Chapter 12
The physical states of the reactants
A chemical reaction between two or more substances requires intimate contact between the reactants. When reactants are in diff physical states, or phases (solid, liquid, gaseous, dissolved) the reaction takes place only at the interface between the phases. Consider the heterogenous reaction between the solid phase and either a liquid or a gaseous phase. Compared with the reaction rate for large solid particles, the rate for smaller particles will be greater b/c the SA in contact with the other reactant phase is greater. For example, large pieces of iron react more slowly with acids than they do with finely divided iron powder. Large pieces of wood smolder, smaller pieces burn rapidly, and saw dust burns explosively. Figure 12.6 (a) Iron powder reacts rapidly with dilute hydrochloric acid and produces bubbles of hydrogen gas: 2Fe(s) + 6HCl(aq) ⟶ 2FeCl3(aq) + 3H2(g). (b) An iron nail reacts more slowly because the surface area exposed to the acid is much less.
A convenient approach for determining Ea...
A convenient approach for determining Ea for a reaction involves the measurement of k at two or more different temps and using an alternative version of the Arrhenius equation that takes the form of a linear equation lnk = (-Ea/R)(1/T) + lnA y = mx+b A plot of ln k versus 1/T with a slope equal to -Ea/R and a y-interecept equal to lnA.
Heterogeneous catalyst
A heterogeneous catalyst is a catalyst that is present in a different phase (usually a solid) than the reactants. Such catalysts generally function by furnishing an active surface upon which a reaction can occur. Gas and liquid phase reactions catalyzed by heterogeneous catalysts occur on the surface of the catalyst rater than within the gas or liquid phase. Heterogeneous catalysis typically involves the following processes: 1. Absorption of the reactant(s) onto the surface of the catalyst 2. Activation of the absorbed reactant(s) 3. Reaction of the absorbed reactant(s) 4. Desorption of product(s) from the surface of the catalyst. Figure 12.23 illustrates the steps of a mechanism for the reaction of compounds containing a carbon-carbon double bond with hydrogen on a nickel catalyst. Nickel is the catalyst used in the hydrogenation of polyunsaturated fats and oils (which contain several carbon-carbon double bonds) to produce saturated fats and oils (which contain only carbon-carbon single bonds). Many important chemical products are prepared via industrial processes that use heterogeneous catalysts, including ammonia, nitric acid, sulfuric acid, and methanol. Heterogeneous catalysts are also used in the catalytic converters found on most gasoline-powered automobiles (Figure 12.24).
Rate
A rate is a measure of how some property varies with time. Speed is a familiar rate that expresses the distance traveled by an object in a given amount of time. Wage is a rate that represents the amount of money earned by a person working for a given amount of time. Likewise, the rate of a chemical reaction is a measure of how much reactant is consumed, or how much product is produced, by the reaction in a given amount of time.
Catalysis
Among the factors affecting chemical reaction rates discussed earlier in this chapter was the presence of a catalyst, a substance that can increase the reaction rate without being consumed in the reaction. The concepts introduced in the previous section on reaction mechanisms provide the basis for understanding how catalysts are able to accomplish this very important function. Figure 12.19 shows reaction diagrams for a chemical process in the absence and presence of a catalyst. Inspection of the diagrams reveals several traits of these reactions. Consistent with the fact that the two diagrams represent the same overall reaction, both curves begin and end at the same energies (in this case, b/c products are more energetic than reactants, the reaction is endothermic). The reaction mechanisms, however, are clearly different. The uncatalyzed reaction proceeds via a one-step mechanism (one transitions state observed), whereas the catalyzed reaction proceeds via a two-step mechanism (two transition states observed) with a notably lesser activation energy. This difference illustrates the means by which a catalyst functions to accelerate reactions, namely, by providing an alternative reaction mechanism with a lower activation energy. Although catalyzed reaction mechanism for a reaction needn't necessarily involve a different number of steps than the uncatalyzed mechanism, it must provide a reaction path whose rate determining step is faster (lower Ea)
First order reactions
An equation relating the half-life of a first-order reaction to its rate constant may be derived from the integrated rate law as follows: ln([A]0/[A]t)= kt t = ln([A]0/[A]t) x 1/k Invoking the definition of half-life, symbolized t1/2, requires that the concentration of A at this point is one-half its initial concentration: t = t1/2, [A]t = 1/2[A]0 Substituting these terms into the rearranged integrated rate law and simplifying yields the equation for half-life t1/2 = ln([A]0/[A]t) x 1/k =ln2 x 1/k = 0.693 x 1/k t1/2 = 0.693/k This equation describes an expected inverse relation and its rate constant, k. Faster reactions exhibit larger rate constants and correspondingly shorter half-lives. Slower reactions exhibit smaller rate constants and longer half-lives.
Rate laws
As described in the previous module, the rate a reaction is often affected by the concentrations of the reactants. Rate laws (sometimes called differential rate laws) or rate equations are mathematical expressions that describe the relationship between the rate of a chemical rxn and the concentration of its reactants. As an example, consider the rxn described by the chemical equation aA+bB -> products where a and b are stoichiometric coefficients. The rate law for this reaction is written as: rate = k[A]^m[B]^n I which [A] and [B] represent molar concentrations of reactants, and k is the rate constant, which is specific for a particular reaction at a particular temp. The exponents m and n are the reaction orders and are typically positive integers, though they can be fractions, negative, or zero. The rate constant k and the reaction orders m and n must be determined experimentally by observing how the rate or a rxn changes as the concentrations of the reactants are changed. The rate constant k is independent of the reactant concentrations, but it does vary with temp.
First-order reactions
As for other reaction orders, an equation for zero-order half-life may be derived by half-life: t = 1/2 and [A] = [A]0/2. Substituting these terms into the zero-order integrated rate law yields: [A]0/2 = -kt1/2 + [A]0 kt1/2 = [A]0/2 t1/2 = [A]0/2k As for all reaction orders, the half-life for a zero-order reaction is inversesly propotional to its rate constant. However, the half-life of a zero-order reaction increases as the initial concentration increases.
Factors affecting reaction rates
By the end of this section, you will be able to: -describe the effects of chemical nature, physical state, temp, conc, and catalysis on reaction rates The rates at which reactions are consumed and products are formed during chemical reactions vary greatly. Five factors typically affecting the rates of chemical reactions will be explored in this section: the chemical nature of the reacting substances, the state of subdivision (one large lump versus many small particles) of the reactants, the temp of the reactants, the conc of the reactants, and the presence of a catalyst.
Temp of the reactants
Chemical reactions typically occur faster at higher temps. Food can spoil quickly when left on the kitchen counter. However, the lower temp inside of the fridge slows that process so that the same food remains fresh for days. Gas burners, hot plates, and ovens are often used in the lab to increase the speed of reactions that proceed slowly at ordinary temps. For many chemical processes, reaction rates are approx doubled when the temp is raised by 10°C.
Reaction mechanism
Chemical reactions very often occur in a step-wise fashion, involving two or more distinct reactions taking place in sequence. A balanced equation indicates what is reacting and what is produced, but it reveals no details about how the reaction actually takes place. The reaction mechanism (or reaction path) provides details regarding the precise, step-by-step process by which a reaction occurs. The decomposition of ozone, for example, appears to follow a mechanism with two steps: O3(g) -> O2(g) + O O + O3 -> 2O2 (g) Each of these steps in a reaction mechanism is an elementary reaction. These elementary reactions occur precisely as represented in the step equations, and they must sum to yield the balanced chemical equation representing the overall reaction. 2O3(g) -> 3O2(g) Notice that the oxygen atom produced in the first step of this mechanism is consumed in the second step and therefore does not appear as a product in the overall reaction. Species that are produced in one step and consumed in a subsequent step are called intermediates. While the overall reaction equation for the decomposition of ozone indicates that two molecules of ozone react to give three molecules of oxygen, the mechanism of the reaction does not involve the direct collision and reaction of two ozone molecules. Instead, one O3 decomposes to yield O2, and an oxygen atom, and a second O3 subsequently reacts with the oxygen atom to yield two additional O2 molecules. Unlike balanced equations representing an overall reaction, the equations for elementary reactions are explicit representations of the chemical change taking place. The reactant(s) in an elementary reaction's equation undergo only the bond-breaking and/or making events depicted to yield the product(s). For this reason, the rate law for an elementary reaction may be derived directly from the balanced chemical equation describing the reaction. This is not the case for typical chemical reactions, for which rate laws may be reliably determined only via experimentation.
Reaction diagrams
Figure 12.14 shows how the energy of a chemical system changes as it undergoes a reaction converting reactants to products according to the equation A+B -> C+D These reaction diagrams are widely used in chemical kinetics to illustrate various properties of the reaction of interest. Viewing the diagram from left to right, the system initially comprises reactants only, A + B. Reactant molecules with sufficient energy can collide to form a high-energy activated complex or transition state. The unstable transition state can then subsequently decay to yield stable products, C+D. The diagram depicts the reaction's activation energy, Ea, as the energy difference between the reactants and the transition state. Using a specific energy, the enthalpy, the enthalpy change of the reaction is estimated as the energy difference between the reactants and products. In this case, the reaction is exothermic since it yields a decrease in system enthalpy.
Second-order reactions
Following the same approach as used for first-order reactions, an equation relating the half-life of a second-order reaction to its rate-constant and initial concentration may be derived from its integrated rate law. 1/[A]t = kt + 1/[A]0 or 1/[A]-1/[A]0 = kt restrict t to t1/2 t = t1/2 define [A]t as one-half [A]0 [A]t = 1/2[A]0 and then substitute into the integrated rate law and simplify: 1/.5[A]0-1/[A]o = kt1/2 2/[A]0-1/[A]0 = kt1/2 1/[A]0 = kt1/2 t1/2 = 1/k[A]0 For a second-order rxn, t1/2 is inversely proportional to the concentration of the reactant, and the half-life increases as the reaction proceeds because the concentration of the reactant decreases. Unlike with first-order reactions, the rate constant of a second-order reaction cannot be calculated directly from the half-life unless the initial concentration is known.
Zero-order reactions
For a zero-order reaction, the differential rate law is: rate = k A zero-order reaction thus exhibits a constant reaction rate, regardless of the concentration of its reactant(s). This may seem counterintuitive, since the reaction rate certainly can't be finite when the reactant conc is zero. For purposes of this intro text, it will suffice to note that zero-order kinetics are observed for some reactions only under certain specific conditions. These same reactions exhibit different kinetic behaviors when the specific conditions aren't met, and for this reason the more prudent term pseudo-zero-order is sometimes used. The integrated rate law for a zero order reaction is a linear function. [A]t = -kt + [A]0 y = mx+b A plot of [A] vs t for a zero-order reaction is a straight line with a slope of -k and y-interecept of [A]0. Shows a plot of [NH3] versus t for the thermal decomposition of ammonia at the surface of two different heated solids. The decomposition reaction exhibits first order behavior at a quartz (SiO2) surface, as suggested by the exponentially decaying plot of concentration versus time. On a tungsten surface, however, the plot is linear, indicating zero-order kinetics.
Reaction order and rate constant units
In some of our examples the reaction orders in the rate law happen to be the same as the coefficients in the chemical equation for the reaction. This is merely a coincidence and very often not the case. Rate laws may exhibit fractional orders for some reactants, and negative reaction orders are sometimes observed when an increase in the concentration of one reactant causes a decrease in the reaction rate. It is important to note that rate laws are determined by experiment only and are not reliably predicted by reaction stoichiometry. The units for a rate constant will vary as appropriate to accommodate the overall reaction order of the rxn. The unit for the rate constant for the the second-order rxn described in example 12.4 was determined to be L mol^-1 s^-1. For the third-order reaction described in 12.5 the unit k was derived to be L^2 mol^-2 s^-1. Dimensional analysis requires the rate constant unit for a reaction whose overall order is x to be L^x-1 mol^1-x s^-1.
First-order reactions
Integration of the rate law for a simple first-order reaction (rate=k[A]) results in an equation describing how the reactant concentration varies with time. [A]t = [A]0e^-kt where [A]t is the concentration of A at any time t, [A]0 is the initial concentration of A, and k is the first-order rate constant. For mathematical convenience, this equation may be rearranged to other formats, including direct and indirect proportionalities: ln([A]t/[A]0]) = kt or ln([A]t/[A0]) = -kt and a format showing a linear dependence of concentration in time: ln[A]t = ln[A]0-kt
rate-limiting step
It's often the case that one step in a multistep reaction mechanism is significantly slower than the others. Because a reaction cannot proceed faster than its slowest step, this step will limit the rate at which the overall reaction occurs. The slowest step is therefore called the rate-limiting step (or rate-determining step_ of the reaction. As described earlier, rate laws may be derived directly from the chemical equations for elementary reactions. This is not the case, however, for ordinary chemical reactions. The balanced equations most often encountered represent the overall change for some chemical system, and very often this is a result of some multistep reaction mechanisms. In every case, the rate law must be determined from the experimental data and the reaction mechanism subsequently deduced fromt he rate law (and sometimes other data). The reaction of NO2 and CO provides an illustrative example: NO2 (g) + CO(g) -> CO2(g) + NO(g) For temps above 225°C, the rate law has been found to be: rate = k[NO2][CO] The reaction is first order with respect to NO2 and first order with respect to CO. This is consistent with a single-step bimolecular mechanism and it is possible that this is the mechanism for this reaction at high temps. At temps below 225°C, the reaction is described by a rate law that is second order with respect to NO2: rate = k[NO2]^2 This rate law is not consistent with the single-step mechanism, but is consistent with the following two step mechanism: NO2(g) + NO2(g) -> NO3(g) + NO(g) (slow) NO3(g) + CO(g) -> NO2(g) + CO2(g) (fast) The rate-determining (slower) step is the first step in the mechanism, the rate law for the overall reaction is the same as the rate law for this step. However, when the rate-determining step is preceded by a step involving a rapidly reversible reaction the rate law for the overall reaction may be more difficult to derive. As discussed in several chapters of this text, a reversible reaction is at equilibrium when the rates of the forward and reverse processes are equal. Consider the reversible elementary reaction in which NO dimerizes to yield an intermediate species, N2O2. When this reaction is at equilibrium" NO+NO <--> N2O2 rate forward = rate reverse k1 [NO]^2 = k-1 [N2O2] This expression may be rearranged to express the concentration of the intermediate in terms of the reactant NO: (k1[NO] if ^2/K-1) = [N2O2] Since the intermediate species concentrations are not used in formulating rate laws for overall reactions, this approach is sometimes necessary, as illustrated in the following example exercise.
The presence of a catalyst
Relatively dilute aqueous solutions of hydrogen peroxide, H2O2, are commonly used as topical antiseptics. Hydrogen peroxide decomposes to yield water and oxygen gas according to the equation: 2H2O2(l) -> 2H2O(l) + O2(g) Under typical conditions, this decomposition occurs very slowly. When dilute H2O2 (aq) is poured onto an open wound, however, the reaction occurs rapidly and the solution foams b/c of the vigorous production of oxygen gas. This dramatic difference is caused by the presence of substances within the wound's exposed tissues that accelerate the decomposition process. Substances that function to increase the rate of the reaction are called catalysts, a topic treated in greater detail later in this chapter.
Arrhenius equation
The Arrhenius equation relates the activation energy and the rate constant, k, for many chemical reactions: k = Ae^-Ea/RT In this equation, R is the ideal gas constant, which has a value of 8.314 J/mol/K, T is temperature on the kelvin sccale, Ea is the activation energy in joules per mole, e is the constant 2.7183, and A is a constant called the frequency factor, which is related to the frequency of collisions and the orientation of the reacting molecules. Postulates of the collision theory are nicely accomodated by the Arrhenius equation. The frequency factor, A, reflects how well the reaction conditions favor properly oriented collisions between reactant molecules. An increased probability of effectively oriented collisions results in larger values for A and faster reaction rates. The exponential term, e^-Ea/RT, describes the effect of activation energy on the reaction rate. According to kinetic molecular theory (see chapter on gases) the temp of matter is a measure of the average kinetic energy of its constituent atoms or molecules. The distribution of energies among the molecules composing a sample of matter at any given temp is described by the plot shown in...
Second-order reactions
The equations that relate the concentrations of reactants and the rate constant of second-order reactions can be fairly complicated. To illustrate the point with minimal complexity, only the simplest second-order reactions will be described here, namely, those whose rates depend on the concentration of just one reactant. For these types of reactions, the differential rate law is written as: r = k[A]^2 For these second-order reactions, the integrated rate law is: 1/[A]1 = kt + 1/[A]0 Where the terms in the equation have their usual meanings as defined earlier The integrated rate law for second-order reactions has the form of the equation of a straight line: 1/[A]t = kt + 1/[A]0 y = mx+b A plot of 1/[A]t versus t for a second-order reaction is a straight line with a slope of k and a y-intercept of 1/[A]0. If the plot is not a straight line, then the reaction is not second order.
In the next example...
The integrated rate law will be convenient. ln[A]t = (-k)(t) + ln[A]0 y = mx+t A plot of ln[A]t versus t for a first order reaction is a straight line with a slope of -k and a y intercept of ln[A]0. If a set of rate data are plotted in this fashion but do not result in a straight line, the reaction is not first order in A.
Lizard in the sun
The lizard in pic not just enjoying sun or tanning. The heat from the sun's rays is critical to lizard's survival. A warm lizard can move faster than a cold one because the chemical reactions that allow its muscles to move occur more rapidly at higher temps. A cold lizard is a slower lizard and an easier meal for predators. From baking a cake to determining the useful lifespan of a bridge, rates of chemical reactions play important roles in our understanding of processes that involve chemical changes. Two questions are typically posed when planning to carry out a chemical reaction. The first is: "Will the rxn produce the desired products in useful quantities?" The second question is: "How rapidly will the reaction occur?" A third question is often asked when investigating reactions in greater detail: "What specific molecular-level processes take place as the reaction occurs?" Knowing the answer to this question is of practical importance when the yield or rate of a rxn needs to be controlled. The study of chemical kinetics concerns the second and third questions- that is, the rate at which a reaction yields products and the molecular-scale means by which the reaction occurs. This chapter examines the factors that influence the rate of chemical reactions, the mechanisms by which reactions proceed, and the quantitative techniques used to describe the rates at which reactions occur.
Activation energy and the Arrhenius equation
The minimum energy necessary to form a product during a collision between reactants is called the activation energy (Ea). How this energy compares to the kinetic energy provided by colliding reactant molecules is a primary factor affecting the rate of a chemical reaction. If the activation energy is much larger than the average KE of the molecules, the reaction will occur slowly since only a few fast-moving molecules will have enough energy to react. If the activation energy is much smaller than the average kinetic energy of the molecules, a large fraction of molecules will be adequately energetic and the reaction will proceed rapidly.
Unimolecular elementary reaction
The molecularity of an elementary reaction is the number of reactant species (atoms, molecules, or ions). For example, a unimolecular reaction involves the reaction of a single reactant species to produce one or more molecules of product: A-> products The rate law for a unimolecular reaction is first order. rate = k[A] A unimolecular reaction may be one of several elementary reactions in a complex mechanism. For example, the reaction: O3->O2+O illustrates a unimolecular elementary reaction that occurs as one part of a two-step reaction mechanism as described above. However, some unimolecular reactions may e the only step of a single-step reaction mechanism. (In other words, an "overall" reaction may also be an elementary reaction in some cases.) For example, the gas-phase decomposition of cyclobutane, C4H8, to ethylene, C2H4, is represented by the following chemical equation... This equation represent the overall reaction observed, and it might also represent a legitimate unimolecular elementary reaction. The rate law predicted from this equation, assuming it is an elementary reaction, turns out to be the same as the rate law derived experimentally for the overall reaction, namely, one showing first-order behavior: rate = -(delta[CH4H8]/deltaT) = k[C4H8] This agreement between observed and predicted rate laws is interpreted to mean that the proposed unimolecular, single-step process is a reasonable mechanism for the butadiene reaction.
Relative rates of reaction
The rate of a reaction may be expressed as the change in concentration of any reactant or product. For any given reaction, these rate expressions are all related simply to one another according to the reaction stoichiometry. The rate of the general reaction aA-> bB can be expressed in terms of the decrease in the concentration of A or the increase in the concentration of B. These two rate expressions are related by the stoichiometry of the reaction: rate = -(1/a)(deltaA/deltat)(deltaA/deltaT) = (1/b)(deltaB/deltat) The reaction represented by the following equation: (2NH3/deltaT) x (1 mol N2/ 2 mol NH3) = delta mol N2/deltaT This may be represented by an abbreviated format by omitting the units of the stoichiometric factor: (-1/2) delta mol NH3/delta T = delta mol N2/delta T Note that a negative sign has been included as a factor to account for the opposite signs of the two amount changes (the reactant amount is decreasing while the product amount is increasing). For homogeneous reactions, both the reactants and products are present in the same solution and thus occupy the same volume, so the molar amounts may be replaced with molar concentrations: -1/2 delta[NH3]/deltaT = delta[N2]/deltat Similarly the rate of formation of H2 is three times the rate of formation of N2 because three moles of H2 are produced for each mole of N2 produced. 1/3 delta[H2]/deltat = delta[N2]/deltat
Figure 12.2
The rate of decomposition of H2O2 in an aqueous solution decreases as the concentration of H2O2 decreases. To obtain the tabulated results for this decomposition, the concentration of hydrogen peroxide was measured every 6 hours over the course of a day at a constant temp of 40°C. Reaction rates were computed for each time interval by dividing the change in concentration by the corresponding time increment, as shown here for the first 6-hour period. -delta[H2O2]/deltaT = -(0.500 mol/L-1.000 mol/L)/(6.00 h-0.00 h) = 0.0833 mol L^-1 h^-1 Notice that the reaction rates vary with time, decreasing as the reaction proceeds. Results for the last 6-hour period yield a reaction rate of: -delta[H2O2]/deltaT = -(0.0625 mol/L - 0.125 mol/L)/(24.00 h- 18.00 h) = 0.010 mol L^-1 h^-1
Rate of reaction
The rate of reaction is the change in the amount of reactant or product per unit time. Reaction rates are therefore determined by measuring the time dependence of some property that can be related to reactant or product amounts. Rates of reaction that consume or produce gaseous products, for example, are determined by measuring changes in volume or pressure. For reactions involving one or more colored substances, rates may be monitored via measurements of light absorption. For reactions involving aqueous electrolytes, rates may be measured via changes in a solution's conductivity. For reactants and products in solution, their relative amounts (concentrations) are conveniently used for purposes of expressing reaction rates. For example, the concentration of hydrogen peroxide, H2O2, in an aqueous solution changes slowly over time as it decomposes according to the equation: 2H2O2(aq) -> 2H2O(l) + O2(g) The rate at which the hydrogen peroxide decomposes can be expressed in terms of rate of change of its concentration, as shown here: rate of decomposition of H2O2 = -(change in concentration of reactant)/time interval =(-[H2O2]t2-[H2O2]t1)/t2-t1 =-delta[H2O2]/deltaT
The chemical nature of the reacting substances
The rate of the reaction depends on the nature of the participating substances. Reactions that appear similar may have different rates under the same conditions, depending on the identity of the reactants. For ex, when small pieces of the metals iron and sodium are exposed to air, the sodium reacts completely with air overnight, wheras the iron is barely affected. The active metals calcium and sodium both react with water to form hydrogen gas and a base. Yet calcium reacts at a moderate rate, whereas sodium reacts so rapidly that the reaction is almost explosive.
overall reaction order
The reaction orders in a rate law describe the mathematical dependence of the rate on reactant concentrations. Referring to the generic rate law above, the reaction is m order with respect to A and n order with respect to B. For example, if m=1 and n=2, the reaction is first order in A and second order in B. The overall reaction order is simply the sum of the orders for each reactant. For the example rate law here, the reaction is third order overall (1+2=3). A few specific examples are shown below to illustrate this concept. The rate law: rate = k[H2O2] describes a rxn that is first order in hydrogen peroxide and first order overall. The rate law: rate = k[C4H6]^2 describes a rxn that is second order in C4H6 and second order overall. The rate law: rate=k[H+][OH-] describes a rxn that is first order in H+, first order in OH-, and second order overall.
figure 12.15
Two shaded areas under the curve represent the number of molecules possessing adequate energy (RT) to overcome the activation barriers (Ea). A lower activation energy results in a greater fraction of adequately energized molecules and a faster reaction. The exponential term also describes the effect of temperature on rxn rate. A higher temp represents a correspondingly greater fraction of molecules possessing sufficient energy (RT) to overcome the activation barrier (Ea) as shown in figure 12.15. This yields a greater value for the rate constant and a correspondingly faster reaction rate.
Collision theory
We should not be surprised that atoms, molecules, or ions must collide before they can react with each other. Atoms must be close together to form chemical bonds. This simple premise is the basis for a very powerful theory that explains many observations regarding chemical kinetics, including factors affecting reaction rates. Collision theory is based on the following postulates: 1. The rate of a reaction is proportional to the rate of reactant collisions. reactant rate proportional #collisions/time 2. The reacting species must collide in an orientation that allows contact between the atoms that will become bonded together in the product 3. The collision must occur with adequate energy to permit mutual penetration of the reacting species' valence shells so that the electrons can rearrange and form new bonds (and new chemical species) We can see the importance of the two physical factors noted in postulate 2 and 3, the orientation and energy of collisions, when we consider the rxn of carbon monoxide and oxygen: 2CO(g) + O2(g) -> 2CO2 (g) Carbon monoxide is a pollutant produced by the combustion of hydrocarbon fuels. To reduce this pollutant, automobiles have catalytic converters that use a catalyst to carry out this reaction. It is also a side reaction of the combustion of gun powder that results in muzzle flash for many firearms. If carbon monoxide and oxygen are present in sufficient amounts, the reaction will occur at high temps and pressure. The first step in the gas-phase reaction between carbon monoxide and oxygen is a collision between the two molecules: CO(g) + O2(g) -> CO2(g) + O(g) Although there are many different possible orientations the two molecules can have relative to each other, consider the two presented in figure 12.13. In the first case, the oxygen side of the carbon monoxide molecule collides with the oxygen molecule. In the second case, the carbon side of the carbon monoxide molecule collides with the oxygen molecule. The second case is clearly more likely to result in the formation of carbon dioxide, which has a central carbon atom bonded to two oxygen atoms. This is a rather simple example of how important the orientation of the collision is in terms of creating the desired product of the reaction. If the collision does take place with the correct orientation, there is still no guarantee that the reaction will proceed to form carbon dioxide. In addition to a proper orientation, the collision must also occur with sufficient energy to result in product formation. When a reactant species collide with both proper orientation and adequate energy, they combine to form an unstable species called an activated complex or a transition state. These species are very short lived and usually undetectable by most analytical instruments. In some cases, sophisticated spectral instruments have been used to observe transition states. Collision theory explains why most reaction rates increase as concentrations increase. With an increase in the concentration of any reacting substance, the chances for collisions between molecules are increased because there are more molecules per unit of volume. More collisions mean a faster reaction rate, assuming the energy of the collisions is adequate.
average rate
^^^ This behavior indicates the reaction continually slows with time. Using the concentrations at the beginning and end of a time period over which the reaction rate is changing results int he calculation of an average rate for the reaction over this time interval. At any specific time, the rate at which a reaction is proceeding is known as its instantaneous rate. The instantaneous rate of a reaction at "time zero," when the reaction commences, is its initial rate. Consider the analogy of a car slowing down as it approaches a stop sign. The vehicle's initial rate- analogous to the beginning of a chemical reaction- would be the speedometer reading at the moment the driver begins pressing the breaks (t0). A few moments later, the instantaneous rate at a specific moment- call it t1- would be somewhat slower, as indicate by the speedometer reading at that point in time. As time passes, the instantaneous rate will continue to fall until it reaches zero, when the car (or reaction) stops. Unlike instantaneous speed, the car's average speed is not indicated by the speedometer, but it can be calculated as the ratio of the distance traveled to the time required to bring the vehicle to a complete stop (delta T). Like the decelerating car, the average rate of a chemical rxn will fall somewhere between its initial and final rates. The instantaneous rate of a reaction may be determined one of two ways. If experimental conditions permit the measurement of concentration changes over very short time intervals, then average rates computed as as described as described earlier provide reasonably good approximations of instantaneous rates. Alternatively, a graphical procedure may be used that, in effect, yields the results that would be obtained if short time interval measurements were possible. In a plot of the concentration of hydrogen peroxide against time, the instantaneous rate of decomposition of H2O2 at any time t is given by the slope of a straight lien that is tangent to the curve at that time. These tangent line slopes may be evaluated using calculus, but the procedure for doing so is beyond the scope of this chapter.
Rate expression
^^^ This mathematical representation of the change in species concentration over time is the rate expression for the reaction. The brackets indicate molar concentrations, and the symbol delta indicates "change in." Thus, [H2O2]t1 reprresents the molar concentration at some time t1; likewise, [H2O2]t2 represents the molar concentration of hydrogen peroxide at a later time t2; and delta[H2O2]t2 represents the molar concentration of hydrogen peroxide at a later time t2; and delta[H2O2] represents the change in molar concentration of hydrogen peroxide during the time interval delta T (that is, t2-t1). Since the reactant concentration decreases as the reaction proceeds, delta[H2O2] is a negative quantity. Reactoin rates are, by convention, positive quantities, and so this negative change in concentration is multiplied by -1. Figure 12.2 provides an example of data collected during the decomposition of H2O2... (next slide)
bimolecular reaction
a bimolecular reaction involves two reactant species, for example: A + B-> products and 2A-> products For the first type, in which the two reactant molecules are different, the rate law is first-order in A and first order in B (second-order overall): rate = k[A][B] For the second type, in which two identical molecules collide and react, the rate law is second order in A: rate = k[A][A] = k[A]^2 Some chemical reactions occur by mechanisms that consist of a single bimolecular elementary reaction. One example is that the reaction of nitrogen dioxide with carbon monoxide: NO2(g) + CO(g) -> NO(g) + CO2(g) Figure 12.17 The probable mechanism for the reaction between NO2 and CO to yield NO and CO2. Bimolecular elementary reactions may also be involved as steps in a multitask reaction mechanism. the reaction of atomic oxygen with ozone is the second step of the two-step ozone decomposition mechanism discussed earlier in the section: O(g) + O3(g) -> 2O2(g)
method of initial rates
a common experimental approach to the determination of rate laws is the method of initial rates. This method involves measuring reaction rates for multiple experimental trials carried out using different initial reactant concentrations. Comparing the measured rates for these trials permits determination of the reaction orders and, subsequently, the rate constant, which together are used to formulate a rate law.
Homogeneous catalyst
a homogeneous catalyst is present in the same phase as the reactants. It interacts with a reactant to form an intermediate substance, which then decomposes or reacts with another reactant in one or more steps to regenerate the original catalyst and form product. As an important illustration of homogeneous catalysis, consider the earth's ozone layer. Ozone is the upper atmosphere, which protects the earth from ultraviolet radiation, is formed when oxygen molecules absorb ultraviolet light and undergo the reaction. 3O2(g) -> 2O3(g) Ozone is a relatively unstable molecule that decomposes to yield diatomic oxygen by the reverse of this equation. This decomposition reaction is consistent with the following two-step mechanism. O3->O2+O O+O3->2O2 A number of substances can catalyze the decomposition of ozone. For ex, the nitric oxide-catalyzed decomposition of ozone is believed to occur via the following three-step mechanism: NO(g) + O3(g) -> NO2(g) + O2(g) O3(g)-> O2(g)+O(g) NO2(g)+O(g)->NO(g)+O2(g) As required, the overall reaction is the same for both the two-step uncatalyzed mechanism and the three-step NO-catalyzed mechanism: 2O3(g)->3O2(g) Notice that NO is a reactant in the first step of the mechanism and a product in the last step. This is another characteristic trait of a catalyst: Though it participates in the chemical reaction, it is not consumed by the reaction.
termolecular reaction
an elementary termolecular reaction involves the simultaneous collision of three atoms, molecules, or ions. Termolecular elementary reactions are uncommon because the probability of three particles colliding simultaneously is less than one-thousandth of the probability of two particles colliding. There are, however, a few established termolecular elementary reactions. The reaction of nitric oxide with oxygen appears to involve termolecular steps. 2NO + O2 -> 2NO2 rate = k[NO]^2[Cl2] Likewise, the reaction of nitric oxide with chlorine appears to involve termolecular steps: 2NO + Cl2 -> 2NOCl rate = k[NO]^2[Cl2]
In order to distinguish a first-order reaction from a second-order rxn...
prepare a plot of ln[A]t vs t and compare it to a plot of 1/[A]t versus t.
Integrated rate laws
the rate laws discussed thus far relate the rate and the concentrations of reactants. We can also determine a second form of each rate law that relates the concentrations of reactants and time. These are called integrated rate laws. We can use an integrated rate law to determine the amount of reactant or product present after a period of time or to estimate the time required for a reaction to proceed to a certain extent. For example, an integrated rate law is used to determine the length of time a radioactive material must be stored for its radioactivity to decay to a safe level. Using calculus, the differential rate law for a chemical reaction can be integrated with respect to time to give an equation that relates the amount of reactant or product present in a reaction mixture to the elapsed time of the reaction. This process can either be very straightforward or very complex, depending on the complexity of the differential rate law. For purposes of discussion, we will focus on the resulting integrated rate laws for first-, second-, and zero-order reactions.
Concentrations of the reactants
the rates of many reactions depend on the concentrations of the reactants. Rates usually increase when the concentration of one or more of the reactants increases. For example, calcium carbonate (CaCO3) deteriorates as a result of its reaction with the pollutant sulfur dioxide. The rate of this reaction depends on the amount of sulfur dioxide in the air. An acidic oxide, sulfur dioxide combines with water vapor in the air to produce sulfurous acid in the following reaction: SO2 (g) + H2O(g) -> H2SO3(aq) Calcium carbonate reacts with sulfurous acid as follows: CaCO3(s) + H2SO3(aq) -> CaSo3(aq) + CO2(g) + H2O(l) In a polluted atmosphere where the concentration of sulfur dioxide is high, calcium carbonate deteriorates more rapidly than in less polluted air. Similarly, phosphorus burns more rapidly in an atmosphere of pure oxygen than in air, which is only about 20% oxygen.
half-life of a reaction (t1/2)
the time required for one-half of a given amount of reactant to be consumed. In each succeeding half-life, half of the remaining concentration of the reactant is consumed. Using the decomposition of hydrogen peroxide as an example, we find that during the first half-life (from 0.00 hours to 6.00 hours) the concentration of H2O2 decreases from 1.000 M to 0.500 M. During the second half life (from 6 to 12 hours), it decreases from 0.500 M to 0.250 M; during the third half-life, it decreases from 0.250 M to 0.125 M. The concentration of H2O2 decreases by half during each successive period of 6 hours. The decomposition of hydrogen peroxide is a first-order reaction is a first-order reaction, and, as can be shown, the half-life of a first-order reaction is independent of the concentration of the reactant. However, half-lives of reactions with other orders depend on the concentrations of the reactants.
