Chapter 14 Chemical Kinetics

What does ‘kinetics’ mean?

Factors governing reaction rates: What can make a reaction speed up or slow down? Chemical nature / contact ability (solids / liquids / gases) Concentration Temperature Presence of a Catalyst Consider a mixture of gaseous molecules A and B in a sealed container. A and B react with each other; what will happen to the reaction rate if the pressure in the container increases?

The Reaction Rate How fast are products formed / reactants used up? Reaction of A (red)  B (blue) Reaction rate =  concentration /  time Units of rate?

Calculating Average Rates Average rate of disappearance of A over 20 s? Average rate of formation of B over 40 s?

Instantaneous Rates Look at the rate of a reaction over time: C 4 H 9 Cl (aq) + H 2 O (l)  C 4 H 9 OH (aq) + HCl (aq) Is the rate constant? Tangent lines show the rates at specified times (instantaneous rates) What is the instantaneous rate at t=600s? Units of rate?

Instantaneous Rates Looked at one component of a reaction Rate expression that includes all reactants A + B  Products Rate  [A] m [B] n (exponents m and n determined experimentally- look at very soon) Rate Law: Shows how initial reaction rate changes wrt concentration of species involved; introduces rate constant, k Rate = k [A] m [B] n Calculate rate with k, m and n (any concentration of A and B)

Reaction Rates and Stoichiometry C 3 H 8 (g) + 5O 2 (g)  3CO 2 (g) + 4H 2 O(g) propane In a particular experiment, rate of loss of C 3 H 8 is 3.55 x mol / L.s How can we calculate the corresponding rate of formation of CO 2 ? Rate of formation of H 2 O?

Reaction Rates and Stoichiometry Dinitrogen pentoxide (N 2 O 5 ) decomposes to NO 2 and O 2 (all are gases). Balanced equation for this? Rate of decomposition of N 2 O 5 at a particular instant is 4.2 x M/s – what are the rates of formation of NO 2 and O 2 ?

The Rate Law Rate potentially depends on both [NH 4 + ] and [NO 2 - ] Rate Law:Rate = k [NH 4 + ] x [NO 2 - ] y x and y (exponents): indicate how the initial rate is affected by change in concentration of the reactants. Can be determined. k = Rate constant (shows how temperature affects rate) NH 4 + (aq) + NO 2 - (aq)  N 2 (g) + 2H 2 O(l)

Exponents and Rate Laws A + B  C; Rate = k[A] n [B] m ; values of n and m? Vary concs. of A and B separately, and observe effect on rate. Expt. #Initial Concs (mol/L)Initial Rate (mol L -1 s -1 ) [A] [B] x x x Rate Law: Rate = k What is the value of the rate constant? (remember units!) What is the rate of the reaction when [A] = M, and [B] = M?

What is the rate law? Consider the reaction of nitric oxide with hydrogen: 2 NO(g) + 2H 2 (g)  N 2 (g) + 2H 2 O(g) Expt. # Initial Concs (mol/L)Initial Rate (mol L -1 s -1 ) [NO] [H 2 ] x x x (a)What is the rate law for this reaction? (b)Calculate the rate constant. (c)Calculate the rate when [NO]=0.050 M and [H 2 ] = M.

The rate constant, k Let’s compare the rate constants (and their units) for the previous two problems just worked. What do you notice about the two that looks a little odd?

The Integrated Rate Law Rate Law: Shows how initial rate varies with concentration. Integrated Rate Law: Shows what the concentration of products or reactants is at a particular time during the reaction. 1 st order reactions:Rate = -  [A] /  t = k [A] ln [A] t = -kt + ln[A] o 2N 2 O 5  2N 2 O 4 + O 2 ; Rate = k[N 2 O 5 ] At 45 °C, k = 6.22 x s -1. If initial conc. Of N 2 O 5 is 0.10M, how many minutes for [N 2 O 5 ] to drop to 0.01 M?

Integrated Rate Law – 2 nd order 2 nd order reactions; Rate = -  [A] /  t = k [A] 2 1/ [A] t = kt + 1/[A] o Decomposition of NO 2 (g)  NO(g) + ½ O 2 (g) 2 nd order in NO 2, with k = L / mol.s. [NO 2 ] o = M What is the remaining concentration after h?

Graphical representations How to tell if a reaction is 1 st order: Insert Figure 14.8

Graphical Representations How to tell if a reaction is 2 nd order:

Half-life (t 1/2 ) – 1 st order reactions Half-life of a particular chemical t for ½ reactant to disappear 3g A  t 1/2 = / k

Half-life (t 1/2 ) – 1 st order reactions t 1/2 = / k 131 I; t 1/2 = 8 days. 10g sample of 131 I, after 8 days….decayed down to…. Radioactive emission (  -,  -,  -, X-rays) to stable isotope Fraction of 131 I present after 24 days? Amount of 131 I?

Half-life (t 1/2 ) – 2 nd order reactions t 1/2 = 1/ k[A] o 2HI(g)  I 2 (g) + H 2 (g); Rate = k[HI] 2 ; k = Lmol -1 s -1 Initial conc. of HI = 0.050M; t 1/2 = ?

Temperature and Rate Value of k varies with change in T Light sticks in hot vs. ice water

How do reactions occur? Model for Chemical Kinetics Collision Model (Collision Theory) Molecules must successfully collide to react. 2 reasons for ineffective collisions: 1. Insufficient K.E to overcome E a (Activation Energy) barrier 2. Orientation issues

Orientation Issues Cl + NOCl  NO + Cl 2

Activation Energy (E a )

Changing T changes rate; also changes k Extent of k variation with  T depends on E a. To calculate E a for a reaction: ln (k 1 /k 2 ) = -E a /RT (1/T 2 – 1/T 1 ) Decomposition of HI has rate constants: k = L mol -1 s -1 at 508 °C k = 0.24 L mol -1 s -1 at 540 °C What is the E a for the reaction, in kJ / mol?

The Reaction Mechanism What happens during a chemical reaction? NO(g) + O 3 (g)  NO 2 (g) + O 2 (g) Occurs in a single step. Rate Law = k This is an elementary reaction What is the molecularity of this elementary reaction? NO(g) + Cl 2 (g)  NOCl(g) + Cl(g)

The Reaction Mechanism Multi-Step Reactions NO 2 (g) + CO(g)  NO(g) + CO 2 (g) Rate = k[NO 2 ] 2 ; Single step? Possible Mechanism: Step 1: NO 2 (g) + NO 2 (g)  NO 3 (g) + NO(g) Step 2: NO 3 (g) + CO(g)  NO 2 (g) + CO 2 (g) If mechanism is correct, Step 1 + Step 2 = overall reaction Intermediates? Rate Determining Step?

Mechanism problem Decomposition of N 2 O (nitrous oxide) occurs by a 2-step mechanism: Step 1:N 2 O(g)  N 2 (g) + O(g) (slow) Step 2:N 2 O(g) + O(g)  N 2 (g) + O 2 (g) (fast) What is the overall equation for the reaction? Write the rate law for the reaction.

Catalysts Change rates of reactions without being used up Lowers activation energy of reaction (changing mechanism) Homogeneous catalysts Heterogeneous catalysts

Catalytic Convertors