Equilibrium Constants at

The equilibrium constant at constant temperature is directly related to the maximum energy, called the free energy AG. which is obtainable from a reaction, the relationship being... 

Equimolal proportions of the reactants are used. Thermodynamic data at 298 K are tabulated. The specific heats are averages. Find (1) the enthalpy change of reaction at 298 and 573 K (2) equilibrium constant at 298 and 573 K (3) fractional conversion at 573 K. 

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... 

Graphs giving the vapor-solid equilibrium constants at various temperatures and pressures are given in Figures 4-1 through 4-4. For nitrogen and components heavier than butane, the equilibrium constant is taken as infinity. 

The equilibrium constants determined by Brandts at several temperatures for the denaturation of chymotrypsinogen (see previous Example) can be used to calculate the free energy changes for the denaturation process. For example, the equilibrium constant at 54.5°C is 0.27, so... 

The equilibrium constant at room temperature corresponds to pKi, = 4.74 and implies that a 1 molar aqueous solution of NH3 contains only 4.25 mmol 1 of NH4+ (or OH ). Such solutions do not contain the undissociated molecule NH4OH, though weakly bonded hydrates have been isolated at low temperature ... 

The coefficients a, b, and c for hydrogenation were obtained from the literature [13] and those for nitrile and hydrogenated nitrile were calculated from a group contribution method reported by Rihani and Doraiswami [14]. All the necessary data are listed in Table 1. The integration constant / and AHq have been calculated by incorporating the values of AG° and AH° at 298 K in Eqs. (3) and (4). The equilibrium constant at atmospheric pressure and various temperature has been calculated according to the relationship ... 

Kp = equilibrium constant at a given temperature X = fraction paraffin converted to mono-olefms P = reaction pressure in atmospheres... 

The value for the equilibrium constant at 25°C given in the last column of Table 10 is 4.52 X 10 7. Multiplying logoff by RT, we find for AF° the value 8683 cal/mole. The heat of dissociation has been measured calorimetrically1 and found to be 1843 cal/mole. By subtraction we find... 

Values for the equilibrium constant at temperatures between 0 and 60°C were included in Table 9. From the value at 25° we find —log,K = 23.8. Multiplying by RT, we obtain AF° = 13,983 cal/mole. From the temperature coefficient of AF° we obtain for the heat of dissociation the value AH° = 3500 cal. Hence... 

To illustrate how this equation is used, let us apply it to calculate the equilibrium constant at 100°C for the system... 

K is the equilibrium constant at a particular temperature and is usually known as the ionisation constant or dissociation constant. If 1 mole of the electrolyte is dissolved in Vlitres of solution (V = l/c, where c is the concentration in moles per litre), and if a is the degree of ionisation at equilibrium, then the amount of un-ionised electrolyte will be (1 — a) moles, and the amount of each of the ions will be a moles. The concentration of un-ionised acetic acid will therefore be (1 — a)/ V, and the concentration of each of the ions cl/V. Substituting in the equilibrium equation, we obtain the expression ... 

The effect of temperature on the equilibrium composition arises from the dependence of the equilibrium constant on the temperature. The relation between the equilibrium constant and the standard Gibbs free energy of reaction in Eq. 8 applies to any temperature. Therefore, we ought to be able to use it to relate the equilibrium constant at one temperature to its value at another temperature. 

EXAMPLE 9.13 Predicting the value of an equilibrium constant at a different temperature... 

Calculate the equilibrium constant at 25°C for each of the following reactions, using data in Appendix 2A ... 

These four equations are perfectly adequate for equilibrium calculations although they are nonsense with respect to mechanism. Table 7.2 has the data needed to calculate the four equilibrium constants at the standard state of 298.15 K and 1 bar. Table 7.1 has the necessary data to correct for temperature. The composition at equilibrium can be found using the reaction coordinate method or the method of false transients. The four chemical equations are not unique since various members of the set can be combined algebraically without reducing the dimensionality, M=4. Various equivalent sets can be derived, but none can even approximate a plausible mechanism since one of the starting materials, oxygen, has been assumed to be absent at equilibrium. Thermodynamics provides the destination but not the route. 

The experimental results imply that the main reaction (eq. 1) is an equilibrium reaction and first order in nitrogen monoxide and iron chelate. The equilibrium constants at various temperatures were determined by modeling the experimental NO absorption profile using the penetration theory for mass transfer. Parameter estimation using well established numerical methods (Newton-Raphson) allowed detrxmination of the equilibrium constant (Fig. 1) as well as the ratio of the diffusion coefficients of Fe"(EDTA) andNO[3]. 

The relationship between the equilibrium constant and free energy provides a connection between thermodynamics and equilibrium constants. At equilibrium, A G = 0 and Q — Teq. We can substitute these... 

Figure 7.17 shows fits of this equation along with optimized values for the equilibrium constants at 400 °C. 

Both the integrated and differential forms show that a plot of log K against 1/T should yield a straight line with a slope equal to -AH0/2.303 R. Thus, a measured value of AH0 can be employed to calculate the equilibrium constant at temperatures other than that for which it is given. Conversely, it is possible to use measurements of the equilibrium constant at a number of temperatures to evaluate the standard enthalpy change for the reaction. 

Table 6.3 Variation of equilibrium composition with AG° and the equilibrium constant at 298 K.

In this expression, Ka is the equilibrium constant at T), and Ka2 is the equilibrium constant at l2. AH0 is the standard heat of reaction (kJ) when all the reactants and products are at standard state, given by ... 

Equation 6.39 can be used to estimate the equilibrium constant at the required temperature given enthalpy of formation data at some other temperature. Enthalpy of formation data is usually available at standard temperature, and therefore Equation 6.39 can be used to estimate the equilibrium constant at the required temperature given data at standard temperature. However, Equation 6.39 assumes ATT0 is constant. If data is available for AH0 at standard... 

The reaction takes place in a gas phase. Component C is the desired product and the equilibrium constant at 400 K is Ka = 1. Calculate the equilibrium conversion and explain what... 

Arts. According to Le Chatelier s principle, raising the temperature would shift this equilibrium to the left. That means that there would be less C and more A and B present at the new equilibrium temperature. The value of the equilibrium constant at that temperature would therefore be lower than the one at the original temperature. 

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