Ideal gases at equilibrium

Chemical Potentials for a Mixture of Ideal Gases at Equilibrium... 

Recall from Section 12.1 that a true reversible process is an idealization it is a process in which the system proceeds with infinitesimal speed through a series of equilibrium states. The external pressure therefore, can never differ by more than an infinitesimal amount from the pressure, P, of the gas itself. The heat, work, energy, and enthalpy changes for ideal gases at constant volume (called isochoric processes) and at constant pressure (isobaric processes) have already been considered. This section examines isothermal (constant temperature) and adiabatic (q = 0) processes. 

Rate constants of heterogeneous reactions are usually represented in the three-parameter form discussed above. However, this form has a clear physical sense only for reactions in ideal gases at a strictly kept equilibrium Maxwell-Boltzman distribution. Despite several attempts to adopt transition-state theory to heterogeneous reactions, and to those proceeding in adsorbed layers in particular (e.g., Krylov et al., 1972 Zhdanov et al., 1988), its applicability in these cases is doubtful. 

Intcrmolecular bonds arc the weak interactions that hold liquids and solids together. Atoms and molecules repel each other when they are too close, attract when they are further apart, and are stable at the equilibrium bond length in between. Intcrmolecular attractions make the pressures of van der Waals gases lower than the pressures of ideal gases at low densities. To a first approximation, intcrmolecular attractions can be explained as electrostatic interactions between charge distributions, due to internal charge asymmetries in molecules, to the freedom of molecules to rotate, or to molecular polarizabilities. 

Example 12.1 Estimate the chemical equilibrium composition of a gaseous mixture of -butane and isobutane at 298.15 K and 1 bar, based on direct minimization of Gibbs energy. Assume that -butane and isobutane form an ideal solution of ideal gases at this T and P. 

Example 12.5 For ideal gases at 25°C = 298 K, the calculated equilibrium constant (based on Table A.8) for Reaction 12.Z is K=29.6. If water, ethylene, and ethanol are in equilibrium at 1 bar and 298 K with the same feed ratios as in Example 12.4, what are the concentrations of reactants and products ... 

Within experimental error, Guldberg and Waage obtained the same value of K whatever the initial composition of the reaction mixture. This remarkable result shows that K is characteristic of the composition of the reaction mixture at equilibrium at a given temperature. It is known as the equilibrium constant for the reaction. The law of mass action summarizes this result it states that, at equilibrium, the composition of the reaction mixture can be expressed in terms of an equilibrium constant where, for any reaction between gases that can be treated as ideal,... 

The feed stream consists of 60 mole percent hydrogen, 20% nitrogen, and 20% argon. Calculate the composition of the exit gases, assuming equilibrium is achieved in the reactor. Make sure that you take deviations from the ideal gas law into account. The equilibrium constant expressed in terms of activities relative to standard states at 1 atm may be assumed to be equal to 8.75 x 10 3. The fugacity of pure H2 at 450 °C and 101.3 MPa may be assumed to be equal to 136.8 MPa. 

Here AGr° is the Gibbs free energy change in the ideal gas phase reaction system when all the gases are in their respective standard states. The equilibrium constant Kp is given in terms of the partial pressures at equilibrium by... 

The superscript 0 indicates the standard state, which is taken at equilibrium temperature, standard pressure P° and standard composition x. The standard pressure is usally taken as 1 bar or 10+5 Pa.. For liquid and solid components the standard state is usually the pure liquid or solid component, for gases the standard state is the pure gaseous component in the ideal gas state at P° and T. So, for a gaseous component f°(P°,T,x0) = P°. 

The mathematical relationship between pressure, volume, temperature, and number of moles of a gas at equilibrium is given by its equation of state. The most well-known equation of state is the ideal gas law, PV=RT, where P = the pressure of the gas, V = its molar volume (V/n), n = the number of moles of gas, R = the ideal gas constant, and T = the temperature of the gas. Many modifications of the ideal gas equation of state have been proposed so that the equation can fit P-V-T data of real gases. One of these equations is called the virial equation of state which accounts for nonideality by utilizing a power series in p, the density. 

PI5.1 Show that in reaction (15.1), assuming ideal behavior of the gases, the maximum (equilibrium) conversion of nitrogen and hydrogen into ammonia at a given temperature and total pressure, is obtained when the reacting gases are in the proportion of 1 to 3. (To do so, suppose that the N2 and H2 molecules are present in the ratio of 1 to r, with x as the mole fraction of NH3 present at equilibrium. Then express Kp in terms of mole fractions and the total pressure, and find the condition that makes dx/dr equal to zero.)... 

The number of isomers in an isomer group is represented by Njso. At chemical equilibrium, all of the isomers have the same chemical potential, and this chemical potential is represented by iso. The amount of an isomer group is represented by niso = En . For a group of gaseous isomers at equilibrium, the chemical potential of the isomer group in a mixture of ideal gases is given by... 

Historically, the state of reaction at chemical equilibrium was evaluated for fairly simple reactions, with only a few species, from the "Law of Mass Action. 1 In recent years, high-temperature reactions, including many possible species (as many as 20 or more), have become of interest and newer techniques suitable for numerical solution on high-speed digital computers have been developed.2 Initially, we will discuss chemical equilibrium from the vantage point of the "Law of Mass Action." It states that the rate at which a chemical reaction proceeds is proportional to the "active" masses of the reacting substances. The active mass for a mixture of ideal gases is the number density of each react-... 

If the system initially contains 6 mol HC1 for each mole of oxygen, what is the composition of system at equilibrium Assume ideal gases. 

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