Ideal gas reaction

In the case of bunolecular gas-phase reactions, encounters are simply collisions between two molecules in the framework of the general collision theory of gas-phase reactions (section A3,4,5,2 ). For a random thennal distribution of positions and momenta in an ideal gas reaction, the probabilistic reasoning has an exact foundation. Flowever, as noted in the case of unimolecular reactions, in principle one must allow for deviations from this ideal behaviour and, thus, from the simple rate law, although in practice such deviations are rarely taken into account theoretically or established empirically. 

An ideal gas reaction, A 2B, occurs at 5 atm and 500 K, starting with pure A. The rate equation is... 

For ideal gas reactions, there are two temperature regions where the behaviour of the equilibrium constant is simple at low temperatures (generally much below room temperature), the natural logarithm of K (In K) follows l/7 where T is the absolute temperature and at high temperatures, the approximation becomes In ii - l/T. ... 

Table 4.11 Equilibrium constants and compositions for ideal-gas reaction (4.14) at P° = 1 bar. x is a mol fraction of a component, is a degree of conversion...

Discuss similarities and differences between the two forms for the equilibrium constant of an ideal gas reaction, Eqs. (37) and (59). 

The f, fg, f , and f,are determined for the pure gas at the pressure of the mixture and depend on the pressure and the temperature. In gaseous mixtures, the quantity Kp as defined by Equation 2-38 is used. For an ideal gas reaction mixture, Kf = Kp. For a non-ideal system, Equation 2-39 can be used to calculate Kp from the measured equilibrium compositions Ky using Equation 2-42. The composition... 

Figure 2.3 shows the relation between enthalpy H and each of the variables of T, p, and for an ideal gas reaction, in which we assume that the heat of reaction is constant irrespective of the extent of reaction. 

Fig. 2.3. Enthalpy as a function of temperature, pressure, and extent of reaction for an ideal gas reaction.

Although Eq. (15.25) holds only for an ideal-gas reaction, we can base some conclusions on it that are true in general. 

In Other words, —AH for ideal-gas reactions is independent of both the pressure and the composition of the mixture in which the reaction occurs. ... 

Although —dH/de —AH in general, for ideal-gas reactions the substitution of equation (37) into the right-hand side of equation (41) yields ... 

In order to obtain —AH at conditions other than 1 atm and 25 C from equation (43) and tables of standard heats of formation, it is necessary to compute the enthalpy change of the reactant mixture and of the product mixture in going from 1 atm and 25°C to the given p and T additional tables are available to facilitate these computations for a number of materials [13], [15] [17], [26]-[28]. Usually the pressure dependence of —AH is negligible, and from equation (38) it follows that for ideal-gas reactions,... 

For ideal-gas reactions, equation (47) determines the temperature dependence of the equilibrium constant. Since pi = N,, it follows... 

In equation (49), which is the van t Hoff equation, —dH/de may be replaced by — AH, since these two quantities are equal for ideal-gas reactions. Relationships analogous to equation (49) may be derived for each of the equilibrium constants defined in Section A. 3, but for reactions in systems other than ideal-gas mixtures, — AH and — dH/de may not, in general, be equated in these expressions. Heats of reaction can be determined directly either by spectroscopic measurements followed by the application of statistical mechanics (for ideal-gas reactions) or by calorimetric measurements of Q (for arbitrary reactions). Since the measurement of equilibrium compositions may be simpler than either of the above procedures, in practice equation (49) is often used to obtain heats of reaction from experimental values of Kp at neighboring temperatures. 

I) The more recent rate constants from the compilation of Tsang and Hampson (20) and Tsang (21) were used as a basis for low pressure, ideal gas reaction systems, typical of gas—phase combustion systems. 

The thermodynamic description of reactions in solution parallels the discussion just completed for ideal gas reactions. Although the result is not derived here, the Gibbs free energy change for n mol of a solute, as an ideal (dilute) solution changes in concentration from Ci to Ci mol is... 

Hence, for an isothermal constant-pressure ideal gas reaction system,... 

The Equilibrium Constant in Terms of Molar Concentrations of Gases Gas-phase equilibria (ideal gas reaction mixture)... 

From Eq. (1-9) it is clear that K = Kp for an ideal-gas reaction mixture. For nonideal systems Eq. (1-14) may still be employed to calculate Kp from measured equilibrium compositions (Ky). However, then no equal To X detennined Tfbm Iherin for example, from Eq. (1-4). 

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