Equilibrium in Gases

The constant Ke, which was not present in Equation 15-15, is a new constant (the ratio of the forward and reverse rate constants) called the equilibrium constant. Each of the quantities in brackets is the equilibrium concentration of the substance shown. At any given temperature, the value ofKe remains constant no matter whether you start with A, B, and C or with M and N, and regardless of the proportions in which they are mixed. Ke varies with temperature because k, and kT vary with temperature, but not by exactly the same 

Special cases of chemical equilibrium in solution are considered in several later chapters, so here we deal only with gaseous reactions. When concentrations are expressed in moles/liter (as they usually are in solution) in Equation 16-1, the equilibrium constant is designated as Kc, whereas for concentrations expressed as partial pressures in atm (as they usually are for gases) the equilibrium constant is designated as Kt . For gaseous equilibria, then, Equation 16-1 becomes 

The relationship between K,. and K is easily established by means of the ideal gas law because 

Substitution of P IRTYor each molar concentration in Equation 16-1 gives 

Values of the equilibrium constant may be obtained by allowing the reactants to come to equilibrium at a given temperature, analyzing the equilibrium mixture, and then substituting the equilibrium concentrations into Equation 16-2. 

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In the section on chemical equilibrium in gases we introduced a magnitude called the molecular chemical potential of a component ... 

Types of Phases in Binary Systems.—A two-component system, like a system with a single component, can exist in solid, liquid, and gaseous phases. The gas phase, of course, is perfectly simple it is simply a mixture of the gas phases of the two components. Our treatment of chemical equilibrium in gases, in Chap. X, includes this as a special case. Any two gases can mix in any proportions in a stable way, so long as they cannot react chemically, and we shall assume only the simple case where the two components do not react in the gaseous phase. 

A mixture of electrons, ions, and atoms forms a system similar to that which we considered in Chap. X, dealing with chemical equilibrium in gases. Equilibrium is determined, as it was there, by the mass action law. This law can be derived by balancing the rates of direct and inverse collisions, but it can also be derived from thermodynamics, and the equilibrium constant can be found from the heat of reaction and the chemical constants of the various particles concerned. The heats of reaction can be found from the various ionization potentials, quantities susceptible of independent measurement, and the chemical constants are determined essentially as in Chap. VIII. Thus there are no new principles involved in studying the equilibrium of atoms, electrons, and ions, and we shall merely give a qualitative discussion in this section, the statements being equivalent to mathematical results which can be established immediately from the methods of Chap. X. 

In Chap. XX, Sec. 3, we spoke about the detachment of electrons from atoms, and in Sec. 4 of that chapter we took up the resulting chemical equilibrium, similar to chemical equilibrium in gases. But electrons can be detached not only from atoms but from matter in bulk, and particularly from metals. If the detachment is produced by heat, we have thermionic emission, a process very similar to the vaporization of a solid to form a gas. The equilibrium concerned is very similar to the equilibrium in problems of vapor pressure, and the equilibrium relations can be used, along with a direct calculation of the rate of condensation, to find the rate of thermionic emission. In connection with the equilibrium of a metal and its electron gas, we can find relations between the electrical potentials near two metals in an electron gas and derive information about the so-called Volta difference of potential, or contact potential difference, between the metals. We begin by a kinetic discussion of the collisions of electrons with metallic surfaces. 

Under mechanical equilibrium on a molecular scale, the exchange of momentum proceeds faster than the exchange of mass and heat for liquids. On the other hand, the molecular exchange of momentum, matter, and heat is on the same order as gases. The rate of exchange of transport processes is measured by the Schmidt number Sc and the Prandtl number Pr. Usually, the assumption of mechanical equilibrium in gases for heat and mass transfer is not reliable. 

Equilibrium in gases. Applications. In dealing with applications, we come now to the methods by which we may determine the quantity of each substance present in a gaseous mixture in the state of chemical equilibrium, or more generally in any homogeneous mixture. Two ways are open. 

Chemical equilibrium in gases We may now turn to the further consideration of gaseous equilibria. Thermodynamic principles lead to the equations... 

If the reactants A and B were truly in equilibrium with an A-B complex, the statistical mechanical theory of chemical equilibrium in gases could be applied. The number of such systems would be... 

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