Perfect gas mixture

In a mixture of gases whether they are perfect or not, we define the partial pressure pi of component i as the product of the total pressure and the mole fraction of i in the mixture  

We say that a mixture of gases in volume V at temperature T, is perfect if the free energy F is equal to the sum of the free energies which the separate constituents would have if each were confined alone in the same volume at the same temperature. We can then apply equation (10.12) to obtain 

The partial pressure of i is thus equal to the pressure which would be exerted by % moles of pure i in the same volume, and at the same temperature. 

If we employ the molar concentration, Ci—UilV, this expression can be written 

Formula (10.26) gives the free energy of the mixture in terms of the variables T, V,. .. Uq. All the other properties of the system can therefore be derived from this equation cf. chap. IV, 4). Thus from (c/. 4.29) 

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Start with a basis of 1 lb-mole of the natural gas at T = 80°F = 540°R and P = 40 psig = 54.7 psia. The volume percent and mole percent compositions are identical for a perfect-gas mixture. 

A consequence of mechanical equilibrium in a perfect gas mixture is that the pressures developed by each species sum to give the mixture pressure. This is known as Dalton s law, with the species pressure called the partial pressure, / , ... 

Subtracting Equation (3.47) from Equation (3.42) gives, for a perfect gas mixture with uniform properties in the control volume,... 

Equation 2.63 is valid for any homogeneous or heterogeneous reaction. The only difference is in the definition of activities. For a species in a perfect gas-phase mixture a = pi/p°, where pi is the partial pressure of species i andp° is the standard pressure (1 bar). For a real gas-phase mixture a =f/p°, where is the fugacity of i. The fugacity concept was developed for the same reason as the activity to extend to real gases the formalism used to describe perfect gas mixtures. In the low total pressure limit (p -> 0), fi = pi. 

The differences between the gas-phase and solution algorithms appear from this point on. To derive equation 3.3, the perfect gas mixture was assumed, and A related to an equilibrium constant given in terms of the partial pressures of the reactants and the activated complex [1], This Kp is then easily connected with A H° and A .S ". As stated, the perfect gas model is a good assumption for handling the results of the large majority of gas-phase kinetic experiments. 

Written in cylindrical coordinates and specialized for a perfect-gas mixture the conservation laws are ... 

Therefore, the partial pressure of a component i in n mol of a perfect gas mixture with a total pressure p is ... 

Mole per cent or mole fraction, weight per cent or weight fraction, and volume per cent or volume fraction may be employed to designate the composition of a solution. Avogadro s Law is not applicable to liquids, and equal volumes of different liquids do not contain the same number of molecules. Consequently, mole per cent and volume per cent are not equivalent in liquid solutions as they were in perfect-gas mixtures. To convert mole per cent to weight per cent the procedure is identical with that previously described for gases. To calculate the volume per cent of a liquid solution from the mole per cent or weight per cent the densities of the pure components must be known. 

We see then that a perfect gas mixture is an ideal system as defined in chapter VII 1. The properties established generally in that chapter can be applied directly to the present case. Perfect gas mixtures differ from other ideal systems in that the function /x (P, p) depends upon pressure in the simple logarithmic manner given in (10.36),... 

We can now make use of the above expressions for chemical potentials to calculate the affinity of a reaction in a perfect gas mixture, and to deduce the conditions for chemical equilibrium. 

I Perfect gas mixtures are ideal over the whole concentration range so that = A . 

The partial molar quantities in a perfect gas mixture are given by... 

For a perfect gas mixture all the activity coefficients are unity the values of 1 - y or In may be used as measures of deviations from the perfect gas laws. 

Equation (15.61) shows that this condition is always satisfied in an ideal system so that in a perfect gas mixture, stable equilibrium with respect to changes at constant T, V, also implies stabihty at constant T, p,... 

If the vapour does not behave as a perfect gas mixture, then we must employ the fugacity p instead of the partial pressure p c/. for example, J. N. Bronsted and J. G. Koefoed, Det. Kgl. Danske Vid. Selsk. (Mat-fys) 22, part 17 (194G). 

This equation between the partial pressures is valid no matter what are the deviations from ideal behaviour, and depends only on the assumptions that the gas phases consist of a perfect gas mixture, and that the partial molar volumes of the components in the solution are negligible,t (c/. 1). 

With the additional assumptions that the latent heats are independent of temperature, and that the vapour phase is a perfect gas mixture we obtain ... 

Furthermore, if the vapour phase behaves as a perfect gas mixture yf and y are both unity and the equations can be solved for x and xf to give... 

By definition all gases in a perfect gas mixture obey the perfect gas law such that PVf = RT Lfij, where is the total volume and En denotes the sum of the moles of gases within Vp Also, for a perfect gas... 

Describe perfect gases, perfect gas mixtures, and partial pressure. How does Henry s law apply to gas solubilities ... 

Consider a perfect gas mixture at constant temperature and pressure (therefore the molar concentration C is constant and there is no bulk motion of the gas) in which a mole fraction gradient exists in one direction as shown in Fig. 2.3-1. Molecules within some dismace a, which is proportional to the mean free path of the gas (A), can cross the i = plane. The net molar flux from left to right across the z = 0 plane would be proportions to the product of the menu molecular speed u. and the difference between the average concentration on the left and on the right. 

For Ihe case of a perfect gas mixture whose molar concentration is independent of composition, the continuity and species balance equations reduce to the slataments... 

To account for the deviation of an actual mixture from a perfect gas mixture, it has been demonstrated that the virtual values of the partial molar enthalpies H( may be used in lieu of the partial molar enthalpies / , to obtain the correct enthalpy of the mixture,13 that is,... 

The path used for evaluation of the thermodynamic functions of mixtures in terms of temperature, pressure, and composition is shown in Fig. 14-3. The standard state of each component is taken to be the pure component in the perfect gas state T0 and P0. Again, in the limit as P is allowed to approach zero, the container at P and T (see Fig. 14-3) becomes a convertor in the sense that a perfect gas mixture enters and an actual gas mixture leaves. The resulting expressions for the thermodynamic functions are presented in Table 14-1. 

The composition of the liquid phase can have a profound effect on the K value for a given component of a mixture. In fact, experimental evidence shows that large variations in the ICs result from changes in the liquid compositions at pressures so low that the vapor not only forms an ideal solution but may also behave as a perfect gas mixture. Thus, for many systems, Eq. (14-37) reduces to... 

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