Equilibrium constant in terms of pressures

We will see functions like the one occurring under the logarithm operator quite often. For efficiency, this is generally written as In(Products)/(Reactants), where (Products) and (Reactants) denote the partial pressures of the species relative to the standard state pressure raised to a power that is equal to the stoichiometric coefficients. Kp is the equilibrium constant in terms of pressures. Since all pressures are in the same units, Rp is dimensionless. Note that in some literature there may be a combination of some power of P with Kp to obtain an equilibrium constant with pressure units. In this case. 

The link between Gibbs free energy and equilibrium constant can be appreciated qualitatively at this stage. The equilibrium constant in terms of pressures is given by ... 

What is the proper expression for the equilibrium constant, in terms of pressures, for the following chemical equilibrium Assume that conditions are near standard pressures. 

These data can be used to obtain the value of the equilibrium constant at any temperature and this in turn can be used to calculate the degree of dissociation through the equation for the conceiiuation dependence of the constant on the two species for a single element, die monomer and the dimer, which coexist. Considering one mole of the diatomic species which dissociates to produce 2x moles of the monatomic gas, leaving (1 — jc) moles of the diatomic gas and producing a resultant total number of moles of (1 +jc) at a total pressure of P atmos, the equation for the equilibrium constant in terms of these conceiiU ations is... 

We have seen that the value of an equilibrium constant tells us whether we can expect a high or low concentration of product at equilibrium. The constant also allows us to predict the spontaneous direction of reaction in a reaction mixture of any composition. In the following three sections, we see how to express the equilibrium constant in terms of molar concentrations of gases as well as partial pressures and how to predict the equilibrium composition of a reaction mixture, given the value of the equilibrium constant for the reaction. Such information is critical to the success of many industrial processes and is fundamental to the discussion of acids and bases in the following chapters. 

We can define the left side of Equation 10.20 as AG, where the process described is one mole of reaction at constant chemical potential for reactants and products, that is, for a system large enough so that one mole of reaction can take place in the mixture without any significant change in composition or chemical potential, an infinite-copy model. As AG is a constant at constant temperature, the quantity in brackets is also a constant at constant temperamre, and, in particular, independent of the total pressure and the initial composition of the system. We therefore designate the quantity in brackets as Kp, which is the equilibrium constant in terms of partial pressures for a... 

The equilibrium constant of the above reaction in terms of partial pressures (Kp) is 6 at 167 °C. What is the equilibrium constant in terms of concentration (K ) ... 

We can rewrite this equation as Kc = [C02], where the new equilibrium constant is Kc = "fCc"[CaCO3]/[CaO]. The analogous equilibrium equation in terms of pressure is Kp = Pco2 where Pcc>2 is the equilibrium pressure of C02 in atmospheres ... 

A g,is is the change in the number of moles of gas in the reaction and Kx is the equilibrium constant in terms of mole fractions of gaseous reactants and products, which can be seen to be a function of both temperature and pressure ... 

In a gaseous reaction, the partial pressure ip) of the gas is proportional to its molecular concentration. Therefore, the equilibrium constant in terms of partial pressures, will be... 

These quantities are not in general dimensionless. One can define in an analogous way an equilibrium constant in terms of fugacity Kf, etc. At low pressures Kp is approximately related to K by the equation K Kp/(p )lv, and similarly in dilute solutions Kc is approximately related to K by K Kc/(c )lv however, the exact relations involve fugacity coefficients or activity coefficients [24]. 

This step was verified by isolating anhydrous HCIO4 as the only vapor phase species during the early phases of the reaction. The equilibrium constants in terms of the pressure of HCIO4 were determined as a function of temperature and are given by the following expression. 

The equilibrium constant actually involves a ratio of partial pressures, since the stoichiometry coefficients of the reagents are negative. Eq. (2.9.5b) is in the standard form used to represent equilibrium constants in terms of composition variables. 

Kp - chemical equilibrium constant in terms of partial pressure M - symbol of optimal reaction assemblage 0PY - observed peak yield P - pressure... 

Although we commonly write equilibrium quotients and equilibrium constants in terms of molar concentrations, any concentration-like term can be used, including mole fraction and molality. Sometimes the symbols Kc, Kx, and Km are used to denote these forms of the equilibrium constant. We will not make use of the latter two in this course, but there is one other formulation that is important for you to know, and is commonly preferred when the reaction components are gases. The concentration of a gaseous substance in moles (n) per liter varies directly with its partial pressure ... 

Alternatively, we can express the equilibrium constant in terms of the pressure of CI2 ... 

The pressure of a gas is directly proportional to its concentration (n/V). For reactions in which all substances that appear in the equilibrium constant expression are gases, we sometimes prefer to express the equilibrium constant in terms of partial pressures in atmospheres (Kp) rather than in terms of concentrations (Kf). 

According to the Le Chatelier principle, high pressures favor the association reactions, which are accompanied by a decrease in the number of moles in the reaction mixture as the product molecules are formed. Thus the formation of higher-molecular-weight products is more favorable at high pressures. To demonstrate this 127], let us consider the reaction aA + bB cC + dD. The equilibrium constant in terms of partial fugacities is... 

Both the symbols K and are used commonly for an equilibrium constant in terms of concentrations. We will always use K in this book. The symbol Kp represents an equilibrium constant in terms of partial pressures. 

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