Rate of a reaction

Reactions proceed at different rates. The rate of a reaction refers to the amount of a reactant consumed or a product formed in a reaction in a definite unit of time. The quantity consumed or produced is expressed in concentration units (gram-moles per litre) if the substance is in solution, or in partial prc.ssurc units if the substance is a gas. The time may be expres.sed in microseconds for very rapid reactions such as explosion of household gas and oxygen in seconds or minutes for reactions proceeding at moderate rates at room temperature such as decomposition of H2O2 or oxidation of oxalic acid by permanganate in days or months for slow reactions and in years lor very slow reactions such as half-life period of 45 Ra (1590 years). 

The rate of a reaction depends on a large number of (actors such as 

By a knowledge of how various factors influence the rale of a reaction, it becomes possible to bring the reaction under control, i.e., the speed of a reaetkm can be regulated to gain the desired effect. The economic viability of the process can Ihcrefore be ascertained. 

T his effect is best summarised in terms of the Law of Ma.ss Action which slates that the rate at which a substance reacts is proportional to its active mass and the rate of a chemical reaction is proportional to the product of the active, ma.sses of 

A reaction between reacting molecules or ions can lake place only when they come sufficiently close tc ether. The rate of reaction will thus depend on the frequency with which the reacting particles collide (Collision Theory). The increase in concentration of one or more reactants by admitting their additional amounts (or by increasing the pressure in case of gaseous reactants) will increase the frequency of collision and is therefore expected to increase the rate of the reaction. 

The rate of a reaction such as reaction (3) can be expressed as the decrease in the number of moles of reactants, [CoCl(NH3)5] or H2O, per second 

In order to maintain the intensive nature of the speed of a reaction, we will define a new form of speed that is the speed of the fractional extent or rate as the derivative of the fractional extent with respect to time  

Note 1.5.- Most books do not give a specific name to this quantity, which is a reaction frequency. They just call it speed . Other books use the term rate for the absolute speed, which increases confusion. 

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The rate of a reaction r is dependent on the reactant concentrations. For example, a bimolecular reaction between the reactants B and C could have a rate expression, such as... 

Remember that a catalyst af fects the rate of a reaction but not the energy relation ships between reactants and products Thus the heat of hydrogenation of a particu lar alkene is the same irre spective of what catalyst is used... 

Recall that the term kinetics refers to how the rate of a reaction varies with changes m concentration Consider the nucleophilic substitution m which sodium hydroxide reacts with methyl bromide to form methyl alcohol and sodium bromide... 

The change in a property s value per unit change in time the rate of a reaction is a change in concentration per unit change in time. 

One important application of the variable-time integral method is the quantitative analysis of catalysts, which is based on the catalyst s ability to increase the rate of a reaction. As the initial concentration of catalyst is increased, the time needed to reach the desired extent of reaction decreases. For many catalytic systems the relationship between the elapsed time, Af, and the initial concentration of analyte is... 

Direct-Computation Rate Methods Rate methods for analyzing kinetic data are based on the differential form of the rate law. The rate of a reaction at time f, (rate)f, is determined from the slope of a curve showing the change in concentration for a reactant or product as a function of time (Figure 13.5). For a reaction that is first-order, or pseudo-first-order in analyte, the rate at time f is given as... 

The rate of a reaction is temperature-dependent. To avoid a determinate error resulting from a systematic change in temperature or to minimize indeterminate errors due to fluctuations in temperature, the reaction cell must have a thermostat to maintain a constant temperature. 

A rate law describes how the rate of a reaction is affected by the concentration of each species present in the reaction mixture. The rate law for reaction A5.1 takes the general form of... 

Several important points about the rate law are shown in equation A5.4. First, the rate of a reaction may depend on the concentrations of both reactants and products, as well as the concentrations of species that do not appear in the reaction s overall stoichiometry. Species E in equation A5.4, for example, may represent a catalyst. Second, the reaction order for a given species is not necessarily the same as its stoichiometry in the chemical reaction. Reaction orders may be positive, negative, or zero and may take integer or noninteger values. Finally, the overall reaction order is the sum of the individual reaction orders. Thus, the overall reaction order for equation A5.4 isa-l-[3-l-y-l-5-l-8. 

The rate of a process is expressed by the derivative of a concentration (square brackets) with respect to time, d[ ]/dt. If the concentration of a reaction product is used, this quantity is positive if a reactant is used, it is negative and a minus sign must be included. Also, each derivative d[ ]/dt should be divided by the coefficient of that component in the chemical equation which describes the reaction so that a single rate is described, whichever component in the reaction is used to monitor it. A rate law describes the rate of a reaction as the product of a constant k, called the rate constant, and various concentrations, each raised to specific powers. The power of an individual concentration term in a rate law is called the order with respect to that component, and the sum of the exponents of all concentration terms gives the overall order of the reaction. Thus in the rate law Rate = k[X] [Y], the reaction is first order in X, second order in Y, and third order overall. 

In tills chapter we consider systems in which a reaction between two gaseous species is carried out in die adsorbed state on die surface of a solid. The products of die reaction will be gaseous, and die solid acts to increase die rate of a reaction which, in die gaseous state only, would be considerably slower, but would normally yield die same products. This effect is known as catalysis and is typified in industty by die role of adsorption in increasing die rate of syndiesis of many organic products, and in die reduction of pollution by die catalytic converter for automobile exliaust. 

If we postulate diat die chemical potentials of all species are equal in two phases in contact at any interface, dieii Einstein s mobility equation may be simply applied, in Pick s modified form, to describe die rate of a reaction occun ing dirough a solid product which separates die two... 

Many examples of intramolecular reactions leading to ring closure have served to establish a correlation between the rate of a reaction and tiie size of the ring being formed. "... 

The details of proton-transfer processes can also be probed by examination of solvent isotope effects, for example, by comparing the rates of a reaction in H2O versus D2O. The solvent isotope effect can be either normal or inverse, depending on the nature of the proton-transfer process in the reaction mechanism. D3O+ is a stronger acid than H3O+. As a result, reactants in D2O solution are somewhat more extensively protonated than in H2O at identical acid concentration. A reaction that involves a rapid equilibrium protonation will proceed faster in D2O than in H2O because of the higher concentration of the protonated reactant. On the other hand, if proton transfer is part of the rate-determining step, the reaction will be faster in H2O than in D2O because of the normal primary kinetic isotope effect of the type considered in Section 4.5. 

Rate-determining step (Section 4.9) Slowest step of a multi-step reaction mechanism. The overall rate of a reaction can be no faster than its slowest step. 

Because the rate of a reaction is related to the height of the energy barrier on the... 

A catalyst is a substance that increases the rate of a reaction without affecting the position of equilibrium. It follows that the rate in the reverse direction must be increased by the same factor as that in the forward direction. This is a consequence of the principle of microscopic reversibility (Section 3.3), which applies at equilibrium, and rates are often studied far from equilibrium. 

A catalyst is a substance that increases the rate of a reaction, other than by a medium effect, regardless of the ultimate fate of this substance. For example, in hydroxide-catalyzed ester hydrolysis the catalyst OH is consumed by reaction with the product acid some writers, therefore, call this a hydroxide-promoted reaction, because the catalyst is not regenerated, although the essential chemical event is a catalysis. 

Pertiaps the most obvious experiment is to compare the rate of a reaction in the presence of a solvent and in the absence of the solvent (i.e., in the gas phase). This has long been possible for reactions proceeding homolytically, in which little charge separation occurs in the transition state for such reactions the rates in the gas phase and in the solution phase are similar. Very recently it has become possible to examine polar reactions in the gas phase, and the outcome is greatly different, with the gas-phase reactivity being as much as 10 greater than the reactivity in polar solvents. This reduced reactivity in solvents is ascribed to inhibition by solvation in such reactions the role of the solvent clearly overwhelms the intrinsic reactivity of the reactants. Gas-phase kinetic studies are a powerful means for interpreting the reaction coordinate at a molecular level. 

A novel use of the salt [BMIM][PFg] is to enhance microwave absorption and hence accelerate the rate of a reaction. Ley found that [BMIM][PFg] enhanced the rate of the microwave-promoted thionation of amides by a polymer-supported thionating agent [64]. 

A catalyst is a substance that increases the rate of a reaction without being consumed by it It does this by changing the reaction path to one with a lower activation energy. Frequently the catalyzed path consists of two or more steps. In this case, the activation energy for the uncatalyzed reaction exceeds that for any of the steps in the catalyzed reaction (Figure 11.11). 

Let us see what the expression the rate of a reaction means in terms of an example—the reaction between carbon monoxide gas, CO, and nitrogen dioxide, N02. Chemical tests show that... 

In the laboratory you have observed the reaction of ferrous ion, Fe+i(aq), with permanganate ion, MnOiYaqJ, and also the reaction of oxalate ion, CiOi2(aq), with permanganate ion, MnO (aq). These studies show that the rate of a reaction depends upon the nature of the reacting substances. In Experiment 14, the reaction between IO and HSO3" shows that the rate of a reaction depends upon concentrations of reactants and on the temperature. Let us examine these factors one at a time. 

Many reactions proceed quite slowly when the reactants are mixed alone but can be made to take place much more rapidly by the introduction of other substances. These latter substances, called catalysts, are not used up in the reaction. The process of increasing the rate of a reaction through the use of a catalyst is referred to as catalysis. You have seen at least one example of catalytic action, the effect of Mn+2(aq) in speeding up the reaction between CzO YaqJ and MnO Yaqj. 

Give two factors that would increase the rate of a reaction and explain why these do increase the rate. 

A number of variables influence the rate of a reaction. The major ones are the following ... 

The intensity of absorbed radiation. Sunlight or room lights may alter the rate of a reaction. Usually this effect is to be avoided unless the object is to study photochemical effects. The light level in an optical spectrometer that uses monochromatic light is not likely to cause problems, but if white light strikes the sample, as in a diode-array spectrophotometer, this is a possibility. 

This chapter also considers concentration variables that do not themselves necessarily play a role in the mechanism. For example, pH variations may affect the rate of a reaction because an acidic species (HA) is ionized (to A ). The size and direction of the pH effect depend in this instance on how either or both of these species enter the mechanism. Of course, in aqueous solution H+ and OH- may play direct roles as well. 

If the rate of a reaction is governed by the encounter frequency, it is said to be diffusion-controlled. This frequency imposes an upper limit on the rate of reaction that can be evaluated by the use of Fick s laws of diffusion. The mathematical expression of this phenomenon was first presented by von Smoluchowski.2 We shall adopt a simple approach,3,4 although more rigorous derivations have been given.5... 

This equation says that the rate of a reaction between two anions or two cations will increase with ionic strength, whereas that for a reaction of oppositely charged ions will decrease. The validity of this equation has been tested time and again. 

The rate of a reaction that shows specific acid (or base, or acid-base) catalysis does not depend on the buffer chosen to adjust the pH. Of course, an inert salt must be used to maintain constant ionic strength so that kinetic salt effects do not distort the pH profile. 

Sometimes a catalyst, a substance that increases the rate of a reaction but is not itself consumed in the reaction, is added. For example, vanadium pentoxide, V>05, is a catalyst in one step of the industrial process for the production of sulfuric acid. The presence of a catalyst is indicated by writing the formula of the catalyst above the reaction arrow ... 

To avoid the ambiguity associated with several ways of reporting a reaction rate, we can report a single unique average rate of a reaction without specifying the species. The unique average rate of the reaction a A + b > r C + d D is any of the following four equal quantities ... 

The average rate of a reaction is the change in concentration of a species divided by the time over which the change takes place the unique average rate is the average rate divided by the stoichiometric coefficient of the species monitored. Spectroscopic techniques are widely used to study reaction rates, particularly for fast reactions. 

From now on, whenever we speak of a reaction rate, we shall always mean an instantaneous rate. The definitions in Eqs.l and 2 can easily be adapted to refer to the instantaneous rate of a reaction. 

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