Ammonia synthesis equilibrium

Temperature changes affect not only systems at equilibrium but also the value of equilibrium constants. In fact, equilibrium constants changing with temperature is the reason that equilibria change with temperature. For example, consider Kgq for the ammonia synthesis equilibrium. 

Consider the ammonia synthesis equilibrium at 460 °C (723 K) and 300 atm. The reduced temperaturesand pressures are as given in Table 6, together with the interpolated values of x om the graph. 

The most accurate experimental values appear to be those by Haber, Rossignol (18), by Schultz, Schaefer [53], by Haber et al. [21] for 30 atm pressure, by Larson, Dodge [32] for 10, 30, 50, and 100 atm, and by Larson [30] for pressures of 300, 600, and 1000 atm. Experimental and calculated data on ammonia synthesis equilibrium at pressures from 1000 atm to 3500 atm have been given by Winchester, Dodge [61]. 

The equilibrium eonstant K is independent of pressure with standard states. The effeet of the pressure is shown in Equation 6-6. K. is usually insensitive and may either inerease or deerease slightly with pressure. When (r -i- s) > (a -i- b), the stoiehiometrie eoeffieients, an inerease in pressure P results in a deerease in eonversion of the reaetants to the produets (i.e., A -i- B o R -i- S). Alternatively, when (r -I- s) < (a -I- b), an inerease in pressure P results in an inerease in the equilibrium eonversion. In ammonia synthesis (Nj -i- SHj o 2NH3), the reaetion results in a deerease in the number of moles. Therefore, an inerease in pressure eauses an inerease in equilibrium eonversion due to this faetor. 

In ammonia synthesis, high temperatures eonespond to small reaetor volumes. For exothermie reaetions, the equilibrium eonversion deereases as the temperature inereases. Therefore, these reaetions are often earried out in a series of adiabatie beds with either intermediate heat exehangers to eool the gases or bypass the eold feed to deerease the temperatures between the beds. Some eompromise ean be aehieved between high temperatures involving small reaetor volumes and high equilibrium eonversions. 

The equilibrium eonstant for ammonia synthesis is expressed as a funetion of the partial pressure as... 

Table 6-5 shows the eonditions for whieh NH3 produetion is possible. Both low temperatures or very high pressures aehieve favorable equilibrium. At 25°C, the equilibrium eonstant is very high, while at higher temperatures, both and deerease rapidly. Generally, ammonia synthesis reaetors operate at about 350°C and 200 atm with an equilibrium eonversion of about 70% in eaeh pass. The NH3 is separated from unreaeted Hj and N2, whieh are reeyeled baek to the reaetor. For the overall proeess involving tlie tubular reaetor, separation and reeyele produee about 100% ammonia eonversion. 

Fig ure 6-12. Profiles of equilibrium conversion Xg versus temperature T for ammonia synthesis. (Source Schmidt, L. D., The Engineering of Chemical Reactions, Oxford University Press, New York, 1998.)... 

The production of ammonia is of historical interest because it represents the first important application of thermodynamics to an industrial process. Considering the synthesis reaction of ammonia from its elements, the calculated reaction heat (AH) and free energy change (AG) at room temperature are approximately -46 and -16.5 KJ/mol, respectively. Although the calculated equilibrium constant = 3.6 X 108 at room temperature is substantially high, no reaction occurs under these conditions, and the rate is practically zero. The ammonia synthesis reaction could be represented as follows ... 

Write the equilibrium constant for the ammonia synthesis reaction, reaction C. 

Self-Test 9.7A The equilibrium constant for the ammonia synthesis (reaction C) is K = 41 at 127°C. What is the value of Kc at that temperature ... 

As an indispensable source of fertilizer, the Haber process is one of the most important reactions in industrial chemistry. Nevertheless, even under optimal conditions the yield of the ammonia synthesis in industrial reactors is only about 13%. This Is because the Haber process does not go to completion the net rate of producing ammonia reaches zero when substantial amounts of N2 and H2 are still present. At balance, the concentrations no longer change even though some of each starting material is still present. This balance point represents dynamic chemical equilibrium. 

In our calculation we assume that the gas mixture approaches equilibrium under conditions where the pressure is constant. This situation corresponds, for instance, to a volume of gas moving through a plug flow reactor with a negligible pressure drop. (Note that if the ammonia synthesis were carried out in a closed system, the pressure would decrease with increasing conversion.)... 

We will list the elementary steps and decide which is rate-limiting and which are in quasi-equilibrium. For ammonia synthesis a consensus exists that the dissociation of N2 is the rate-limiting step, and we shall make this assumption here. With quasi-equilibrium steps the differential equation, together with equilibrium condition, leads to an expression for the coverage of species involved in terms of the partial pressures of reactants, equilibrium constants and the coverage of other intermediates. 

For ammonia synthesis, we still need to determine the coverages of the intermediates and the fraction of unoccupied sites. This requires a detailed knowledge of the individual equilibrium constants. Again, some of these may be accessible via experiments, while the others will have to be determined from their respective partition functions. In doing so, several partition functions will again cancel in the expressions for the coverage of intermediates. 

Equilibrium. Forward and reverse reactions occurring at the same rate, resulting in a concentration of reactants. A + B C + D. Ammonia synthesis is an equilibrium reaction (N2 + 3H2 2NH3). 

Figure 3-17 Plot of eqdlibrimn convereion Xg vasus terr5)er-ature for ammonia synthesis starting with stoichiomeh ic feed. While the equilibrium is favorable at anbient tar5)erature (where bactaia fix N2), the convasion r dly falls off at elevated temperature, and commercial ammonia synthesis reactors operate with a Fe catalyst at pressiues as high as 300 atm to att 2 high equilibrium conversion.

Several important conclusions can be drawn from Figure 4.38. It appears that in general a simple catalytic reaction, which includes the dissociation of a diatomic molecule, will have this dissociation as the rate-determining step, when the reaction takes place under conditions close to equilibrium. This agrees well with the ammonia synthesis being dissociation rate-determined, as this process is the prototype of an equilibrium-limited reaction [128]. When the reaction is taking place far from equilibrium, the actual approach to equilibrium becomes unimportant, and the volcano plot very closely follows the volcano defined by the minimum value among the maximal possible rates for all reaction steps. 

The above are equilibrium reactions, and their successful exploitation requires that they be carried out under conditions in which the equilibrium favors the product. Specifically, this requires that the adsorbed species in Reactions (D)-(I) not be held so tightly on the catalyst surfaces as to inhibit the reaction. On the other hand, strong interaction between adsorbate and catalyst is important to break the bonds in the reactant species. Optimization involves finding a compromise between scission and residence time on the surface. Although we are especially interested in metal surfaces, those constituents known as promoters in catalyst mixtures are also important. It is known, for example, that the potassium in the catalyst used for the ammonia synthesis shifts Equilibrium (F) to the right and also increases the rate of Reaction (D) by lowering its activation energy from 12.5 kJ mole to about zero. 

As example of the caculation of the equilibrium composition of a homogeneous gas reaction the ammonia synthesis reaction at 450 °C will be considered ... 

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