Equilibrium extent of reactions

The science of chemical kinetics is concerned primarily with chemical changes and the energy and mass fluxes associated therewith. Thermodynamics, on the other hand, is concerned with equilibrium systems. .. systems that are undergoing no net change with time. This chapter will remind the student of the key thermodynamic principles with which he should be familiar. Emphasis is placed on calculations of equilibrium extents of reaction and enthalpy changes accompanying chemical reactions. 

This equation is extremely useful for calculating the equilibrium composition of the reaction mixture. The mole numbers of the various species at equilibrium may be related to their values at time zero using the extent of reaction. When these values are substituted into equation 2.6.9, one has a single equation in a single unknown, the equilibrium extent of reaction. This technique is utilized in Illustration 2.1. If more than one independent reaction is occurring in a given system, one needs as many equations of the form of equation 2.6.9 as there are independent reactions. These equations are then written in terms of the various extents of reaction to obtain a set of independent equations equal to the number of unknowns. Such a system is considered in Illustration 2.2. 

Equations 5.1.5, 5.1.6, and 5.1.8 are alternative methods of characterizing the progress of the reaction in time. However, for use in the analysis of kinetic data, they require an a priori knowledge of the ratio of kx to k x. To determine the individual rate constants, one must either carry out initial rate studies on both the forward and reverse reactions or know the equilibrium constant for the reaction. In the latter connection it is useful to indicate some alternative forms in which the integrated rate expressions may be rewritten using the equilibrium constant, the equilibrium extent of reaction, or equilibrium species concentrations. 

From the requirement that the reaction rate must become zero at equilibrium, equation 5.1.4 indicates that the equilibrium extent of reaction per unit volume ( ) is given by... 

The analysis is very similar to that employed in proceeding from equation 5.1.12 to equation 5.1.16, but the physical situation is somewhat different. The reaction is first allowed to come to equilibrium with Ae and Be representing the equilibrium concentrations of species A and 5, and the equilibrium extent of reaction per unit volume in a constant volume system. Under these conditions the net rate of reaction is zero. 

At some assigned values of p and T, the equilibrium extent of reaction, q, is such that the corresponding rate of reaction is zero ... 

Using the results from Example 1.2.3, calculate the two equilibrium extents of reaction. Answer... 

Then use these expressions and the given equilibrium relation to derive an equation for the equilibrium extent of reaction, in terms of rtAu. io- (see Example 4.6-2.)... 

In this elementary case, we see that there is a unique solution to the problem of finding the equilibrium extent of reaction. We can substitute from the relation... 

To find the equilibrium mole fractions, Eq. 13.1-8 is first solved for the equilibrium extent of reaction X, and this is used with the initial mole numbers and stoichiometric information (i.e.. Table 13.1-1) to find the mole fractions. 

Thus, it is clear that the equilibrium extent of reaction X is proportional to and that... 

In trying to find the economically optimal operating conditions for design, it is frequently necessary to consider a wide range of conditions. Therefore, determine the equilibrium extent of reaction over the temperature range of 500 to 800 K and the pressure range from 1 bar to 1000 bar. 

There are several things to be noted from these figures. The first is that at any temperature, the equilibrium extent of reaction increases rapidly with increasing pressure. Second, at any pressure, the equilibrium conversion decreases with increasing temperature. Next, the fugacity ratio can be quite small in value at high pressures, especially at low temperatures. Consequently, the gas-phase nonidealities have an important effect on the equilibrium conversion. This is evident in Figure 2, which shows the equilibrium extent of reaction versus temperature and pressure, and where we have also plotted the ideal gas results Km = 1) at 500 and 800 K. ... 

If stoichiometric amounts of ethylene and water are used, compute the equilibrium constant and the equilibrium extent of reaction at... 

The adiabatic reaction temperature and the equilibrium extent of reaction X that satisfy both the equilibrium and the energy balance relations for a given value of 7i are found at the intersection of the equilibrium and energy balance curves in the figure. For the reactor feed at 300 K this occurs at... 

We see that at zero time the values of dimensionless A and B concentration are as they should be, and at long time they tend to 0.73 and 0.27, respectively. We can check this by computing the equilibrium extent of reaction a from the expression for the equilibrium constant. Recall that the magnitude of the equilibrium constant at any temperature is given by the ratio of the forward to the reverse rate constants and the concentration of the products at equilibrium in this case is just a Cao and the reactant is (1 — a) Cao- This gives the following expression to be solved ... 

Now we can write some code that will evaluate the kinetics and the equilibrium and then graph the relevant gas and surface phase concentrations for us all at once. The equilibrium extent of reaction can be computed as follows for any given value of the equilibrium constant ... 

Using this equation, knowing the value of K, the reaction stoichiometry, the initial concentrations, and the volume of the system, the equilibrium extent of reaction can be determined. 

Although two roots exits, only one is physically possible since both components A and B are reactants and one of the two will be in excess. In this instance, component A is the limiting reactant. It follows that = Vi = 0-5 mol/L is the equilibrium extent of reaction. The corresponding concentrations at equilibrium are then found by mass balance... 

Table2. Final or equilibrium extent of reaction x, fortrans->cis photoisomerization of azobenzene group molecularly dispersed, bound to side chain (s), chain end (e), or incorporated in main ch (m) of various polymers...

Statistical thermodynamics thus provides tools for us to predict equilibrium constants of reactions knowing little other than the energy levels of the equilibrium species. This is a powerful predictive tool, one that chemists use to estimate the equilibrium extent of reactions under conditions that might not be directly measurable. 

To relate the mole fractions to the quantity of CO reacted, let s choose a basis of 1 mol of CO entering the reactor. Therefore, 1 mol of Q2 also enters, but there is noCOCl2(or anything else)in the feed. Let be the equilibrium extent of reaction, i.e., the number of moles of CO that are consumed when the reaction has reached equiUbrium. By stoichiometry, the moles of each species in the equilibrium mixture are... 

The reaction is carried out at 60°C and low pressure, with a feed of twice as much water as methanol. The equilibrium extent of reaction is = 0.87. How many moles of Hg can be produced per mole of CH3OH in the feed What is the mole fraction of H2 ... 

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