Kinetics Dependence of rate on Concentration (RATE LAW) Reaction Mechanisms Dependence of rate on temperature Activation Energy E a Activated Complex Arrhenius Equation Mary J. Bojan Chem 112 1 A MECHANISM is a description of what is happening on a molecular level. REACTION MECHANISM The process or series of elementary steps by which a reaction occurs Elementary step: process that occurs as written. Postulate a MECHANISM for the IN AN conversion Chem 112 2
To fully understand the mechanism of a reaction, generate an Energy Profile for the reaction. Energy Profile for the proposed mechanism 1. Reactants must approach the barrier. There is a probability (A) associated with this. Chem 112 3 Costs energy to break the C N bond This is the energy barrier. E a is energy need to get to the transition state. To get over the hill need to put energy in 2. How does a molecule get over the barrier? Where does the energy come from? Chem 112 4
The average kinetic energy of a collection of molecules is proportional to the temperature. Recall KMT All molecules in a gas sample are in motion. The speeds of the molecules are related to their kinetic energy. Chem 112 5 Kinetic Molecular Theory can be used to determine the % of molecules with sufficient energy to react. Fractio on of molecu ules T 1 T 2 Average Kinetic Energy fraction of molecules (f) with energy E f α e E/RT As T increases the fraction of molecules with energy greater than E a increases. (The number of molecules with sufficient energy to get over the barrier increases.) Mary J. Bojan Chem 112 6
Collision Theory Most molecules do NOT have sufficient energy to react. No reaction How do they get the energy to react if they don t already have it? Energy is transferred upon collision. Reaction rate is proportional to # of collisions Chem 112 7 A successful collision must have the proper orientation. Even if there is sufficient energy in a collision to overcome the activation energy, a collision might not be successful! Example: Bimolecular reaction NOCl + Cl NO + Cl 2 Chem 112 8
The reaction profile can be used to summarize these results. Activated complex (transition state) E a = activation energy reactants products ΔE: reaction energy If the collision energy is < E a or orientation is incorrect: no reaction If the collision i energy is > E a and orientation ti is incorrect: REACTION Mary J. Bojan Chem 112 9 Using collision theory we learned: Reaction rates depend d on 1. # of Collisions rate # of successful collisions time 2. Activation Energy (E a ) 3. Frequency factor and orientation (A) this is essentially a probability that reactants will collide AND have the correct orientation for reaction to occur. (How often reactants approach reaction per unit time.) If we hold temperature constant, what can we do to change the rate? Chem 112 10
If we hold temperature constant, what can we do to change the rate? rate If we increase # collisions o s # of successful collisions time E a A At constant T, rate concentration. The constant of proportionality = k, called the rate constant. Mary J. Bojan Chem 112 11 Rate Law: relationship between the rate of a reaction and concentration of its reactants. We can measure concentrations of reactants If a step is elementary, then the rate of that reaction is proportional to the concentration of the reactants. Examples: Unimolecular Rate Law Bimolecular Termolecular The Rate Law for an elementary process can be determined from its molecularity larit (how many molecules les are involved in a collision). Mary J. Bojan Chem 112 12
Rate Law: relationship between the rate of a reaction and concentration of its reactants. We can measure concentrations of reactants The rate law is: rate = k[a] x [B] y k is the rate constant independent of [A] and [B]; varies with T x and y are exponents 0, not necessarily integers Order of reaction = sum of exponents Overall order of reaction = x + y Mary J. Bojan Chem 112 13 We want to use this theory to predict the rate law for a reaction. What is the rate law for the following reaction? NO 2 +CO NO + CO 2 Assuming this is an elementary process: Experimental result: Mary J. Bojan Chem 112 14
If a step is elementary, then the rate of that reaction is proportional p to the concentration of the reactants. We can t tell if a reaction is an elementary process or the result of a mechanism unless we do an experiment. RECALL: An elementary step is a reaction that proceeds as written. PROBLEM: Most reactions do not occur in a single step. They occur as the result of several elementary steps. If the experimental rate law does not match the rate law predicted by the reaction, then we must try to elucidate the MECHANISM. Study of kinetics can help us elucidate reaction MECHANISMS Chem 112 15 What is the Mechanism for the following reaction? NO 2 +CO NO + CO 2 REACTION MECHANISM The process or series of elementary steps by which a reaction occurs Propose a mechanism: NO 2 + NO 2 NO 3 + NO 1 NO 3 + CO NO 2 + CO 2 2 NO 2 + CO NO + CO 2 NOTE: Elementary steps in a mechanism must add up to give the balanced equation for the overall process. NO 3 is produced in step 1 and consumed in step 2 Intermediate: a stable molecule Intermediates do not (should not) appear in the rate law. (Concentration dependence of intermediates cannot be measured.) Chem 112 16
The schematic reaction profile for a mechanism can be drawn. Proposed mechanism: NO 2 + NO 2 NO 3 + NO 1 transition states NO 3 + CO NO 2 + CO 2 2 NO 2 + CO NO + CO 2 Energy intermediate reactant product Reaction coordinate Chem 112 17 Find the Rate Law for each step in a multi-step mechanism Experimental Rate Law: Propose a mechanism: NO 2 + NO 2 NO 3 + NO 1 NO 3 +CO NO 2 +CO 2 2 NO 2 + CO NO + CO 2 rate 1 NO 2 t k NO 2 CO rate 2 k 3 t Then compare them with the 2 experimental result. NO CO Chem 112 18
How do you know which step is the Rate Determining Step Chem 112 19 Summarize points related to mechanisms Elementary steps in a mechanism must add up to give the balanced equation for the overall process. transition states NO 3 is produced in step 1 and consumed in step 2 Intermediate: a stable molecule Note: it is NOT the same as the transtion state (or activated complex) Rate determining step = slow step En nergy intermediate reactant product Reaction coordinate Intermediates do not (should not) appear in the rate law. (Concentration dependence of intermediates cannot be measured.) Chem 112 20
To find mechanisms 1. Find the experimental rate law 2. Postulate elementary steps 3. Find the rate law predicted by the mechanism and compare to experiment. No rate can be written in terms of intermediates Experiments can be used to support a proposed reaction mechanism or be proof that a proposed mechanism is incorrect. Chem 112 21 Mechanism Example Problem Rate = k obs [Cl 2 2] 1/2 [CHCl 3 3] Cl 2 + CHCl 3 HCl + CCl 4 Postulate the following mechanism: is it consistent with the experimental rate law? Cl 2 2Cl fast Cl + CHCl 3 HCl + CCl 3 slow Cl + CCl 3 CCl 4 fast 22 Chem 112
We have focused on reaction rates at constant T. Reaction rates depend on 1. # of Collisions Related to concentration ti Can be used to help elucidate reaction mechanisms 2. Activation Energy (E a ) 3. Frequency factor and orientation (A) this is essentially a probability that reactants will collide AND have the correct orientation for reaction to occur. (How often reactants approach reaction per unit time.) What happens when temperature changes? Chem 112 23 As T increases, the fraction of molecules with energy greater than E a increases. raction of mo olecules Fr T 1 T 2 Average Kinetic Energy fraction of molecules (f) with energy E f E a RT Mary J. Bojan Chem 112 24
Temperature dependence shows up in the rate constant: k Measure the rate of the same reaction (same conditions) at different temperatures Plot rate constant vs. T Chem 112 25 Temperature dependence of the rate constant is given by the Arrhenius Equation k Ae E a RT k = rate constant is temperature dependent A = frequency factor Related to reaction frequency and orientation E a = Activation energy R = gas constant (usually 8.314 J/mol-K) T = temperature in K Chem 112 26
Use the linear form of the equation to find the activation energy for a reaction. ln k ln A E a RT Arrhenius plot plot of ln k vs 1/T is a straight line slope = E a /R intercept = ln A Chem 112 27 It is possible to find E a when the frequency factor A is not known. SAMPLE PROBLEM Understanding the high-temperature behavior of nitrogen oxides is essential for controlling pollution generated in automobile engines. 2NO(g) N 2 (g)+o( 2 (g) The decomposition of nitric oxide (NO) to N 2 and O 2 is second order with a rate constant of 0.0796 M 1 s 1 at 737 C and 0.0815 M 1 s 1 at 947 C. Calculate the activation energy for the reaction. ln k k 2 Ea R 1 1 T2 T1 1 1 Chem 112 28
FYI Where does this equation come from? k ln k E 1 T2 1 1 a 2 R T1 We want to eliminate A from the Arrhenius equation. This can be done if we know the reaction rate at two different temperatures: At T 1 At T 2 ln k 1 E a RT 1 ln k 2 E a RT 2 R = 8.314 J/mol-K ln A ln A Eliminate A by subtracting equation two from equation one. ln k 1 ln k 2 E a E a RT 1 RT 2 ln k 1 E a 1 1 k 2 R T 2 T 1 Chem 112 29 RATE VS TEMPERATURE How does rate vary over a 10 temperature t range? (e.g. from T 1 = 300 K to T 2 = 310 K) Most reactions have E a = 20 200 kj/mol A typical E a might be 50 kj/mol Use this equation to find the ratio of the rates (= ratio of the rate constants). k 065 2 /k 1 = e 0.65 = 19 1.9 ln k k E 1 T2 1 1 a 2 R T1 Rate at T 2 (=310K) is twice as fast as rate at T 1 (= 300 K) k = 0.65 2 /k 1 e = 19 1.9 rule of thumb: reaction rates double for every 10 rise in temperature (assumes E a 50 kj/mol) Chem 112 30
Using collision theory we learned: Reaction rates depend on 1. # of Collisions 2. Activation Energy (E a ) 3. Frequency factor and orientation (A) this is essentially a probability that reactants will collide AND have the correct orientation for reaction to occur. (How often reactants approach reaction per unit time.) At constant temperature: Collisions are related to concentration. Rate law is the relationship between rate and concentration). Rate = k [A] x [B] y Activation energy (E a a) and A are related to the rate constant: k. which varies with temperature. ln k ln A E a RT Chem 112 31