Chapter 15: Chemical Kinetics

Rate of a reaction Reaction rate – how fast a reaction occurs 𝑅𝑎𝑡𝑒= ∆[𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛] ∆𝑡𝑖𝑚𝑒 Rate can be related to reactants or products Actual reaction rates must be determined experimentally

Writing out reaction rates For general reaction, aA + bB  cC + dD 𝑅𝑎𝑡𝑒=− 1 𝑎 ∆[𝐴] ∆𝑡 =− 1 𝑏 ∆[𝐵] ∆𝑡 =+ 1 𝑐 ∆[𝐶] ∆𝑡 =+ 1 𝑑 ∆[𝐷] ∆𝑡 𝑅𝑎𝑡𝑒=− 1 1 ∆[ 𝐻 2 ] ∆𝑡 =− 1 1 ∆[ 𝐼 2 ] ∆𝑡 =+ 1 2 ∆[𝐻𝐼] ∆𝑡

Calculating average rates

Calculating instantaneous rates As concentration changes, the rate at a given point in time changes To calculate the instantaneous rate of a reaction, use the slope of the tangent curve of a concentrations vs time graph

What is the instantaneous rate for the reaction at 50 seconds? 𝑅𝑎𝑡𝑒=− ∆ 𝐻 2 ∆𝑡 −(−0.28𝑀) 40𝑠 =0.007 𝑀 𝑠 𝑅𝑎𝑡𝑒=+ 1 2 ∆[𝐻𝐼] ∆𝑡 1 2 (0.56𝑀) 40𝑠 =0.007 𝑀 𝑠

Practice Define the rate of the reaction with respect to H2? If the initial H2 concentration is 1.000 M, and the final concentration is 0.750 M after 10 seconds, what is the average rate of the reaction in this time frame? 3H2 + N2  2NH3

The rate law General simple reaction, A products 𝑅𝑎𝑡𝑒 𝐿𝑎𝑤=𝑘 [𝐴] 𝑛 k = rate constant n = reaction order Depending on the reaction order, the rate depends on the concentration differently

Reaction orders If n = 0 (zero order), rate is independent of concentration A If n = 1 (first order), rate is directly proportional to concentration A If n = 2 (second order), rate is proportional to the square of concentration A

Determining reaction order Method of initial rates – observe initial rates at different concentrations, then assign order of reaction based on concentration dependence of the initial rate values

Reaction order for multiple reactants General Reaction aA + bB  cC + dD Rate law = k[A]m[B]n Assign reaction order for each reactant based on exponent Overall reaction order determined by the sum of the exponents(orders) of each reactant Example Rate = k[Cl2]3[H2]2 [Cl2] = third order [H2] = second order Overall = fifth order

Practice NO2(g) + CO(g)  NO(g) + CO2(g) What is the rate order for NO2? What is the rate order for CO? Write the rate law for the reaction What is the overall order of the reaction?

The integrated rate law relates the concentration of the reactants with respect to time based on the reaction order A straight fit line can help determine reaction order based off integrated rate law Integrated Rate Law

Straight line fit for zero order Chapter 13, Figure 13.10 Zero-Order Integrated Rate Law

Straight line fit for first order Chapter 13, Figure 13.8 First-Order Integrated Rate Law

Straight line fit for second order Chapter 13, Figure 13.8 First-Order Integrated Rate Law

Using the straight line fit to find reaction order

Concentration versus time – zero order???

ln[Concentration] versus time – first order?? Chapter 13, Unnumbered Figure 1, Page 577

1/[Concentration] versus time – second order?? Chapter 13, Unnumbered Figure 1, Page 577

Practice Determine the reaction order from the following data Which graph represent the correct order of the reaction?

Half-Life of a Reaction Half-life (t1/2) the required time it takes for the concentration of a reactant to be half of its initial value Derived from integrated rate law equations k = rate constant A0 = initial concentration

Derivation of the half-life equation: First order 𝑙𝑛 [𝐴] 𝑡 =−𝑘𝑡+𝑙𝑛 𝐴 0 𝑙𝑛 [𝐴] 𝑡 −𝑙𝑛 𝐴 0 =−𝑘𝑡 𝑙𝑛 [𝐴] 𝑡 [𝐴] 0 =−𝑘𝑡 [𝐴] 𝑡 [𝐴] 0 =50%= 1 2 𝑙𝑛 1 2 =−𝑘 𝑡 1/2 𝑙𝑛 1 2 =−0.693 −0.693=−𝑘 𝑡 1/2 𝟎.𝟔𝟗𝟑 𝒌 = 𝒕 𝟏/𝟐 Derivation of the half-life equation: First order

Chapter 13, Figure 13.11 Half-Life: Concentration versus Time for a First-Order Reaction

How long will it take to get 17.89% of the original concentration? How long will it take for the initial concentration to decrease to 25% of the original concentration? For a first order reaction with a half life of 17.8s, what is the rate constant? Practice

The Arrhenius Equation Reactions rates are dependant on temperature. This is expressed through the rate constant “k” which is constant at a given temperature Arrhenius Equation R = 8.314 J/mol·K Universal gas constant k = rate constant A = frequency factor Ea = Activation energy or Activation barrier = exponential factor

Ea or the activation energy/barrier Energy that must be overcome to transform reactants into products At top of hill, reactants are in a transition state or activated complex Chapter 13, Figure 13.12 The Activation Energy Barrier

Chapter 13, Unnumbered Figure, Page 582

Chapter 13, Unnumbered Figure 1, Page 583

Chapter 13, Figure 13.13 The Activated Complex

A or Frequency factor Relates to the number of approaches to the activation barrier Higher frequency factor = more approaches to activation barrier Chapter 13, Unnumbered Figure 2, Page 583

The exponential factor The fraction of molecules that can successfully overcome the activation energy and transform into product Dependence on Ea and T Lower Ea and higher T = higher ex factor Higher Ea and lower T = lower ex factor Chapter 13, Figure 13.14 Thermal Energy Distribution

Arrhenius Plots

Chapter 13, Unnumbered Table, Page 584

Chapter 13, Unnumbered Figure, Page 584

Two-point form Arrhenius equation If you have the rate constants at two different temperatures (Kelvin), you can relate it to the activation energy of the reaction 𝑙𝑛 𝑘 2 𝑘 1 = 𝐸 𝑎 𝑅 1 𝑇 1 − 1 𝑇 2

The activation energy of a reaction is 56 The activation energy of a reaction is 56.8 kJ/mol and the frequency factor is 1.5 x 1011 (1/s). What is the rate constant of the reaction at 25 °C? y = -1.12x104(x) + 26.8 Using the equation from the graph from the previous slide, solve for the frequency factor and the activation energy of the reaction Practice

Collision Theory Reaction needs Reactants colliding Correct orientation Sufficient energy Chapter 13, Figure 13.15 The Collision Model

Chapter 13, Unnumbered Figure 1, Page 587

Chapter 13, Unnumbered Figure 2, Page 587

Reaction Mechanisms General chemical equation usually represents the overall reaction and no the individual steps by which a reaction occurs H2 + 2ICl  2HCl + I2 The reaction mechanism is the individual or elementary steps that leads to the overall reaction Step 1 H2 + ICl  HI + HCl Step 2 HI + ICl  HCl + I2 Overall H2 + 2ICl  2HCl + I2

Rate Laws for Elementary Steps

Chapter 13, Unnumbered Figure, Page 590

Rate Determining Step and Overall Reaction Rate Laws Step 1 H2 + ICl  HI + HCl slow Step 2 HI + ICl  HCl + I2 fast The slow step determines the rate law For a valid mechanism the predicted rate law must match the experimental rate law The elementary steps must sum to the overall reaction A valid mechanism is only a possibility but not the guaranteed reaction route

Chapter 13, Figure 13.16 Energy Diagram for a Two-Step Mechanism

Catalysts!!! Speed up reactions by lowering the activation energy by incorporating lower energy transition states to a reaction It makes the reaction faster without being consumed Chapter 13, Figure 13.18 Homogeneous and Heterogeneous Catalysis

Chapter 13, Figure 13.17 Catalyzed and Uncatalyzed Decomposition of Ozone

Chapter 13, Figure 13.20 Catalytic Hydrogenation of Ethene

Chapter 13, Figure 13.21 Enzyme–Substrate Binding

Chapter 13, Unnumbered Figure, Page 597

Chapter 13, Figure 13.22 An Enzyme-Catalyzed Reaction

Reaction rates!!! – calculating average and instantaneous rates Rate laws – zero, first, and second order reactions Intergrated rate law – straight line fit plots Half-life – the initial concentration decreases to 50% of initial value Arrhenius equations and plots – reactions dependant on temperature Collision Theory - what a reaction needs to occur Reaction Mechanisms – elementary steps of a reaction Catalysts – speed up reaction through lower energy transition states Chapter 15 Summary