Chemical Kinetics: Reaction Rates Charles D. Mickey Texas A&M University at Galveston Galveston. TX 77553
There is much information that can be derived from a chemical equation: for example, the products that can be expected from a given set of reactants and the stoicbiometric relationship between the substances involved in the reaction ( 1 ) . The equation, however, does not reveal anything about the conditions under which the reaction will take place, its efficiency, or the "rate" at which the reaction occurs. By rate is meant the number of chemical changes which take place on n -~~ molecular scale per unit of time (2). .~ By examination of numerous chemical reactions, one observes that certain types of chemical reactions proceed faster than others. For example, the explosion of nitroglycerine proceeds rapidly, while the rusting of iron generally occurs so slowly that i t is scarcely perceptible. Some reactions go essentially to completion (little or no reactant remains), whereas others are in a state of dynamic equilibrium, a situation in which reactanb form products a t the same rate that products are transformed into reactants. In chemical reactions, rates are usually measured in terms of how fast products appear or how fast reactants disappear. Color, pressure, concentration, and mass changes are some parameters that are frequently used to monitor a reaction's propress. Reaction rates and reaction efficiency are of great importance to the chemist: often the practicability of a chemical reaction, particularl$ a commeriial process, depends on the reaction's rate and efficiency. If the reaction is too slow or the equilibrium is not shifted in favor of the products, it may not be economically feasible. The study of chemical equilibrium deals only with the limit or extent to which a reaction can occur; it is only concerned with the initial and final states of the chemical system. Chemical kinetics, however, is concerned with the reaction mechanism, i.e., the sequence of steps by which a chemical reaction proceeds, the rates of these steps, and the factors, like nature of reactants, concentration, temperature, and catalysis, which affect the rate. ~
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The Colllslon Theory of Reaction Rates A concept, known as the collision theory, has been developed to explain why certain factors, such as the nature of reactants, concentration, and temperature, affect the rare of a chemical reaction. This theory is based on the idea that for n reaction to occur. there must he collisions between reactant particles. ~ c c o r d i " ~the l ~ ,rate of reaction depends upon the number of collisions per unit of time and the fraction of these collisions that are effectiue. By effectiue collisions is meant interoarticle contacts between reactants that are successful in the formation of products. Nature of Reactants Substances differ in activitv and hence in the rate with which they react with other substances. For example, an actlve metal like ootassium will displace hydrogen vigorously and rapidly from acids, while lessactive metals, like lead or platinum, react very slowly, if a t all as in the case of platinum. A more detailed discussion of the relative activities of metals can be found in an earlier article in this series (3). Another factor to be considered is that a chemical reaction is a process in which existing honds are broken and new honds are formed. Therefore, the reaction rate will depend on the specific honds involved and hence on the nature of the reac-
tant. As a result, one should expect to find that reaction rates vary greatly with changes in molecular structure. This can he seen by comparing the rate of reaction of iron(I1) and permanganate ions with that of oxalic acid molecules and permanganate 2MnOa-I,,) + 10Fe(.,12+ + 16H(.,)+ (purple) 2Mn(JC + 10Fe(,13+ + 8H&) (pink) 2Mn041.d + +6Hwt (purple) ~MII(,)~+ + 10C02(,l+ 8H,O(t, (pink) In both cases the purple permanganate disappears as the pink manganese(I1) ion appears; however, in the first reaction the purple color disappears almost instantaneously upon addition of a stoichiometric quantity of iron(I1) indicating that the reaction occurs very rapidly. On the other hand, the disappearance of the purple color in the second reaction requires a much longer period of time; therefore, the reaction must occur more slowlv. Even at elevated temperatures the second reaction is slow unless catalyzed by ma&nese(11) ion. (This is an example of autocatalysis, i.e., Mn2+,a reaction product, serves to catalyze its own formation.) Everything is identical in these two reactions except for the nature of one of the reactants; iron(I1) is an ion whereas oxalic acid is a molecule. Generallv, ionic reactants are found to yield products a t a much faker rate than covalent molecules. Two reasons can be suggested for the observed difference in rate of reaction. First. the Dermaneanate and iron(I1) are hoth ions. Reactions occurring hetween ions of opposite charge and essentiallv. spherical charpe distribution are usually rapid . because effective interparticle contact can occur from any relative direction of approach. That is, the influence of mo.. lecular size and geometry (4) on reaction rate, commonly referred to as the "steric" effect, is minimal in ionic reactions. The second reason concerns the probability that properly oriented oxalic acid molecules will collide with properly oriented permanganate ions. The probability of a permanganate ion colliding with a nonreactive part of the molecule is considerably greater for the oxalic acid molecule than for the iron(I1) ion. Consequently, the rate of effective collision, and the rate of overall reaction, should he slower for the oxalic acid than for the iron(I1) ion.
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Concentration of Reactants
From a kinetic standpoint, chemical change takes place as result of molecular collisions. The ereater the numher of collisions per unit of time, the greaterihe probahility of conversion of reactants into oroducts Der unit of time, i.e., the greater the rate of reaction. By increasing the concentration of any or all of the reactants, each molecule has a greater probability of colliding with another molecule and particinatine in a reaction. Tu develop the quantitative notions of reaction rate, consider the reaction between raseous iodine and hromine to form gaseous iodine monohrom~de a
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+ Bw8) 21Br1~1 Volume 57, Number 9, September 1980 1 659
s E F
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M I J
T R
The progress of the reaction can be monitored by the disappearance of the violet color of iodine vapor. For IZand Brz molecules to react, i t is necessary that they collide. The number of molecules reacting per unit of time will be proportional to the number of collisions. If the number of collisions between Iz and Brz molecules in one case were twice as ereat as that in another in a eiven time. then twice as manv 11 i n d Brz molecules would react. TO determine the dependence of the rate of the reaction upon the concentrations of I2 and Brz, i t is necessary to determine the manner in which the number of collisions between Iz and Brz molecules varies with their respective concentrations. T o do this, consider a closed vessel containing only I2 and Brz molecules and, for simplicity, suppose that there are four 12 molecules and four BIZ molecules in the vessel. The chance of Iz colliding with Brz can be indicated by drawing lines between 12 and Brz molecules, as shown in Figure 1.
constant. The term k includes the effects of temperature, catalysts, and nature of reactants-all the parameters except concentration which influence the rate of a reaction. The concentrations of the reactants, expressed in moles per liter, are represented by the term C. Now consider a case in which two molecules of the same kind react with each other, for example,
Figure 1. A schematic representation of the effect of concentrationon the cotlision frequency between l2 and Br2. Increasing the concentration increases the coilision frequency and, hence, the rate of reaction.
Figure 2. A schematic representation ofthe effect of concentrationon the collision frequencybetween IBr molecules. Increasing the concentration increases the collision frequency and, hence, the rate of reaction.
Under the conditions chosen, the chance that any IZmolecule will collide with any Brz molecule is 16 (16 lines). In other words, each I2 molecule has four chances of colliding with a Brg molecule: since there are four I7 molecules and four Brz milecules, the total chance becomes 4 X 4 = 16. ~ b v i o u s l ~ c llisions between like molecules are not to be included since t .,ey do not lead to reactions. Bv extension of the device used in Figure 1, i t can be shown t h a t b y doubling the concentration of12 molecules, that is, when there are eight IZmolecules and four Br2 molecules in the same vessel, the chance that any I2 molecule will collide with any Brz molecule is 32 (8 X 4 lines). The numher of 12 molecules in the second case is twice that in the first and the chance for collision between 1 2 and Brz molecules is doubled. With eieht 11molecules and eieht Br7 molecules. the chance of collision bktween Iz and Br;moleiules is 64 (8 X 8 lines). For the general case the chance of collision is equal to N A X NB, where NAand N B represent the numher of A and B molecules, respectively. In alicases, the volume of the reaction vessel is constant, so the number of reactant molecules, expressed in proper units, corresnonds to the reactant concentrations. Therefore. the rhanrc for cnllislnn of reactant molertlles is pn~portionalto the urnduct of the reartant conrentrations. The effect of such manipulations can be expressed in tern of a rate law. For the Iz and BIZ reaction the rate law is, ~
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Rate of formation of 1Br = kC&arX and in the general case, the rate law is, Rate of formation of D = kCaCe where k is a proportionality constant called the specific rate 860 1 Journal of Chemical Education
2 IBqpl
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Ixg)+ B w p )
Two molecules of iodine monobromide react with each other to form one molecule of 1%and one of BIZ. T o determine the chance of collision between any two IBr molecules, consider a vessel containing six IBr molecules. Counting the chances as was done in the previous examples, one finds that there are fifteen (5 4 3 2 1lines, Figure 2). That is. the first IBr molecule to be considered has five chances of collision, the next molecule has four chances (not countine" the same chance twice). the third molecule has three chances, etc. By doubling the number of IBr molecules, the chance in-
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creasesto66(11+10+9+8+7+6+5+4+3+2+1 lines). In general, f o r N molecules the chance for collision will be (N - 1) ( N - 2) ( N - 3) . . . 1.The mathematical formula for determining the sum of such a series of combinations is (N - I)N -
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Consequently, the numher of collisions is proportional to ( N - 1)N . I51 . . .Y reorewnts the number of molecules in the reaction vessel. 1; real chemical systems N is a very large number, so ( N - 1) c= N, and ( N - 1)N N2. This reasoning is logical because the lowest possible vacuum probably contains billions of molecules (remember Avogadro's number) per unit volume, obviously one molecule more or less will not make any appreciable difference, and ( N - 1)= N. Accordingly, the number of collisions in such cases is proportional to N2. Since N can be expressed as the concentration of reactants, in this case IBr molecules, the numher of collisions is proportional to the concentration of IBr molecules squared. In other words
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Rate of the IBr reaction = k C h Similar results can be obtained for the reaction 2A+B-D+2E
Bv considerine the collisions between two A molecules and one ~ m n l e c u l ethe , rate of reaction would be proportional ro the number of B moleculh times the number ol'collisionsbetween two A molecules. Since the numher of collisions between two A molecules is proportional to N A ~the , number of collisions between two A molecules and one B molecule will be proportional to N A X~NB. According to the arguments used previously, the rate of reaction is Rate = ~ C A ~ C B
For, the general reaction: rA+sB-xD+zE
in which r, s, x, and z represent the coefficients of A, B, D, and E, respectively in the balanced equation, the formulation of the rate law is
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Rate = hCA'CB6 Complex Reactions and the Colllslon Theory To illustrate the collision theory as applied to complex reactions it is instructive to consider the reaction: A+2B-D+2E
Based on the preceding arguments, one is tempted to write the rate law for this reaction as Ratp = ~ C A C B ~ However, testing this expression with the experimental data may show that the proposed rate law is grossly inaccurate. Why? Suppose the reaction A 2B -takes place in several steps, the first step resulting in the formation of some intermediate, for example Bz, which in turn reacts with A. Such a mechanism could he represented as a series of reactions,
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2B
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A + Bz
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B2 (slow)
D
+ 2E (fast)
If the first step occurs very slowly and the second step is very rapid, then the measured rate for the overall reaction is approximately equal to the rate of the first step. The slow step in the overall reaction is the rate-determining step. If the proposed mechanism is correct, then the rate of reaction is probably proportional to the concentration of B squared, i.e., Rate = ~ C B ~ Alternatively, some other intermediate, such as AB, could be formed by the reaction
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A+B
AB (slow)
which, in turn, reacts with B, AB
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D
2E (fast)
If the first step, resulting in the formation of AB, is the ratedetermining step, the rate of reaction will probably be proportional to the concentration of A times the concentration of B Rote = kCACB The important point being emphasized is that rate laws must be experimentally determined; they cannot be determined from the stoichiometric equation for the reaction. Order of Reaction and Molecularlty Generally, the rate of a chemical reaction is proportional to the concentrations of the reactants. In the decomposition of nitrogen tetroxide N204
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2N02
the rate of reaction is proportional to the concentration of just one reactant and the rate = k C ~ , o , this ; is called a first-order reaction. When the rate of a reaction, as determined experimentally, is proportional to the concentration of two reactants, the reaction is called a second-order reaction. Alternately, a second-order reaction occurs when the rate of reaction is proportional to the square of the concentration of a single reactant. Examples of second-order reactions include: NO + 03-NOz + 0% Rate = kcKO, Iz + BTP 21B1. Rate = kC12C~n
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2NO + O2
Rate = hC~oCo, Reactions of order higher than second are occasionally found. This may he shown with the third-order reaction hetween nitric oxide and chlorine, for which the balanced equation is 2NOz
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2NO + CIS
2NOC1
The rate of formation of nitrosyl chloride, based on experimental data, is proportional ro the square of the nitric oxide cuncentmtion times the mncentrarion of chlorine. The rate law for this third-order reaction is Rate = ~ C N O ~ C C I , In general, the order of the reaction with respect to a reactant is eaual to its exponent in the rate law. and the overall reaction G~rierispive~bg t h e s u ~ otheexponents l in therate / n u . The exponents in the rate lau. ure usualls sin& r)ositive integers, h& occasionally they may he fra&io
