Chapter 15: Kinetics • The speed with which the reactants disappear and the products form is called the rate of the reaction • A study of the rate of reaction can give detailed information about how reactants change into products • The series of individual steps that add up to the overall observed reaction is called the reaction mechanism • There are five principle factors that influence reaction rates: 1) Chemical nature of the reactants 2) Ability of the reactants to come in contact with each other 3) Concentration of the reactants 4) Temperature 5) Availability of of rate-accelerating agents called catalysts The progress of the reaction A B. The number of A molecules (in red) decreases with time while the number of B molecules (in blue) increases. The steeper the concentration versus time curve, the faster the reaction rate. The film strip represents the relative number of A and B molecules at each time. • Chemical nature of the reactants – Bonds break and form during reactions • The most fundamental difference in reaction rates lie in the reactants themselves • Some reactions are fast by nature and others slow • Ability of the reactants to meet – Most reactions require that particles (atoms, molecules, or ions) collide before the reaction can occur – This depends on the phase of the reactants – In a homogeneous reaction the reactants are in the same phase • For example both reactants in the gas (vapor) phase – In a heterogeneous reaction the reactants are in different phases • For example one reactant in the liquid and the second in the solid phase – In heterogeneous reactions the reactants meet only at the intersection between the phases – Thus the area of contact between the phases determines the rate of the reaction Effect of crushing a solid. When a single solid is subdivided into much smaller pieces, the total surface area on all of the pieces becomes very large. • Concentration of the reactants – Both homogeneous and heterogeneous reaction rates are affected by reactant concentration • For example, red hot steel wool bursts into flames in the presence of pure oxygen • Temperature of the system – The rates for almost all chemical reactions increase as the temperature is increased • Cold-blooded creatures, such as insects and reptiles, become sluggish at lower temperatures as their metabolism slows down • Presence of a catalyst – A catalysts is a substance that increases the rate of a chemical reaction without being consumed – Enzymes are biological catalysts that direct our body chemistry • A rate is always expressed as a ratio • One way to describe a reaction rate is to select one component of the reaction and describe the change in concentration per unit of time (conc. of X at time t 2 conc. of X at time t1 ) rate with respect to X (t 2 t1 ) (conc. of X ) t • Molarity (mol/L) is normally the concentration unit and the second (s) is the most often used unit of time • Typically, the reaction rate has the units mol/L -1 -1 or mol L s s • By convention, reaction rates are reported as a positive number even when the monitored species concentration decreases with time • If the rate is known with respect to one species, the coefficients of the balanced chemical equation can be used to find the rates with respect to the other species • Consider the combustion of propane: C3 H 8 ( g ) 5O2 ( g ) 3CO2 ( g ) 4 H 2O( g ) • Compared to the rate with respect to propane: – Rate with respect to oxygen is five times faster – Rate with respect to carbon dioxide is three times faster – Rate with respect to water is four times faster • Since the rates are all related any may be monitored to determine the reaction rate • A reaction rate is generally not constant throughout the reaction • Since most reactions depend on the concentration of reactants, the rate changes as they are used up • The rate at any particular moment is called the instantaneous rate • It can be calculated from a concentration versus time plot A plot of the concentration of HI versus time for the reaction: 2HI(g) H2(g) + I2(g). The slope is negative because we are measuring the disappearance of HI. When used to express the rate it is used as a positive number. • The rate of a homogeneous reaction at any instant is proportional to the product of the molar concentrations of the reactants raised to a power determined from experiment For thegeneral reaction A B products The rate of reaction can be expressedas rate k[ A] [ B] m n k the rate constant for the reaction • Consider the following reaction: H 2 SeO3 6 I 4 H Se 2 I 3 3H 2O • From experiment, the rate law (determined from initial rates) is 3 2 rate k[ H 2 SeO3 ] [ I ] [ H ] 1 • At 0oC, k equals 5.0 x 105 L5 mol-5 s-1 • Thus, at 0oC 1 rate (5.0 10 L mol s ) 5 -5 -5 3 2 [ H 2 SeO3 ][I ] [ H ] • The exponents in the rate law are generally unrelated to the chemical equation’s coefficients – Never simply assume the exponents and coefficients are the same – The exponents must be determined from the results of experiments • The exponent in a rate law is called the order of reaction with respect to the corresponding reactant • For the rate law: 3 2 rate k[ H 2 SeO3 ] [ I ] [ H ] 1 • We can say – The reaction is first order with respect to H2SeO3 – The reaction is third order with respect to I- – The reaction is second order with respect to H+ – The reaction order is sixth order overall • Exponents in a rate law can be fractional, negative, and even zero • Looking for patterns in experimental data provide way to determine the exponents in a rate law • One of the easiest ways to reveal patterns in data is to form ratios of results using different sets of conditions • This technique is generally applicable • Again consider the hypothetical reaction A B products rate k[ A] [ M ] m n • Suppose the experimental concentration- rate data for five experiments is: Inital Conc. [ A] [ B] Initial Rate Expt (mol L-1 ) (mol L-1 ) (mol L-1 s -1 ) 1 0.10 0.10 0.20 2 0.20 0.10 0.40 3 0.30 0.10 0.60 4 0.30 0.20 2.40 5 0.30 0.30 5.40 • For experiments 1, 2, and 3 [B] is held constant, so any change in rate must be due to changes in [A] • The rate law says that at constant [B] the rate is proportional to [A]m m rate2 [ A]2 [ A] rate1 1 rate2 0.40 mol L-1 s -1 0.20 mol L-1 s -1 2 Thus m=1 rate1 m m [ A]2 0.20 mol L -1 [ A] 2m 0.10 mol L-1 1 • This means that the reactions is first order with respect to reactant A • For experiments 3, 4, and 5 [A] is held constant, so any change must be due to changes in [B] • The rate law says that at constant [A] the rate is proportional to [B]n • Using the results from experiment 3 and 4: n rate4 [ B ]4 rate3 [ B ]3 rate4 2.40 mol L-1 s -1 0.60 mol L-1 s -1 4 rate3 Thus n=2 n n [ B ]4 0.20 mol L -1 2n [ B ] 0.10 mol L-1 3 • The reaction is second order in B and rate=k[A][B]2 • The rate constant (k) can be determined using data from any experiment • Using experiment 1: -1 -1 rate 0.20 mol L s k 2 -1 -1 2 [ A][B] (0.10 mol L )(0.10mol L ) 2.0 10 L mol s 2 2 -2 -1 • Using data from a different experiment might give a slightly different value • The relationship between concentration and time can be derived from the rate law and calculus • Integration of the rate laws gives the integrated rate laws • Integrate laws give concentration as a function of time • Integrated laws can get very complicated, so only a few simple forms will be considered • First order reactions – Rate law is: rate = k [A] – The integrate rate law can be expressed as: [ A]0 kt ln kt or [ A]t [ A]0 e [ A]t • [A]0 is [A] at t (time) = 0 • [A]t is [A] at t = t • e = base of natural logarithms = 2.71828… • Graphical methods can be used to determine the first-order rate constant, note [ A]0 ln kt [ A]t ln[ A]0 ln[ A]t kt ln[ A]t ln[ A]0 kt ln[ A]t kt ln[ A]0 y mx b • A plot of ln[A]t versus t gives a straight line with a slope of -k The decomposition of N2O5. (a) A graph of concentration versus time for the decomposition at 45oC. (b) A straight line is obtained from a logarithm versus time plot. The slope is negative the rate constant. • The simplest second-order rate law has the form rate k [ B ] 2 • The integrated form of this equation is 1 1 kt [ B]t [ B]0 [ B]0 the initial concentrat of B ion [ B]t the concentrat of B at time t ion • Graphical methods can also be applied to second-order reactions • A plot of 1/[B]t versus t gives a straight line with a slope of k Second-order kinetics. A plot of 1/[HI] versus time (using the data in Table 15.1). • The amount of time required for half of a reactant to disappear is called the half-life, t1/2 – The half-life of a first-order reaction is not affected by the initial concentration [ A]0 First - order rate law : ln kt [ A]t 1 at t t1/ 2 , [ A]t [ A]0 , substituting 2 [ A]0 ln 2 ln 1 kt1/ 2 or t1/ 2 2 [ A]0 k First-order radioactive decay of iodine-131. The initial concentration is represented by [I]0. – The half-life of a second-order reactions does depend on the initial concentration 1 1 Second- order rate law : kt [ B]t [ B]0 1 at t t1/ 2 , [ B]t [ B]0 , substituting 2 1 1 1 kt1/ 2 2 [ B]0 [ B]0 1 ln 2 kt1/ 2 or t1/ 2 [ B]0 k[ B]0 • One of the simplest models to explain reactions rates is collision theory • According to collision theory, the rate of reaction is proportional to the effective number of collisions per second among the reacting molecules • An effective collision is one that actually gives product molecules • The number of all types of collisions increase with concentration, including effective collisions • There are a number of reasons why only a small fraction of all the collisions leads to the formation of product: – Only a small fraction of the collisions are energetic enough to lead to products – Molecular orientation is important because a collision on the “wrong side” of a reacting species cannot produce any product • This becomes more important as the complexity of the reactants increases The key step in the decomposition of NO2Cl to NO2 and Cl2 is the collision of a Cl atom with a NO2Cl molecules. (a) A poorly orientated collision. (b) An effectively orientated collision. – The minimum energy kinetic energy the colliding particles must have is called the activation energy, Ea – In a successful collision, the activation energy changes to potential energy as the bonds rearrange to for products – Activation energies can be large, so only a small fraction of the well-orientated, colliding molecules have it – Temperature increases increase the average kinetic energy of the reacting particles Kinetic energy distribution for a reaction at two different temperatures. At the higher temperature, a larger fraction of the collisions have sufficient energy for reaction to occur. The shaded area under the curves represent the reacting fraction of the collisions. • Transition state theory explains what happens when reactant particles come together • Potential-energy diagrams are used to help visualize the relationship between the activation energy and the development of total potential energy • The potential energy is plotted against reaction coordinate or reaction progress The potential-energy diagram for an exothermic reaction. The extent of reaction is represented as the reaction coordinate. A successful (a) and unsuccessful (b) collision for an exothermic reaction. • Activation energies and heats of reactions can be determined from potential-energy diagrams Potential-energy diagram for an endothermic reaction. The heat of reaction and activation energy are labeled. • Reactions generally have different activation energies in the forward and reverse direction Activation energy barrier for the forward and reverse reactions. • The brief moment during a successful collision that the reactant bonds are partially broken and the product bonds are partially formed is called the transition state • The potential energy of the transition state is a maximum of the potential-energy diagram • The unstable chemical species that “exists” momentarily is called the activated complex Formation of the activated complex in the reaction between NO2Cl and Cl. NO2Cl+ClNO2+Cl2 • The activation energy is related to the rate constant by the Arrhenius equation Ea / RT k Ae k = rate constant Ea = activation energy e = base of the natural logarithm R = gas constant = 8.314 J mol-1 K-1 T = Kelvin temperature A = frequency factor or pre-exponential factor • The Arrhenius equation can be put in standard slope-intercept form by taking the natural logarithm ln k ln A Ea / RT or ln k ln A ( Ea / R) (1 / T ) y b m x • A plot of ln k versus (1/T) gives a straight line with slope = -Ea/RT • The activation energy can be related to the rate constant at two temperatures k2 Ea 1 1 ln k T T 1 R 2 1 • The reaction’s mechanism is the series of simple reactions called elementary processes • The rate law of an elementary process can be written from its chemical equation • The overall rate law determined for the mechanism must agree with the observed rate law • The exponents in the rate law for an elementary process are equal to the coefficients of the reactants in chemical equation Elementary process: 2NO2 NO3 NO rate k[NO2 ] 2 • Multistep reactions are common • The sum of the element processes must give the overall reaction • The slow set in a multistep reaction limits how fast the final products can form and is called the rate-determining or rate- limiting step • Simultaneous collisions between three or more particles is extremely rate • A reaction that depended a three-body collision would be extremely slow • Thus, reaction mechanism seldom include elementary process that involve more than two-body or bimolecular collisions • Consider the reaction 2NO 2H2 N 2 2H2O rate k[NO] [H2 ] (experimental) 2 • The mechanism is thought to be 2NO N 2O 2 (fast) N 2 O 2 H 2 N 2 O H 2 O (slow) N 2O H 2 N 2 H 2O (fast) • The second step is the rate-limiting step, which gives rate k[ N 2O2 ][H 2 ] • N2O2 is a reactive intermediate, and can be eliminated from the expression • The first step is a fast equilibrium • At equilibrium, the rate of the forward and reverse reaction are equal rate(forwa k f [ NO]2 rd) rate(reverse) k r [ N 2 O 2 ] thus k f [ NO]2 k r [ N 2 O 2 ] or kf [ N 2O 2 ] 2 [ NO] kr • Substituting, the rate law becomes rate k[ N 2 O 2 ][H 2 ] kf rate k [ NO] [H 2 ] or k 2 r rate k '[ NO] [H 2 ] 2 • Which is consistent with the experimental rate law • A catalyst is a substance that changes the rate of a chemical reaction without itself being used up – Positive catalysts speed up reactions – Negative catalysts or inhibitors slow reactions • (Positive) catalysts speed reactions by allowing the rate-limiting step to proceed with a lower activation energy • Thus a larger fraction of the collisions are effective (a) The catalyst provides an alternate, low-energy path from the reactants to the products. (b) A larger fraction of molecules have sufficient energy to react when the catalyzed path is available. • Catalysts can be divided into two groups – Homogeneous catalysts exist in the same phase as the reactants – Heterogeneous catalysts exist in a separate phase • NO2 is a homogeneous catalyst for the production of sulfuric acid in the lead chamber process • The mechanism is: S O 2 SO 2 SO 2 O 2 SO 3 1 2 SO 3 H 2 O H 2SO 4 • The second step is slow, but is catalyzed by NO2: NO2 SO2 NO SO3 NO 1 O2 NO2 2 • Heterogeneous catalysts are typically solids • Consider the synthesis of ammonia from hydrogen and nitrogen by the Haber process 3H 2 N 2 2NH 3 • The reaction takes place on the surface of an iron catalyst that contains traces of aluminum and potassium oxides • The hydrogen and nitrogen binds to the catalyst lowering the activation energy The Haber process. Catalytic formation of ammonia molecules from hydrogen and nitrogen on the surface of a catalyst.
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