The composition at equilibrium

A catalyst is a substance that increases the rate of a chemical reaction without being consumed itself. We shall see a lot more of catalysts later, when we consider reaction rates in Chapter 13. However, it is important to be aware at this stage that a catalyst has no effect on the equilibrium composition of a reaction mixture. A catalyst can speed up the rate at which a reaction reaches equilibrium, but it does not affect the composition at equilibrium. It acts by providing a faster route to the same destination. 

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. 

As a consequence of the determination of the composition at equilibrium of the products of expln reaction, it has been shown that a good approximation to the composition is afforded by the following conventional scheme ... 

Every chemical reaction tends toward a state of dynamic equilibrium, and the composition at equilibrium determines how much product we can expect. We need to understand equilibrium and its relation to thermodynamics in order to manipulate the outcome of a reaction by controlling conditions such as the temperature and pressure. These features have considerable economic and biological significance the control of chemical equilibrium affects the yields of products in industrial processes, and living cells struggle to avoid sinking into equilibrium. The importance of chemical equilibria can be appreciated by noticing that it is the basis of this and the next three chapters. This chapter lays the foundation for the next three. 

The composition at equilibrium can be determined from the equilibrium constant based on molar fractions Kx = Ka/Kr This is, in turn, calculated from the equilibrium-constant-based activities IQ and activity coefficients Kr Figure 8.3 shows the variation over the range 350-475 K [1, 2], IQ takes values between 10 and 50, but the correction by IQ is important bringing IQ between 2 and 10. Above 430 K equilibrium conversion over 80% should be expected. If the water is continuously removed by distillation, then full conversion may be achieved. 

The work of this laboratory extends the defect treatment to intermetallie compounds. The experiments measure simultaneously both the cadmium vapor pressure and the composition at equilibrium for a series of only slightly different alloy compositions. The precision and the relative accuracy of the measurements are high the absolute values suffer from any starting composition uncertainty and from errors in the absolute vapor pressure of cadmium as determined by other techniques. The experimental method is described elsewhere in this symposium (6). It has proved possible to infer the concentration and identity of lattice defects by analyzing the experimental data following the analytical techniques described below. 

The equilibrium constant K is a function of temperature only. However, Eq. (13.25) relates K to fugacities of the reacting species as tliey exist in the real equilibrium mixture. These fugacities reflect the nonidealities of the equilibrium mixture and are functions of temperature, pressure, and composition. Tliis means that for a fixed temperature the composition at equilibrium must change with pressure in such a way that W ifilP ") remains constant. 

When several reversible reactions occur simultaneously, each reaction ty is characterized by its equilibrium constant K. When the are known, the composition at equilibrium can be calculated from a set of equations such as Eq. (7-15) for each reaction. 

The equilibrium constant (based on volumetric concentrations) is defined as the ratio of the forward and reverse rate constants and is related to the composition at equilibrium as follows ... 

The solution of such equations is now rather more complicated but it can be proved that there is a unique solution giving the composition at equilibrium. 

If we follow the development of the glycosidation reaction over time instead of examining the composition at equilibrium, we see that the furanosides are formed at the start, only to disappear thereafter, more or less completely, to the benefit of the pyranosides. 

The molecular heat of combustion of hydrogen is = - 58,000 cals, the minus sign denoting heat evolved, and that of carbon monoxide is Qa = - 68,000 cals What is the composition at equilibrium of the water gas formed from equal volumes of water vapour and carbon monoxide (1) at a temperature Tj = 800° abs, and (2) at a temperature T2 = 1200° abs ... 

Under the usual conditions for enzyme-catalyzed (trans)esterification, the composition at equilibrium is often far from optimal. Complete conversion can be achieved by removal of alcohol and/or water by vacuum or chemical means, i.e. by the use of enol or oxime" esters. We endeavoured to fix the water activity at a low level by adding zeolite to the reaction mixture. Immobilized enzymes which are stable in these very dry media have recently become available. ... 

The equilibrium constant is equal to a ratio of activities. The composition at equilibrium is found by expressing the activities in terms of... 

Consider the gas-phase reaction A B + C at equilibrium, carried out at 3x10 Pa. Consider a molar flow rate of pure A of F = 100 mol s Calculate the composition at equilibrium at the exit of a continuous flow reactor, knowing that Ko=l. 

The full reversibility of the reaction was initially demonstrated by a series of experiments. For instance, the equilibrium mixtures obtained from transacetalation of 5 mM cycUc dimer and 3.33 mM cyclic trimer were practically indistinguishable, so were the equilibrates obtained from 25 mM cychc dimer and 16.7 mM cyclic trimer. Thus, as expected for a truly reversible system, the composition at equilibrium is the same, no matter what ohgomer is used as feedstock, on a condition that the equivalent concentration expressed in monomer units is the same. Another important characteristic of dynamic systems is the ability to readjust the product distribution by changing the factors that mle the equilibrium, even once the system has reached the equilibrium composition dictated by the initial conditions. In a further experiment, an equilibrated reaction mixture in which 8.33 mM cyclic trimer was the starting material was perturbed by adding an amount of solid cyclic trimer such as to double the equivalent monomer concentration (50 mM). Comparison of the distribution of the species analysed immediately after complete dissolution of the solid cyclic trimer with that found after re-equilibration showed that excess cyclic trimer was digested and mosdy transformed into h h molecular weight materials, as the total monomer concentration in the ordinal solution was not far from saturation conditions (close to critical concentration CC). In this case, indeed, equilibrium concentration plots of cyclic dimer, trimer and tetramer... 

Calculating equilibrium concentrations. Once you know the value of for a reaction, you can determine the composition at equilibrium for any set of starting concentrations. 

Using the values of K from Examples 12.8 and Table A.9, we may estimate the effect of changes in temperature on the composition at equilibrium. 

---