Chapter 12 PDF - CHEM 0120 Reaction Rates

Chapter 12 CHEM 0120  Reaction Rates The reaction rate is the speed of a chemical reaction. It is the increase in molar concentration of product of a reaction per unit time (or the decrease in molar concentration of reactant per unit time). The rate of a reac...

Chapter 12 CHEM 0120  Reaction Rates The reaction rate is the speed of a chemical reaction. It is the increase in molar concentration of product of a reaction per unit time (or the decrease in molar concentration of reactant per unit time). The rate of a reaction is a measure of how fast the reaction makes products or uses reactants. The ability to control the speed of a chemical reaction is important. 2  Chemical Kinetics The study of reaction rates, how reaction rates change under varying conditions, and what molecular events occur during the overall reaction. The rate of any given reaction can be affected by numerous variables: Concentrations of Reactants or Catalyst Temperature Nature of Reactants 3  Reactant Concentration Affect on Reaction Rate Generally, the greater the concentration of reactant molecules, the faster the reaction. This increases the frequency of reactant molecule contact. Concentration of gases depends on the partial pressure of the gas. Higher pressure = higher concentration Concentrations of solutions depend on the solute-to-solution ratio (molarity). 4  Temperature Affect on Reaction Rate Increasing temperature increases the reaction rate for most reactions. The Arrhenius equation is a mathematical relationship between the absolute temperature and the speed of a reaction. This relationship will be examined in the next class. 5  Nature of the Reactants Affect on Reaction rate Nature of the reactants refers to what kind of reactant molecules there are and what physical condition they are in. Small molecules tend to react faster than large molecules. Gases tend to react faster than liquids, which react faster than solids. Powdered solids are more reactive than “blocks.” More surface area for contact with other reactants Certain types of chemicals are more reactive than others. For example, potassium metal is more reactive than sodium. Ions react faster than molecules. No bonds need to be broken. 6  Defining Rate Rate is how much a quantity changes in a given period of time. The speed at which you walked to chemistry lecture is a rate: The distance you walked (feet or miles) in a given period of time (1 minute or 1 hour) So, the rate at which you walked has units of ft/min or mi/hr. We can further break it down into different periods of time for average and instantaneous rates. 7  Defining Reaction Rate The rate of a chemical reaction is measured in terms of how much the concentration of a reactant decreases (or the product concentration increases) in a given period of time. Example: H2(g) + I2(g) → 2 HI(g) For reactants, a negative sign is placed in front of the definition. The rate of chemical reaction over two time periods can be written as follows: 8  Concentrations as a Function of Time As time goes on, the rate of a reaction generally slows down because the concentration of the reactants decreases. At some time the reaction stops, either because the reactants run out or because the system has reached equilibrium. 9  Average Rate The average rate is the change in measured concentrations in any particular time period. Linear approximation of a curve The larger the time interval, the more the average rate deviates from the instantaneous rate. 10  Instantaneous Rate The instantaneous rate is the change in concentration at any one particular time. Slope at one point of a curve The instantaneous rate is determined by taking the slope of a line tangent to the curve at that particular point. In calculus: first derivative of the function 11  Reaction Rate and Stoichiometry In most reactions, the coefficients of the balanced equation are not all the same. H2(g) + I2(g) → 2 HI(g) For these reactions, the change in the number of molecules of one substance is a multiple of the change in the number of molecules of another. For the above reaction, for every 1 mol of H2 used, 1 mol of I2 will also be used and 2 mol of HI made. Therefore, the rate of change will be different. To be consistent, the change in the concentration of each substance is multiplied by 1/coefficient. 12  Measuring Reaction Rates To measure the reaction rate you need to be able to measure the concentration of at least one component in the mixture at many points in time. There are two ways of approaching this problem: – For reactions that are complete in less than 1 hour, it is best to use continuous monitoring of the concentration. – For reactions that happen over a very long time, sampling of the mixture at various times can be used. 13  Finding the Rate Law The rate law must be determined experimentally. The rate law shows how the rate of a reaction depends on the concentration of the reactants. Changing the initial concentration of a reactant will therefore affect the initial rate of the reaction. 14  The Effect of Concentration on Reaction Rate The rate law of a reaction is the mathematical relationship between the rate of the reaction and the concentrations of the reactants and homogeneous catalysts as well. Rate = k [A]n The rate of a reaction is directly proportional to the concentration of each reactant raised to a power. For the reaction aA + bB → products, the rate law would have the form given below. n and m are called the orders for each reactant. k is called the rate constant. 15  Dependence of Rate on Concentration Rate Law: an equation that relates the rate of a reaction to the concentration of reactants (and catalysts) raised to various powers. C aA + bB → dD + eE C = catalyst Rate = k[A]m[B]n[C]p m, n and p are called the orders for each reactant. k is called the rate constant – a proportionality constant in the relationship between rate and concentrations. 16  Reaction Order The exponent on each reactant in the rate law is called the reaction order with respect to that reactant, as experimentally determined. The sum of the exponents on the reactants is called the overall order of the reaction. The rate law for the reaction 2 NO(g) + O2(g) → 2 NO2(g) is as follows: Rate = k[NO]2[O2] The reaction is second order with respect to [NO]; first order with respect to [O2]. The reaction is third order overall. 17  Reaction Orders If a reaction is zero order, the rate of the reaction does not change. Doubling [A] will have no effect on the reaction rate. Rate law: Rate = k[A]0 = k If a reaction is first order, the rate is directly proportional to the reactant concentration. Doubling [A] will double the rate of the reaction. Rate law: Rate = k[A]1 = k[A] If a reaction is second order, the rate is directly proportional to the square of the reactant concentration. Doubling [A] will quadruple the rate of the reaction. Rate law: Rate = k[A]2 18  Determining the Reaction Order The reaction order must be determined from the experimental data. 19  Determining the Reaction Order The reaction order must be determined from the experimental data. Example: 2N2O5(g) → 4NO2(g) + O2(g) Initial [N2O5] Initial rate of disappearance of N2O5 Experiment 1 1.0 x 10-2 mol/L 4.8 x 10-6 mol/(L∙s) Experiment 2 2.0 x 10-2 mol/L 9.6 x 10-6 mol/(L∙s) 20 Determining the Rate Law with Multiple Reactants Changing each reactant will affect the overall rate of the reaction. By changing the initial concentration of one reactant at a time, the effect of each reactant’s concentration on the rate can be determined. Example: 21  Change of Concentration with Time For the reaction A + B → products, the rate law depends on the concentrations of A and B. An integrated rate law uses calculus to transform a rate law into a mathematical relationship between concentration and time. 22  Integrated Rate Law: First-Order Rate law: Rate = k[A]1 = k[A] Integrated rate law: ln[A]t = −kt + ln[A]0 [𝐀𝐀]𝒕𝒕 or 𝐥𝐥𝐥𝐥 = −𝒌𝒌𝒌𝒌 [𝐀𝐀]𝟎𝟎 A graph of first order: ln[A] versus time results in a straight line where slope = −k y-intercept = ln[A]initial 23  Integrated Rate Law: Second-Order Rate law: Rate = k[A]2 Integrated rate law: 𝟏𝟏 𝟏𝟏 = 𝒌𝒌𝒌𝒌 + [𝐀𝐀]𝒕𝒕 [𝐀𝐀]𝟎𝟎 A graph of second order: 1/[A] versus time results in a straight line where slope = k y-intercept = 1/[A]initial 24  Integrated Rate Law: Zero-Order Rate law: Rate = k[A]0 = k Integrated rate law: [A]t = −kt + [A]0 A graph of zero order: [A] versus time results in a straight line where slope = −k y-intercept = [A]initial 25 Rate Law Relationships 26  Half-Life of a Reaction Half-life (t1/2) of a reaction: the time it takes for the reactant concentration to decrease to one-half of its initial value. Reactions: 0.693 First-order: 𝑡𝑡1/2 = 𝑘𝑘 1 Second-order: 𝑡𝑡1/2 = 𝑘𝑘[A]0 [A]0 Zero-order: 𝑡𝑡1/2 = 2𝑘𝑘 27  Relationship between Order and Half-Life For a zero order reaction, the lower the initial concentration of the reactants, the shorter the half-life. t1/2 = [A]0/2k For a first order reaction, the half-life is independent of the concentration. t1/2 = 0.693/k For a second order reaction, the half-life is inversely proportional to the initial concentration. Increasing the initial concentration shortens the half-life. t1/2 = 1/(k[A]0) 28  Effect of Temperature on Rate Changing the temperature changes the rate constant of the rate law This relationship is given by the Arrhenius equation: 𝒌𝒌 = 𝑨𝑨𝒆𝒆−𝑬𝑬𝒂𝒂 /𝑹𝑹𝑹𝑹 where T is temperature in Kelvin R is the gas constant in energy units, 8.314 J/(K · mol) Ea is the activation energy, the extra energy needed to start the molecules reacting A is a constant referred to as the frequency factor The rate the reactant energy approaches the activation energy 29  Potential-Energy Curve Exothermic reaction. Heat energy is released when the reaction proceeds in the forward direction. 30  Activation Energy There is an energy barrier to almost all reactions. The activation energy is the amount of energy needed to convert reactants into the activated complex. The activated complex is also know as a transition state. The activated complex is a chemical species with partially broken and partially formed bonds. Always very high in energy because of its partial bonds 31  Energy Profile for the Isomerization of Methyl Isonitrile The activation energy is the difference in energy between the reactants and the activated complex. The frequency is the number of molecules that begin to form the activated complex in a given period of time. As the reaction begins, the C—N bond weakens enough for the CN triple bonded group to start to rotate. The activated complex is a chemical species with partial bonds. 32  The Exponential Factor in the Arrhenius equation The exponential factor in the Arrhenius equation is a number between 0 and 1 It represents the fraction of reactant molecules with sufficient energy so they can make it over the energy barrier. The higher the energy barrier (larger activation energy), the fewer molecules that have sufficient energy to overcome it. That extra energy comes from converting the kinetic energy of motion to potential energy in the molecule when the molecules collide. Increasing the temperature increases the average kinetic energy of the molecules. Therefore, increasing the temperature will increase the number of molecules with sufficient energy to overcome the energy barrier; reaction rate. 33  A Summary of Temperature and Reaction Rate The frequency factor is the number of times that the reactants approach the activation barrier per unit time. The exponential factor is the fraction of the approaches that are successful in surmounting the activation barrier and forming products. The exponential factor increases with increasing temperature but decreases with increasing activation energy. 34  Arrhenius Plots: Experimental Measurements The Arrhenius equation can be algebraically solved to give the following form: 𝐸𝐸𝑎𝑎 ln 𝑘𝑘 = ln 𝐴𝐴 − 𝑅𝑅𝑅𝑅 This equation is in the form y = mx + b, – where y = ln(k) and x = (1/T). A graph of ln(k) versus (1/T) is a straight line 35  Arrhenius Equation: Two-Point Form If you have only two (T,k) data points, the following forms of the Arrhenius equation can be used: 𝑘𝑘2 𝐸𝐸𝑎𝑎 1 1 ln = − 𝑘𝑘1 𝑅𝑅 𝑇𝑇1 𝑇𝑇2 36  Example The rate constant for the formation of hydrogen iodide from the elements is 2.7 x 10-4 L/(mol s) at 600 K and 3.5 x 10-3 L/(mol s) at 650 K. A) Find the activation energy. B) Calculate the rate constant at 700 K. 37  Collision Theory Collision Theory of Reaction Rates: a theory that assumes that, for a reaction to occur, reactant molecules must collide with an energy greater than some minimum value and with the proper orientation. The minimum energy of collision required for two molecules to react is the activation energy (Ea). The rate constant (k) for a reaction is dependent upon: 1. The collision frequency 2. The fraction of collisions having a higher energy than Ea 3. The fraction of collision that occur with the reactant molecules properly oriented. 38  Effective Collisions: Kinetic Energy Factor For a collision to lead to overcoming the energy barrier, the reacting molecules must have sufficient kinetic energy so that when they collide the activated complex can form. 39  Effective Collisions Collision frequency: the number of collisions that happen per second The more collisions there are per second, the more collisions can be effective and lead to product formation. The higher the frequency of effective collisions, the faster the reaction rate. Collisions in which these two conditions are met (and therefore lead to reaction) are called effective collisions. When two molecules have an effective collision, a temporary, high- energy (unstable) chemical species is formed: the activated complex. 40  Orientation Factor The proper orientation results when the atoms are aligned in such a way that the old bonds can break and the new bonds can form. The more complex the reactant molecules, the less frequently they will collide with the proper orientation. 41  Reaction Mechanisms Chemical reactions are generally described with a net chemical equation listing all the reactant molecules and product molecules. The probability of more than three molecules colliding at the same instant with the proper orientation and sufficient energy to overcome the energy barrier is negligible. Most reactions occur in a series of small reactions involving one, two, or (at most) three molecules. Reaction Mechanism: the set of elementary reactions whose overall effect is given by the net chemical equation. Knowing the rate law of the reaction helps us understand the sequence of reactions in the mechanism. 42  Reaction Mechanism Example Overall reaction: H2(g) + 2 ICl(g) → 2 HCl(g) + I2(g) (net chemical equation) Mechanism: H2(g) + ICl(g) → HCl(g) + HI(g) (elementary reaction) HI(g) + ICl(g) → HCl(g) + I2(g) (elementary reaction) The reactions in this mechanism are elementary reactions, meaning that they cannot be broken down into simpler steps and that the molecules actually interact directly in this manner without any other steps. 43  Reaction Intermediates H2(g) + 2 ICl(g) → 2 HCl(g) + I2(g) H2(g) + ICl(g) → HCl(g) + HI(g) HI(g) + ICl(g) → HCl(g) + I2(g) Notice that the HI is a product in step 1, but it is a reactant in step 2. Because HI is made but then consumed, HI does not show up in the overall reaction. Materials that are products in an early mechanism step but reactants in a later step are called intermediates. Reaction intermediates: a species produced during a reaction that does not appear in the net equation because it reacts in a subsequent step in the mechanism. 44  Determining the Rate Equation for an Elementary Reaction The number of reactant particles in an elementary step is called its molecularity. A unimolecular step involves one particle. A bimolecular step involves two particles. These two particles may be the same kind of particle. A termolecular step involves three particles. These are exceedingly rare in elementary steps. 45  Rate Equation for an Elementary Reaction H2(g) + 2 ICl(g) → 2 HCl(g) + I2(g) 1) H2(g) + ICl(g) → HCl(g) + HI(g) Rate = 2) HI(g) + ICl(g) → HCl(g) + I2(g) Rate = Treat each step in the mechanism like its own reaction with its own Ea and rate law. The rate law for an overall reaction must be determined experimentally. But the rate law of an elementary step can be deduced from the equation of the step. 46 Rate Laws for Elementary Steps (from Pearson Education, INC.) 47  Rate-Determining Step Rate-determining step: the slowest step in the reaction mechanism When on step is slower than the other steps, the result is that product production cannot occur any faster than the slowest step; the step determines the rate of the overall reaction. The slowest step has the largest activation energy. The rate law of the rate-determining step determines the rate law of the overall reaction. 48  Reaction Mechanism Example NO2(g) + CO(g) → NO(g) + CO2(g) Rateobs = k[NO2]2 Proposed Mechanism 1. NO2(g) + NO2(g) → NO3(g) + NO(g) Rate = k1[NO2]2 Slow 2. NO3(g) + CO(g) → NO2(g) + CO2(g) Rate = k2[NO3][CO] Fast The first step is slower than the second step because its activation energy is larger. The first step in this mechanism is the rate-determining step: It is the slowest step. The rate law of the first step is the same as the rate law of the overall reaction. 49  Criteria for Validating a Mechanism To validate (not prove) a mechanism, two conditions must be met: 1. The elementary steps must sum to the overall balanced chemical reaction. 2. The rate law predicted by the rate-determining step of the mechanism must be consistent with the experimentally observed rate law. 50  Mechanisms with an Initial Fast Step When a mechanism contains a fast initial step, the rate- limiting step may contain intermediates. When a previous step is rapid and reaches equilibrium, the forward and reverse reaction rates are equal, so the concentrations of reactants and products of the step are related and the product is an intermediate. Substituting into the rate law of the rate-determining step will produce a rate law in terms of just reactants. 51  Example of a Mechanism with an Initial Fast Step 1) 2 NO(g) N2O2(g) Fast 2) H2(g) + N2O2(g) → H2O(g) + N2O(g) Slow Rate = k2[H2][N2O2] 3) H2(g) + N2O(g) → H2O(g) + N2(g) Fast 52  Catalysts Catalysts are substances that affect the rate of a reaction Mechanism without catalyst: without being consumed. O3(g) + O(g) → 2 O2(g) V. Slow Catalysts work by providing an alternative mechanism for Mechanism with catalyst: the reaction with a lower activation energy. Cl(g) + O3(g) ⇌ O2(g) + ClO(g) Fast ClO(g) + O(g) → O2(g) + Cl(g) Slow Catalysts are consumed in an early mechanism step and then made in a later step. 53  Factors Affecting Reaction Rate Catalysts are substances that affect the speed of a reaction without being consumed. Most catalysts are used to speed up a reaction; these are called positive catalysts. – Catalysts used to slow a reaction are called negative catalysts. Homogeneous catalysts: all species present in same phase Heterogeneous catalysts: species present in different phase 54  Catalyst Types Homogeneous catalysts are in the same phase as the reactant particles. Cl(g) in the destruction of O3(g) Heterogeneous catalysts are in a different phase than the reactant particles. Solid catalytic converter in a car’s exhaust system 55 Catalyst Types 56  Catalytic Hydrogenation Reaction 1. Adsorption: The reactants are adsorbed onto metal surfaces. 2. Diffusion: The reactants diffuse on the surface until they approach each other. 3. Reaction: The reactants react to form the products. 4. Desorption: The products desorb from the surface into the gas phase. 57