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Chemical Kinetics. Is a study of how fast chemical reactions occur. Factors affecting rates of reactions. Concentration of reactants. Temperature of reactions. Presence or absence of a catalyst. Surface area of solid or liquid reactants or catalysts.
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Chemical Kinetics Is a study of how fast chemical reactions occur.
Factors affecting rates of reactions. . . . • Concentration of reactants. • Temperature of reactions. • Presence or absence of a catalyst. • Surface area of solid or liquid reactants or catalysts.
Reaction Rates. . .the speed of a chemical reaction. • Speed of a reaction is defined as the change per unit time. • Often determined by measuring the change in concentration of a reactant or product with time. • Is called its reaction rate.
Change in the number of moles of B Average rate = Change in time If A B Change in the number of moles of B = moles B final – moles B initial G. = 1.00molA AF.= average rate R. = t=0 A=1.00mol B=0mol t=10min A=.74mol B=.26mol t=20min A=.54mol B=.46molB
D moles B Average rate = Dt .26 mol – 0 mol Average rate = 10min – 0 min Two ways of measuring rate: appearance of B per unit of time disappearance of A per unit of time OR -D moles A Average rate = Dt = 0.026 mol/min
Hints. . . • The coefficients of the balanced chemical equation tell you relative rates. • Rate of disappearance of reactants is given a negative sign.
Nitrogen monoxide reacts with chlorine gas to form the gaseous substance nitrosyl chloride (NOCl) according to the following equation: • 2NO(g) + Cl2(g) 2NOCl(g) • At the beginning of the reaction, the concentration of chlorine gas is 0.00640 mol/L after 30.0s, the chlorine concentration has decreased to 0.00295mol/L. Calculate the average over time in terms of the disappearance of chlorine.
Rates in terms of Concentration • Determine rate by monitoring change in concentration. (of reactant or product) • Of reactant or product. • Most useful unit is molarity. • Since volume is constant: • Molarity and moles are directly proportional.
C4H9Cl(aq) +H2O(l) C4H9OH(aq) +HCl(aq) • Calculate the average rate in terms of disappearance of C4H9Cl • Units for average rate are mol/L.s or M/s • Average rate decreases with time. • If we plot [C4H9Cl] vs. time • Instantaneous rate = the rate at any instant in time. • Slope of the straight line tangent to the curve at that instant. • Different from average rate.
Reaction Rates and StoichiometryC4H9Cl(aq) +H2O(l) C4H9OH(aq) +HCl(aq) • Rate of appearance of C4H9OH must equal the disappearance of C4H9Cl - D [C4H9Cl] = D [C4H9OH ] Rate = Dt Dt
1 D[HI] D[H2] D[I2] Rate = - * = = 2 DtDtDt 1 D[A] 1 D[B] 1 D[C] 1 D[D] Rate = - - = = = a Dt b Dt c Dt dDt 2HI(g) H2(g) + I2(g) OR aA + bB cC +dD
Rate vs. Concentration • Rate: • Increases when reactant concentration increases. • Decreases as the concentration of reactants is reduced.
Reaction order. . . • If. . . • Rate= k[reactant 1]m[reactant 2]n • m and n are reaction orders. • Overall reaction order is the sum of the reaction orders. • If no number is written, remember it equals 1. • Must be determined experimentally.
unit of the rate constant = (units of rate) = M/s = M-1 s-1 (Units of concentration)2 M2 Units of Rate Constants. . . • Depend on the overall reaction order. • If a reaction is second order: • Unit of rate=(unit of rate constant)(unit of concentration)2 • Therefore. . .
Using Initial Rates To Determine Rate Laws • Observe the effect of changing initial concentrations: • Zero order in a reactant. . . • Changing concentration of that reactant will have no effect on rate. • First order. . . • Doubling concentration will cause rate to double. • Second order. . . • Doubling concentration will result in a 22increase in rate. • Tripling concentration results in a 32 increase in rate. • nth order . . . • If doubling concentration causes a 2n increase in rate.
Hints. . . • The sum of the exponents is called the reaction order. • From the experimental data, determine how rate varies with varying concentration of one while the concentration of the other is held constant. • When solving for rate constant k, pick any equation though it is best to average them.
The Change in Concentration with Time (convert the rate law into a convenient equation that gives concentration as a function of time) • First order, the rate doubles as the concentration of a reactant doubles. • Therefore: • Rate = -D[A]/Dt = k[A] • After integrating: • ln([A]t/[A]0) = -kt • A plot of ln[A]t vs. t is a straight line with slope –k and intercept ln[A]0
Half Life. . .t 1/2 • Is the time required for the concentration of a reactant to decrease to half its original value. • t 1/2 is the time required for [A]0 to reach ½[A]0. • The half life of a first order reaction is independent of the initial concentration of the reactant.
Second Order Reactions • Rate depends on the reactant concentration to the second power or on the concentration of two reactants to the first power. • A plot of 1/[A]t vs. t is a straight line with slope k and intercept 1/[A]0. • A plot of ln[A]t vs. t is not linear. • t 1/2= 1/k[A]0 • Rate=k[A]2 or =k[A][B]
Temperature and Rate • Most reactions speed up as temperature increases. • Reflecting temperature and rate in a rate expression: • Rate law has no temperature term, so rate constant must depend on temperature. • Consider first order reaction: CH3NC CH3CN As temperature increases from 190C-250C the rate constant increases. Approximately doubling with each 10C increase in temperature.
Collision Model. . . • Based on kinetic molecular theory. • In order for molecules to react, they must collide. • The greater the number of collisions, the faster the rate. • Rate should increase with an increase in concentration of reactants. • Higher temperature, more energy,more collisions. • Rate should increase with temperature increase. • Not all collisions lead to products. • Molecules must collide in the correct orientation with enough energy to form products. • http://www.dlt.ncssm.edu/core/Chapter15-Kinetics/Chapter15-Animations/Molecular_collision_Ea.html
Activation Energy. . . • Arrhenius: molecules must possess a minimum amount of energy to react. • Bonds must be broken in the reactants. • Molecules with too little kinetic energy do not react when they collide. • Activation Energy, Ea: is the minimum energy required to initiate a chemical reaction.
Reaction Mechanism. . . • Is the process by which the reaction occurs. • Provide a picture of which bonds are broken and formed during the course of a reaction.
Single Step Reactions. . . • A+B 2C • Rforward = kforward [A][B] • If reversible: Rreverse=kreverse[C]2 • Only if the reaction occurs in one step.occurs at the molecular level just as it is written in the chemical equation.
Elementary Steps. . . • Any processes that occur in a single step. • Number of molecules present in an elementary step gives the molecularity of the elementary step: • Uni-, bi-, ter- • Multistep reactions: consist of a sequence of elementary steps. • Elementary steps add to give the balanced chemical equation. • Multistep reactions will include intermediates. • Appear in an elementary step, but are not products or reactants. • Formed in one elementary step and consumed in another. • Not found in the balanced equation for the overall reaction.
Rate Laws of Elementary Steps • Determine the overall rate law for the reaction. • Rate law of elementary step is determined by its molecularity. • Uni- first order • Bi- second order • Ter- third order
Rate Laws of Multistep Mechanisms • One step is slower than others. • Slow step limits the overall reaction rate. • This is the rate determining step. • This step governs the rate law for the overall reaction.
k1 k2 NO2(g)+CO(g) NO(g)+CO2(g) • Experimentally derived rate law: • Rate= k1[NO2]2 • Mechanism for the reaction: • Step 1:NO2(g)+NO2(g) NO3(g) + NO(g) slow • Step 2: NO3(g)+CO(g) NO2(g) + CO2fast • NO3 is an intermediate • If k2>>k1, then the overall rate depends on first step. • Rate = k1[NO2]2supports but does not prove mechanism.
2NO2(g)+ F 2(g) 2NO2F(g) • A proposed mechanism: • Step 1. NO2+F2 NO2F+F (slow) • Step 2. F+NO2 NO2F (fast) • Identify the rate determining step, and write an acceptable rate law. ANSWER: Combine the two steps, the intermediate F cancels out and we are left with the original equation. The first step is the slow step and is considered the rate determining step. R=k[NO2][F2]
X + 2Y XY2 • This reaction occurs by a single step mechanism. Write the rate law for this reaction, then determine the following effects: • a)doubling the concentration of X • b)doubling the concentration of Y • c) using one third the concentration of Y
Answer: • Single step therefore the rate law can be written from the equation. • The rate will vary directly with the concentration of X, which has the implied coefficient of 1 in the equation. The rate will vary directly with the square of the concentration of Y,which has a coefficient of 2: R=k[X][Y]2
a. double the rate: R=k[2X][Y]2 • b. increase the rate four fold: R=k[X][2Y]2 • c. Reduce the rate to one ninth of its original value: R=k[X][1/3Y]2
k1 K-1 k2 Mechanisms with an Initial Fast Step • Consider: 2NO(g)+ Br2(g) 2NOBr(g) • Experimentally determined rate law is: Rate = k[NO]2[Br2] • Step 1: NO(g) + Br2(g) NOBr2(g)fast • Step 2: NOBr2+NO(g) 2NOBr(g)slow
Theoretical rate law based on step 2: rate=k2[NOBr2][NO] • Problem: • depends on the concentration of an intermediate species. • Intermediates unstable, have low/unknown concentrations. • Find a way to remove term from rate law. • Assuming equilibrium in step 1, express [NOBr2] in terms of NOBr and Br2.
k1 k-1 • By definition of equilibrium, forward rate equals the reverse rate: • k1[NO][Br2] = k-1[NOBr2] • Therefore, the overall rate law becomes: • Rate = k2 [NO][Br2][NO]=k[NO]2[Br2] • Note that the final rate law is consistent with the experimentally observed rate law.
Catalysts. . . Change the rate of a chemical equation without itself undergoing a permanent chemical change in the process. • Two types: • Homogeneous: Present in the same phase as reacting molecules. • Lower activation energy for the reaction. • Increase the number of effective collisions. • From the Arrenhenius equation, catalysts increase k by increasing A or decreasing Ea • Usually provides a completely different mechanism for the reaction. • If an intermediate is added, the activation energy for both steps must be lower than the activation energy for the uncatalyzed reaction.
Heterogeneous catalysts. . . • Exists in a different phase than reactants. • Many industrial catalysts are heterogeneous. • Adsorption is the binding of reactant molecules to the catalyst surface. Happens due to the high reactivity of atoms or ions on the surface of the solid.