Chapter 14Chemical Kinetics• Gibb’s Free Energy shows which reactions will proceed, but it gave no indication how fast the reaction will proceed.• This chapter will answer the question of how fast reactions occur and some of the important factors that control chemical reactions.Key Concepts• Reaction rate: -Δ[A]/Δt• Quantify the influence of chemical concentration on the reaction rate.– Reaction rate law: reaction rate = k[A]m[B]n– Reaction orders (zero, first, second, etc.)• Obtain the first order decay equation via integration (also called the integrated rate law):At= Aoe−kt• Relate reaction rate to temperature:k = Ae−E/RT• Define elementary and multistep reactions.Reaction Speeds• Spontaneous reactions can occur over a wide range of time scales.– Explosives are famous for being fast reactions on the order of milliseconds.– Many of the reactions that you typically think of as “chemical reactions” occur over seconds to hours time scales.• Acid/base neutralization in you stomach after taking an antacid.• Burning a candle– Some reactions are very slow stretching over years or millennia.• Metal rusting, limestone dissolving in rain, etc.Factors Affecting Reaction Rates1) The physical states of the reactants– Reactant molecules must move together to react, so the phases with more mobile molecules tend to react faster.• Zero-order reactions are notable exceptions (e.g. explosives)2) The concentration of the reactants (equivalent to pressure for gases)– The higher the concentration of reactants, the more likely that two molecules collide with enough energy to cause the reaction.3) The temperature at which the reaction occurs.– Reactions generally proceed faster at higher temperatures (biological-catalyzed reactions are an exception)4) The presence of a catalyst– Catalysts speed reactions by lowering the activation energy of the reaction.Chemical reactions occur when molecules collide with enough energy to stretch bonds to the breaking point.Therefore, anything that increases the number or energy of collisions will increase the reaction rate.Reaction Rates• The rate of chemical reaction is defined as the change in the amount of the reactants or products over a given time period.– The “amount” of the chemical can be expressed in many different units.– The book uses molarity “M” as a measure of concentration. This shows a strong bias to aqueous chemistry!– Other units for the amount of chemical are most often concentration units (g/m3, g/L, etc.) but sometimes a simple mass or mole measure is used if the reaction system is closed.Rate of reaction is amount of chemical that reacts over a time intervalTime = 0 100 red molesTime = 5s 50 red molesTime = 10s 25 red molesTime = 15s 13 red molesTime = 20s 7 red molesTime = 25s 4 red molesTime = 35s 1 red molesTime = 30s 2 red molesIn this example, each mole (represented by a red circle) has a 50% chance of reacting every 5 seconds.The rate of reaction can be defined for either the loss of the reactants or the creation of the productsThe rate of reaction for the production of compound B from A over a time period is:Average rate == (change in product concentration)/(change in time)= ([B]final– [B]initial)/(tfinal– tinitial)= [B]/t*The brackets [ ] denote the concentration of a chemical, so [B] is the concentration of compound B.Reaction: A → BAlternatively, the rate of reaction can also be defined as the loss of compound A as it forms B over a time period.The only difference is that the loss equation has a negative in front of it (we’re losing A after all). Note that since [A]final< [A]initialthe negative sign just makes sure that our reaction rate is positive. Average rate ==  (change in reactant concentration)/(change in time)=  ([A]final– [A]initial)/(tfinal– tinitial)= [A]/tReaction: A → BRate of reaction defined as the loss of the reactantTime = 0 100 red molesTime = 5s 50 red molesTime = 10s 25 red molesTime = 15s 13 red molesTime = 20s 7 red molesTime = 25s 4 red molesTime = 35s 1 red molesTime = 30s 2 red molesThe average rate of reaction defined as the loss of red moles between 0 and 5 seconds is == –([Afinal] – [Ainitial])/(tf– ti)= –(50 – 100)/(5s – 0s)= 50 moles/5s = 10 moles/sRate of reaction defined by formation of productTime = 0 100 red molesTime = 5s 50 red molesTime = 10s 25 red molesTime = 15s 13 red molesTime = 20s 7 red molesTime = 25s 4 red molesTime = 35s 1 red molesTime = 30s 2 red molesThe average rate of reaction defined as the formation of blue moles [B] between 0 and 5 seconds is == ([Bfinal] – [Binitial])/(tf– ti)= (50 – 0)/(5s – 0s)= 50 moles/5s = 10 moles/s (same as before)The reaction rate is not constant over time.01020304050607080901000 5 10 15 20 25 30 35 40Concentration (# of moles of yellow chemical)Time (seconds)Rate = 10 mol/sRate = 0.2 mol/s01020304050607080901000 5 10 15 20 25 30 35 40Concentration (# of moles of yellow chemical)Time (seconds)The instantaneous reaction rate is the slope of the tangent line at that time. For example, the instantaneous rate at exactly 10 seconds is the slope of the tangent at 10 seconds. We draw a tangent line at this point and then make a triangle to determine the slope of line (slope = rise over run) at this point.For this example, the instantaneous reaction rate is:Slope = (40 moles −10 moles)/(15 s − 5 s)= (30 moles)/(10 s) = 3 moles/sReaction Rates and Stoichiometry• What if the reaction stoichiometry is not 1?• The reaction rate for the generic reaction:aA + bB  cC + dD is given by:Loss of reactants1a= −Δ[A]Δt1b= −Δ[B]ΔtGain of products1c=Δ[C]Δt1d=Δ[D]ΔtExampleSuppose that phosphoric acid is reacting with sodium hydroxide to form sodium phosphate and water. What is the rate of H3PO4depletion if the consumption rate of NaOH is 0.23 M/s at the same point in time?First, write a balanced chemical reaction:H3PO4+ 3NaOH = Na3PO4+ 3H2ONow write the rate expression for the two chemicals of interest:− (1/1)(H3PO4rate) = − (1/3)(NaOH rate)− (H3PO4rate) = − (1/3)(0.23 M/s)H3PO4rate = 0.077 M/sExample IINitrogen triiodide rapidly detonates to form N2gas and I2gas. If the production of N2gas is 32 moles/ms, then what is the consumption rate of nitrogen triiodide?First, write a balanced chemical reaction:2NI3= N2+ 3I2Now write the rate