a near-ideal solution, showing the progress of a distillation. [Pg.209]

There is a parallel between the composition of a copolymer produced from a certain feed and the composition of a vapor in equilibrium with a two-component liquid mixture. The following example illustrates this parallel when the liquid mixture is an ideal solution and the vapor is an ideal gas. [Pg.429]

We define Fj to be the mole fraction of component 1 in the vapor phase and fi to be its mole fraction in the liquid solution. Here pj and p2 are the vapor pressures of components 1 and 2 in equihbrium with an ideal solution and Pi° and p2° are the vapor pressures of the two pure liquids. By Dalton s law, Plot Pi P2 Pi/Ptot these are ideal gases and p is propor- [Pg.430]

A solution which obeys Raoult s law over the full range of compositions is called an ideal solution (see Example 7.1). Equation (8.22) describes the relationship between activity and mole fraction for ideal solutions. In the case of nonideal solutions, the nonideality may be taken into account by introducing an activity coefficient as a factor of proportionality into Eq. (8.22). [Pg.511]

Comparing Eqs. (8.29) and (8.30) also leads to the conclusion expressed by Eq. (8.22) aj = Xj. Again we emphasize that this result applies only to ideal solutions, but the statistical approach gives us additional insights into the molecular properties associated with ideality in solutions [Pg.513]

Evaluate ASj for ideal solutions and for athermal solutions of polymers having n values of 50, 100, and 500 by solving Eqs. (8.28) and (8.38) at regular intervals of mole fraction. Compare these calculated quantities by preparing a suitable plot of the results. [Pg.518]

We express the calculated entropies of mixing in units of R. For ideal solutions the values of are evaluated directly from Eq. (8.28) [Pg.518]

Vapor pressure lowering. Equation (8.20) shows that for any component in a binary liquid solution aj = Pj/Pi°. For an ideal solution, this becomes [Pg.542]

Precisely the same substitutions and approximations that we wrote in Eq. (8.71) can be applied again to In aj. Thus for the case of dilute, ideal solutions, Eq. (8.78) becomes [Pg.545]

Calculate Apj, ATf, ATj, and n for solutions which are 1% by weight in benzene of solutes for which M = 10 and 10 . Assume that these solutions are adequately described by dilute ideal solution expressions. Consult a handbook for the physical properties of benzene. Comment on the significance of the results with respect to the feasibility of these various methods for the determination of M for solutes of high and low molecular weight. [Pg.547]

Equation (8.85) can be solved for Xj and the latter substituted into Eq. (8.83) to give an expression for H which applies to dilute-but not necessarily ideal—solutions [Pg.551]

At equilibrium, a component of a gas in contact with a liquid has identical fugacities in both the gas and liquid phase. For ideal solutions Raoult s law applies [Pg.19]

Mixtures. A number of mixtures of the hehum-group elements have been studied and their physical properties are found to show Httle deviation from ideal solution models. Data for mixtures of the hehum-group elements with each other and with other low molecular weight materials are available (68). A similar collection of gas—soHd data is also available (69). [Pg.9]

For ideal solutions (7 = 1) of a binary mixture, the equation simplifies to the following, which appHes whether the separation is by distillation or by any other technique. [Pg.84]

All other thermodynamic properties for an ideal solution foUow from this equation. In particular, differentiation with respect to temperature and pressure, followed by appHcation of equations for partial properties analogous to equations 62 and 63, leads to equations 191 and 192 [Pg.497]

The summabihty relation (eq. 122) appHed to the special case of an ideal solution is written as equation 194 [Pg.497]

See also in sourсe #XX -- [ Pg.80 , Pg.81 , Pg.82 , Pg.178 ]

See also in sourсe #XX -- [ Pg.5 ]

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