Rates of Reactions

1. Rates of Reactions

2. Factors affecting rates • Temperature • Increasing temperature increases rate. • More molecules have sufficient energy to react. • Reactant concentrations • Dependence on concentration must be determined experimentally. • Can be used to deduce mechanism. • Catalysts • speed up reactions • heterogeneous (e.g. solids) or homogeneous (same phase)

3. Dependence of concentration on time, in solution For the simple reaction A  C, starting with [A] = 1.0 and [C] = 0 • Concentration of A decreases. • Concentration of C increases at the same rate. • Reaction slows, but continues until A runs out, or until equilibrium is established. • At completion, or equilibrium, concentrations of A and C are constant.

4. Dependence of concentration on time, in solution Rate of reaction can be expressed as the rate of disappearance of A or as the rate of appearance of C. For the reaction A  C, Rate = -D[A]/D t = +D[C]/Dt Once we see how the rate of reaction depends on the concentrations, we will write mathematical expressions for the concentrations as a function of time, these are the integrated rate laws.

5. Dependence of concentration on time, in solution For the reaction A  2C, The rate of appearance of C is twice the rate of disappearance of A + D[C]/ D t = 2(- D[A]/ D t ) In general, for any reaction a A + b B c C - D[A] = - D[B] = + D[C] aD t b D t cD t

6. Measuring the rate of a reaction • The rate is often measured as D[X]/Dt, where X may be a reactant or product. • Depending on the nature of X, the change in concentration may be monitored by a change in • colour (intensity of some wavelength) • pressure (for gases) • pH (for OH- or H3O+) • conductivity (ions) • radioactivity, etc.

7. Measuring the initial rate • The rate of the forward reaction depends on the concentration of reactants, not products. • The dependence may be linear, quadratic, etc., this must be determined experimentally. • The rate is measured at the beginning of the reaction (the initial rate), as a function of the initial reactant concentrations • This determines the reaction order.

8. Initial reaction rates2 NO (g) + 2 H2(g)  N2(g) + 2 H2O (g) Rate = k [NO]2 [H2]1

9. Initial reaction rates reaction order Rate = k [A]2 [B]1 Reaction is second order in A, first order in B and third order overall

10. CONSIDER THE RATE DATA FOR THE REACTION: 2NO + O2 2NO2

11. Reaction order & the rate law • The rate law is: Rate = k[A]x[B]y • The order of a reaction is equal to the value of the exponent in the rate law. • The reaction has an order with respect to each reactant (and each catalyst). • The overall reaction order is the sum of the individual orders. • k is the rate constant, which depends on T.

12. The rate constant • Once the form of the rate law is known, we can fill in the data from any one run of our determination to find the rate constant. e.g. 2 NO (g) + 2 H2(g)  N2(g) + 2 H2O (g) Rate = 0.0339 M·s-1 = k (.210 M)2(.122 M) k = 6.30 M-2 ·s-1 • The units of k depend on the order of the reaction

13. The rate constant • The value of k depends on the nature of the reactants and on the temperature. • Arrhenius found that the temperature dependence could be expressed as k = Ae-Ea / RT • The preexponential factor A, and the activation energy, Ea, are relatively independent of temperature. • What are these parameters? • Why does k have this dependence?

14. Rate Law Determination • Consider the combination reaction of NO and O2 to produce NO2 : • 2 NO(g) + O2(g) 2 NO2 (g) • Determination of the Rate Law (via Methods of Initial Rates) • Initial Concentrations • (mol/ L) Initial RateExperiment [NO] [O2] (mol/L • s) • 1 0.020 0.010 0.028 • 2 0.020 0.020 0.057 • 3 0.020 0.040 0.114 • 4 0.040 0.020 0.227 • 5 0.010 0.020 0.014 • Based on these data, what is the rate equation? What is the value of the rate constant k?

15. Rate Law; Solving for rate Constant The general rate law is: Rate law = k [NO]2 [O2] the rate constant k is determine by selecting one of the experiments and solving the equation. Consider experiment#1: Rate = 0.028 = k [0.020]2 [0.010] k = 0.028 / (4•10-4)(0.010) = 7.1•103 M-2 s-1 Rate Law: Rate = 7.1•103 [NO]2 [O2]

16. Microscopic view • In order to understand our macroscopic observations about temperature and concentration dependence, we should look at the reaction microscopically - on the size scale of atoms and molecules. • The rates of chemical reactions are explained by collision theory, which is based on kinetic theory. • Collision theory views a reaction as the result of a ‘successful’ collision between two or more reactants and/or catalysts. • A few reactions occur without any collision.

17. Collision Theory • The number of collisions between two or more species is proportional to the product of their concentrations. • When the reaction is the result of a single collision – an elementary step – then the concentration dependence is directly related to the stoichiometry of that collision. • The probability that A will collide with B is proportional to [A][B]. • The probability that A will collide with A is proportional to [A]2 • For more complicated processes, the rate law is some combination of these elementary steps. • In order to react, the molecules must collide in a favourable orientation and with sufficient energy. • These factors are accounted for in the rate constant.

18. Molecularity of elementary steps • For an elementary step (arising from one collision), the rate law depends on the stoichiometry of the ‘collision’. • A step involving only one molecule is called unimolecular. Rate = k[A] • A step involving two molecules is called bimolecular. Rate = k[A][B], or Rate = k[A]2 • A step involving three molecules is called termolecular. Rate = k[A][B][C], etc. • Very few elementary steps involve more than 3 molecules.

19. Reaction progress & Ea • For an elementary process we can plot the potential (chemical) energy of the molecules as they approach each other, collide, react and move apart. • For an elementary process which involves only one molecule, we can plot the potential energy as some internal coordinate, such as bond length or angle, changes. • This plot is sometimes called a reaction coordinate diagram, or an energy plot. There is typically a maximum near the ‘collision’. • Molecules move along this reaction coordinate with some initial kinetic energy. K.E. is converted to P. E. to overcome the energy barrier, the activation energy. • Those molecular ‘collisions’ starting with enough kinetic energy can overcome the barrier and react.

20. Arrhenius and Boltzmann • We saw in chapter 13 that only a certain proportion of molecules had enough energy to remain in the gas phase. The same type of energy distribution is at play here. • The Boltzmann distribution tells us that at any particular temperature a certain percentage of the molecules are above some energy cut-off. • The cut-off of interest in this case is the activation energy. • The percentage of molecules with energy above Ea is related to the factor exp(-Ea/RT) in the Arrhenius expression in the rate. • As the temperature increases, so does the percentage of molecules above the cut-off.

21. Calculations with Ea & T k = Ae-Ea / RT ln k = ln A – (Ea/RT) • Increasing the temperature from 300 K to 310 K increases the rate by a factor of 2. What is the activation energy? • Given a set of T and k data, a plot of ln k vs. 1/T has a slope of -Ea/R

22. Rate determining step • When the reaction is a series of elementary steps, rather than a single step, the rate of reaction is determined by the slowest step, which is typically the step with the highest activation barrier. • This step is called the rate determining step, and the rate law for a known mechanism can be written in terms of the rate for this step. • If the rate determining step is not the first step, the rate may depend on some species which do not appear as reactants in the overall reaction equation.

23. Reaction mechanism • Chemists often study reaction rates in order to deduce or confirm a reaction mechanism – the stepwise progress of the reaction. • A proposed mechanism is written as a sum of elementary steps, which may be reversible. • If the rate law derived from the proposed mechanism matched the observed rate law, then we are more confident in our proposal, but still unsure. • If the rate laws do not match, we must come up with a different proposal.

24. 2 NO (g) + Br2(g) 2 BrNO (g) • Step 1 Rate = k1[Br2][NO] Br2(g) + NO (g) NOBr2(g) • Step 2 Rate 2 = k2[Br2][NOBr2] NOBr2(g) + NO(g) 2 BrNO (g) • NOBr2 is an intermediate – it is formed and then used up. • The overall rate will depend on which step is rate determining, and on whether either step is reversible.

25. 2 NO2(g) + F2(g) 2 FNO2(g) • Step 1 rate = k1[NO2][F2] NO2 + F2 FNO2 + Fslow • Step 2 rate = k2[NO2][F] NO2 + F FNO2fast Overall rate = k1[NO2][F2] Rate of reaction = rate of the slowest step k2 >> k1

26. 2 NO (g) + O2(g)  2 NO2 (g) • Step 1 is reversible K1 = [NO3] / [NO][O2] NO + O2NO3fast equilibrium • Step 2 rate = k2[NO3][NO] NO3+ NO  2 NO2slow • Overall rate = k2 [NO3][NO] • Rate of reaction = rate of the slowest step, but NO is an intermediate – difficult to determine its concentration. Want to replace [NO] with known quantities: K1 = [NO3] / [NO][O2] [NO3] = K1 [NO] [O2] Rate = k2(K1 [NO] [O2]) [NO]= k’ [NO]2[O2]

27. Equilibria in reaction mechanisms • Note that this topic is not covered in Kotz and Treichel • In principle all reaction are reversible, but only some are reversible on a time scale relevant to the overall process. • A reaction, or step, which is fast in both the forward and reverse direction will come to equilibrium rapidly. • Dynamic equilibrium is reached when the rate of the forward reaction equals the rate of the reverse reaction. • For an elementary step 2A B + C, at equilibrium rate forward = k1[A]2 = k-1[B][C] = rate reverse = equilibrium constant.