EAN13 for visual basic De nition I: gases in .NET Implement barcode 3 of 9 in .NET De nition I: gases

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8.2.2 De nition I: gases using none todraw none for web,windows applicationean 13 generating Rewriting (8.16) so t none none hat state is any (unsuperscripted) state and state is a standard state designated by superscript , we have. Microsoft Windows Official Website i i = RT ln fi fi (8.17). This is a simple gene ralization of (8.16), and hence a direct result of the definition of fugacity. We now define the activity of species i as.

ai = fi fi (8.18). where fi and fi are t he fugacities of i in the particular solution or state of interest to us and in some reference state at the same temperature. Thus. i i = RT ln ai (8.19). which is of course Eq uation (7.37), arrived at in a different way. We begin now to see why using the activity can be confusing.

In 7 (Equation 7.34). Fugacity and activity the state that i refe rs to is i as a pure liquid or solid, and in this case (8.16) i refers to i existing as a gas or perhaps fluid in some as yet undefined state, which might be, and is in fact, completely arbitrary. It will be interesting to see how it is that we can use i in a multicomponent, multiphase system, where at equilibrium i must be the same in every phase, while limited by the fact that we can only know i as the difference between it in whatever state it is and some other, arbitrary state which will be different for each kind of phase.

We will try to do this in the remainder of this chapter and the next chapter, where activities become part of the equilibrium constant.. 8.2.3 De nition II: solutes We use the same metho d we used in 7.5.3.

We need an expression for the derivative of with a concentration term, which we can integrate. The derivative of i with respect to the molality of i, mi , is i / mi T P mi , where mi means the molality of all solution components except i. If we expand i / mi T P mi by introducing Pi , the pressure on gaseous i which is, or might be, in equilibrium with solute i (whether or not there is such a gas phase is irrelevant), we get.

mi i Pi Pi mi (8.20). where i is the same i n the solution and in the vapor phase, where it can be called Gi (the vapor being assumed an ideal gas), so that i / Pi = Gi / Pi = Vi = RT/Pi , and where Pi / mi = Pi /mi is an expression of Henry s law ( 7.4.2), as mentioned earlier.

Combining all this we get. mi RT mi (8.21). for ideal (Henryan) s olutions. Integrating this equation between two values of molality, mi and mi , we get. = RT ln mi mi (8.22). showing the effect of changing solute concentration on the chemical potential, as we wanted. However, it is limited to ideal (Henryan) solutions. The relationship is generalized to any kind of solution by introducing a correction factor at each concentration.

Thus. = RT ln mi H mi (8.23). 8.2 Activity where H is the Henrya none for none n activity coefficient, and Equation (8.23) now refers to any real solution at a given temperature in which species i changes concentration, all other species remaining unchanged.1 Equation (8.

23) can be generalized and so made more useful by choosing a single concentration mi for all solutes. In choosing this concentration, we should realize that. H in the denominator will be different for all different solutes unless we choose some idealized state, and 2. it would be convenient to have the denominator H m disappear, i.e.

, be unity.. The only state which none for none satisfies these conditions and is equal to 1 molal for all solutes is the ideal (Henryan) one molal solution, and this is universally used as the standard state for solutes. Introducing superscript for the standard state, and dropping the now unnecessary superscript , we get.
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