Extent of a reaction

If for a short time interval di, we perform reaction [1.R1], some of the reactants will be consumed and some of the products will be produced. We will consume, for example, d NO moles of nitric oxide and d H2) moles of hydrogen in order to 

We will say that during At all of these variations of stoichiometric abundances are in fact the variation d of a certain function that we will call the extent of reaction [l.Rl], and therefore  

If we posit that this function is zero when the environment contains only the reactants, the extent of the reaction at a time t is  

The extent is expressed in amounts of substance, i.e. it is given in moles. 

If we generalize this definition to reaction [1.R3] written as [1.R4], for any reactant or product in a closed system with respect to this component we will have  

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The extent of a reaction in these measurements is determined by bare metal cluster ion signal depletion. In most cases products are also observed. Some systems show multiple adducts indicating comparable or higher rates for each successive step up to a saturation level. For other systems the fully saturated product is observed almost as soon as the reaction starts. This later behavior is characteri sti c of an early rate-limiting step. Due to this complexity kinetics have only been reported on the formation of the first adduct, i. e. for the initial chemisorption step. 

Chemists use both thermodynamics and rate to study chemicai reactions. Thermodynamics determines whether a reaction wiii occur at a certain temperature and when equiiibrium wiii be reached. The rate of a reaction determines the time it takes for a certain concentration of product to form. In this section, you wiii iearn about the extent of a reaction the reiative concentrations of products to reactants at equiiibrium. 

In the Sample Problem and Practice Problems below, you will consider how temperature affects the extent of a reaction. Keep in mind that the size of Kc is not related to the time that a reaction takes to achieve equilibrium. Very large values of may be associated with reactions that take place extremely slowly. The time that a reaction takes to reach equilibrium depends on the rate of the reaction. This is determined by the size of the activation energy. 

Explain the difference between the rate of a reaction and the extent of a reaction. 

A beauty of thermodynamics is that it is not concerned with the detailed processes, and its predictions are independent of such details. Thermodynamics predicts the extent of a reaction when equilibrium is reached, but it does not address or care about reaction mechanism, i.e., how the reaction proceeds. For example, thermodynamics predicts that falling tree leaves would decompose and, in the presence of air, eventually end up as mostly CO2 and H2O. The decomposition could proceed under dry conditions, or under wet conditions, or in the presence of bacteria, or in a pile of tree leaves that might lead to fire. The reaction paths and kinetics would be very different under these various conditions. Because thermodynamics does not deal with the processes of reactions, it cannot provide insight on reaction mechanisms. 

FIGURE 13.4 Judging the extent of a reaction. The larger the value of the equilibrium constant Kc, the farther the reaction proceeds to the right before reaching the equilibrium state. 

Fig. 5.25 The reaction energy, the energy difference of products and reactants, determines the extent of a reaction, i.e. its equilibrium constant. The activation energy (the simple ab initio energy difference shown here is not exactly the conventional Arrhenius activation energy), the energy difference of transition state and reactants, partially determines the rate constant. Unfortunately, energy is ambiguous, since chemists use the terms potential energy, enthalpy (heat energy), and free energy see Section 5.5.2.1...

At equilibrium, the change in any thermodynamic property resulting from an infinitesimal change in the extent of a reaction, d, can be calculated by the two different paths shown in Fig. 5. 

For a reaction with positive gas mole change, Eq. (47) indicates that Kx decreases with pressure. Because ce is a monotonically increasing function of Kx, the equilibrium extent of a reaction with positive Avgas always decreases as pressure is increased. This is an example of Le Chatelier s principle, which states that a reaction at equilibrium shifts in response to a change in external conditions in a way that moderates the change. In this case, because the reaction increases the number of moles of gas and thus the pressure, the reaction shifts back to reactants. The isothermal compressibility of a reactive system can, therefore, be much greater than that of a nonreactive system. This effect can be dramatic in systems with condensed phases. For example, in the calcium carbonate dissociation discussed in Example 12, if the external pressure is raised above the dissociation pressure of C02, the system will compress down to the volume of the solid. Of course, a similar effect is observed in simple vaporization or sublimation equilibrium. As the pressure on water at 100°C is increased above 1.0 atm, all vapor is removed from the system. 

Extent of Reaction. The extent of a reaction (f) is defined as the change in the number of moles of any reaction compound (reactant or product) due to the chemical reaction divided by its stoichiometric coefficient. 

To give an idea of the possible magnitude of K, we can cite some extreme values it can acquire for example, from 10 120 (as in the gas-phase decomposition of N2 to atomic nitrogen) to 10+79 (as in the formation of an Ag complex with six thiosulfate ligands). In aqueous solutions the most common values for K are in the range 10-3° to 10+3° (e.g., solubility products, complex formation, dissociation constants, etc.). The magnitude of K signifies the extent of a reaction. 

When there are a number of chemical reactions between the species in a system, we can shift from the independent variables T, P, and n to the smaller number of independent variables T, P, and f, where the are the extents of the k independent reactions. The extent of a reaction is defined by nj = n o + Vjk. where n-p is the amount of the y th species when... 

Provided that there is a change in the number of moles upon reaction, an obvious measure of the extent of a reaction is given by the change in pressure. The latter has to be related to the stoichiometry of the reaction by quantitative analysis of the products and reactant or reactants and by material balance. Abnormal pressure effects sometimes occur due to adiabatic reactions, unimolecular reactions which are in their pressure-dependent regions (particularly in flow systems)... 

The second point concerns changing reaction order. The order may change in the course of the reaction, for instance because one of the reactants or intermediates becomes consumed, thereby leading to a different mix of products and another reaction step dominating the order. This may make it difficult to predict the extent of a reaction after various reaction times from only a few analytical data, the more so since the relation may vary with temperature. 

Two processes that can take place during the photodegradation of polymers are of prime importance because even a small extent of a reaction can alter profoundly the mechanical properties of the sample. These are main chain scission and crosslinking. 

The rate and extent of a reaction are not necessarily related. When the forward and reverse reactions ooour at the same rate, the system has reached dynamic equilibrium and concentrations no longer change. The equilibrium constant (K) is a number based on a particular ratio of produot and reactant concentrations. Kis small for reactions that reach equilibrium with a high concentration of reactant(s) and large for reactions that reach equilibrium with a low concentration of reactant(s). 

Distinguish between the rate and the extent of a reaction understand that the equilibrium constant (K) is a number whose magnitude is related to the extent of the reaction ( 17.1) (EPs 17.1-17.4)... 

Furthermore, it can be shown that at equilibrium AG = 0. To illustrate, consider changes occurring in a system as a function of a given reaction variable that affects its free energy as shown schematically in Fig. 5.3. The variable can be the number of vacancies in a solid, the number of atoms in the gas phase, the extent of a reaction, the number of nuclei in a supercooled liquid, etc. As long as (Fig- 5.3), then AG 0 and the reaction will proceed. When is at a minimum and the system is... 

In Section 11.2 it was stated that trace impurities can affect the extent of a reaction fouling problem. Figs. 11.4 and 11.5 illustrate the effects of relatively small amounts of oxygen in the fouling rate of crude oil processing. 

The extent of a Reaction Reaction Quotient Calculating equilibrium... 

We call a change in the extent of a reaction TZ, A, the conversion of reaction TZ or the conversion according to reaction TZ. Every conversion leads to changes in the amounts of the participating substances, which are proportional to their conversion numbers ... 

When no substances are exchanged with the surroundings but are only transformed inside the system, it is more advantageous to indicate its state by using the momentary extent of a reaction in progress. The main equation then simplifies to... 

Of the extent of a reaction (in solutions) is a decrease of its drive, meaning there is an increase of —Ji (here, too, it is important to notice the sign). 

Le Chatelier-Braun s Principle or Principle of Mobile Equilibrium This principle was presented already at the end of the nineteenth century and is often mentioned in connection with our current discussion. Chemists use it to predict whether the extent of a reaction in equilibrium will be shifted forward or backward when certain parameters are changed, especially pressure, temperamre, amounts of reactants and products, etc. We have found our answers in what we have already discussed, so we can avoid using this principle. For completeness sake, and because of the problems it causes even today, we will deal with it briefly. We will choose one of the various ways it can be formulated which is close to its original version, but we will avoid misunderstandings by using explanatory additions [in square parentheses] ... 

Because reaction rates are closely tied to energy, it is logical that equilibrium also depends in some way on energy. In this chapter we explore the connection between energy and the extent of a reaction. Doing so requires a deeper look at chemical thermodynamics, the area of chemistry that deals with energy relationships. We first encountered thermodynamics in Chapter 5, where we discussed the nature of energy. 

It is important to realize that the fact that a process is spontaneous does not necessarily mean that it will occur at an observable rate. A chemical reaction is spontaneous if it occurs on its own accord, regardless of its speed. A spontaneous reaction can be very fast, as in the case of acid—base neutralization, or very slow, as in the rusting of iron. Thermodynamics tells us the direction and extent of a reaction but nothing about the speed. 

Remember Thermodynamics can tell us the direction and extent of a reaction but tells us nothing about the rate at which it will occur. If a catalyst were foimd that would permit the reaction to proceed at a rapid rate at room temperature, high pressures would not be needed to force the equilibrium toward NH3. 

The use of solution NMR for polymer analysis has become routine in many laboratories. NMR is used to monitor the extent of a reaction, to check the purity of polymers, to identify unknown materials, and to study polymer... 

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