Dependence of Reaction Rate on Reactant Concentration

We saw in Section 14.1 that the rate of reaction between bromine and formic acid is proportional to the concentration of bromine and that the proportionality constant k is the rate constant. We will now explore how the rate, the rate constant, and the reactant concentrations are related. 

---

One approach of kinetics is to describe the dependence of reaction rates on reactant concentrations. For instance, the rate of phosphate fixation depends at least partly on the amount of fertilizer added, and the rate of denitrification (the conversion of soil nitrogen, usually nitrate to N2 and N2O) depends on soil solution nitrate concentrations. Kinetics relates reaction rates and reactant concentrations by means of the reaction order and the reaction rate constant. The denitrification rate (—ANO /At) is presumably related to soil nitrate concentration by... 

Dependence of Reaction Rate on Reactant Concentration The Rate Law... 

Dependence of reaction rates on the concentrations of the reactants (and the products in certain cases) can be very useful in understanding the mechanism of catalysis. Some of the ubiquitous mechanistic steps reveal themselves in empirically derived rate expressions. In other words, such rate expressions, once established by experiments, are characteristic signs of such steps. 

Chemical kinetics emerged as a branch of physical chemistry in the 1880-s with seminal works of Harcourt and Esson demonstrating the dependence of reaction rates on the concentrations of reactants. It was a German scientist K. Wenzel who stated that the affinity of solid materials towards a solvent is inversely proportional to dissolution time and 100 years before Guldberg and Waage (Norway) formulated a law, which was later coined the "law of mass action," meaning that the reaction "forces" are proportional to the product of the concentrations of the reactants. 

They studied this reaction intermittently for about 30 years, performing thousands of careful experiments which rigorously established the dependence of reaction rate on the concentrations of the reactants. In 1895 they described how the rate of reaction varied with temperature. They found that the rate of reaction approximately doubled for every 10°C rise in temperature, and by extrapolation they concluded that at a temperature of -272.6 C no chemical change would take place. 

The dependence of reaction rate on concentration is readily explained. Ordinarily, reactions occur as the result of collisions between reactant molecules. The higher the concentration of molecules, the greater the number of collisions in unit time and hence the faster the reaction. As reactants are consumed, their concentrations drop, collisions occur less frequently, and reaction rate decreases. This explains the common observation that reaction rate drops off with time, eventually going to zero when the limiting reactant is consumed. 

In the search for a better approach, investigators realized that the ignition of a combustible material requires the initiation of exothermic chemical reactions such that the rate of heat generation exceeds the rate of energy loss from the ignition reaction zone. Once this condition is achieved, the reaction rates will continue to accelerate because of the exponential dependence of reaction rate on temperature. The basic problem is then one of critical reaction rates which are determined by local reactant concentrations and local temperatures. This approach is essentially an outgrowth of the bulk thermal-explosion theory reported by Fra nk-Kamenetskii (F2). 

FIGURE 13.14 The characteristic shapes of the time dependence of the concentration of a reactant during a second-order reaction. The larger the rate constant, k, the greater is the dependence of the rate on the concentration of the reactant. The lower gray lines are the curves for first-order reactions with the same initial rates as for the corresponding second-order reactions. Note how the concentrations for second-order reactions fall away much less rapidly at longer times than those for first-order reactions do. 

General Techniques for the Interpretation of Reaction Rate Data for Reversible Reactions. The determination of the mathematical form of a reaction rate expression is generally a two-step procedure. One first determines the dependence of the rate on the concentrations of the various reactant and product species at a fixed temperature and then evaluates the temperature dependence of the various rate... 

Another factor that affects the rate of a chemical reaction is the concentration of reactants. As noted, most reactions take place in solutions. It is expected that as the concentration of reactants increases more collisions occur. Therefore, increasing the concentrations of one or more reactants generally leads to an increase in reaction rate. The dependence of reaction rate on concentration of a reactant is determined experimentally. A series of experiments is usually conducted in which the concentration of one reactant is changed while the other reactant is held constant. By noting how fast the reaction takes place with different concentrations of a reactant, it is often possible to derive an expression relating reaction rate to concentration. This expression is known as the rate law for the reaction. 

While this convention is now widely used, it was not in some early kinetic studies. Thus one must be careful to note exactly how the rate is defined so that the reported rate constants are interpreted and applied correctly. In systems of atmospheric interest, the rate law or rate expression for a reaction, either elementary or overall, is the equation expressing the dependence of the rate on the concentrations of reactants. In a few reactions (mainly those in solution), products may also appear in the rate law. 

Up to this point we have discussed collisional deactivation of vibration-ally excited ions formed by ionization or as products of exoergic particle-transfer ion-molecule reactions. A somewhat different situation prevails with larger vibrationally excited ions, such as those formed as intermediates in ion-molecule association reactions. Reactions in which such excited intermediates are formed generally demonstrate a third-order dependence of the rate on the concentrations of the reactants at relatively low pressures. The general reaction mechanism may be represented as... 

When a solvent is also a reactant, its concentration is so large compared with the extent of reaction that it does not change. Since this is the case, the dependence of the rate on the concentration of ethyl alcohol cannot be determined unless ethyl alcohol becomes a solute in some other solvent. If another substance is the solvent, then the concentration of the alcohol can be varied, allowing the calculation. For the reaction in ethyl alcohol (ethanol), kexp = k[B] with [B] essentially constant. Such reactions are called pseudo-first-order reactions. 

Rate methods. As for reactions with a single reactant, the most primitive and convenient rate method is to guess and then adjust the reaction orders until an approximately straight-line plot of —rk versus the rate versus Ck CB. .. is obtained (see Table 3.1). For example, if a reaction is expected to be second order in A and first order in B, the rate would be plotted versus CACB. For first guesses of reaction orders, the available data can be subdivided so that the concentration of all but one participant are the same within each group. The dependence of the rate on the concentration of that participant then is an indication of the respective order. Often, the evaluation need not be carried beyond this stage. 

If some of the reactant or product species are present in excessive quantities, then the fractional changes in their concentrations over the entire duration of the reaction may be immeasurably small. In such cases the concentrations of the reactants present in excess remain approximately constant and may be absorbed into the rate constant fe. A measurement of the order of the reaction from concentration-time plots then does not reveal the dependence of the rate on the concentrations of the overabundant species the measurement yields the pseudo molecularity of the reaction, that is, the sum of the orders with respect to the species that are not present in excess. Thus a number of higher-order reactions are found to be pseudounimolecular under certain conditions. This observation provides the basis for the isolation method of determining the order of a complex reaction with respect to a particular reactant in this method, the apparent overall order (pseudo-molecularity) of the reaction is measured under conditions in which all of the reactants except the one of interest are present in excess. 

According to the law of mass action, the rate of a chemical reaction at a given temperature, expressed as the amount reacting per unit volume per unit time, depends only on the concentrations of the various substances influencing the rate (and not, for example, on the size of the reaction vessel). The substances that influence the rate are usually one or more of the reactants, occasionally one of the products, and sometimes a catalyst that does not appear in the balanced overall chemical equation. The dependence of the rate on the concentrations can be expressed in many cases as a direct proportionality, in which the concentrations may appear to the zero, first, or second power. The power to which the concentration of a substance appears in the rate expression is called the order of the reaction with respect to that substance. Some examples follow. 

Sometimes, however, this procedure may lead to incorrect conclusions. Suppose, for example, that one reactant is present in large excess, so thdt its concentration does not change appreciably as the reaction proceeds moreover (for example, if it is the solvent) its concentration may be the same in different kinetic runs. If this is so the kinetic investigation will not reveal any dependence of the rate on the concentration of this substance, which would therefore not be considered to be entering into reaction. This situation is frequently found in reactions in solution where the solvent may be a reactant. For example, in hydrolysis reactions in aqueous solution, a water molecule may undergo reaction with a solute molecule. Unless special procedures are employed the kinetic results will not reveal the participation of the solvent. However, its participation is indicated if it appears in the stoichiometric equation. 

---