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## Chemical Kinetics

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**Chemical Kinetics**Chapter 14 AP Chemistry**Chemical Kinetics**• Kinetics – the area of chemistry concerned with the rate (or speed) of a reaction. • Kinetics vs. Thermodynamics • Applications: Medicine, Chemical Engineering**Reaction Rate Factors**• Physical state of reactants • Surface area • Concentration • Rate increases with concentration increase • Temperature • Rate doubles every 10oC increase • Catalyst • Increase the reaction rate w/o being used up**Reaction Rates**• Speed is the change in a particular quantity with respect to a change in time. • In chemistry, we define the reaction rate • The change in concentration of the reactants or products over time • Units are usually M/sec • Rate =**C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)**• A graph of concentration vs. time is often plotted. • Slope of the tangent line at any point along the curve is the instantaneous rate. • Rate decreases with time. • Reactants decrease with time**Average Rate**• Because the rate of reaction changes with time, it is useful to consider an average rate. • Rate = • The average rate for a reaction is usually take as the early stages of a reaction.**Measuring Rates**• To determine the progress of a reaction, we can measure two quantities: • Disappearance of the reactant • Formation of products • Reaction rate is a positive value. • Reaction rate is the same, no matter the method of measurement.**aA + bB cC + dD**• The rate of reaction is given by the following equalities: • A: Rate = • B: Rate = • C: Rate = • D: Rate = • Rate =**H2O2(g) H2(g) + O2(g)**• Write the rate in terms of each species.**SO2(g) + O2(g) SO3(g)**• Write the rate in terms of each species.**H2(g) + O2(g) H2O(g)**• Hydrogen is burning at the rate of 0.85 M/sec. Rate of oxygen consumption? Rate of water vapor formation?**How?**• How is it possible to measure the concentration of reactants or products? • There are a variety of methods. • One of the more common methods is spectroscopy. • Measures the ability to absorb/transmit light and converts the data to a concentration.**Beer-Lambert Law**• There is a linear relationship between the concentration of a sample and its absorbance. • A = -logT • Beer’s Law: A = εbC • Standards to find slope • Convert T to A to C**NH3(g) N2(g) + H2(g)**• Nitrogen is forming at the rate of 0.264 M/sec. Rate of ammonia consumption? Rate of hydrogen formation?**Rate Law**• General Equation: aA + bB cC + dD • Rate = • m is the order of A • n is the order of B • (m+n) is the overall reaction order • k is the rate constant • specific for a rxn, Temperature dependent**Rate = k[A]m[B]n**• The rate law must be experimentally determined. • m and n are NOT the stoichiometric coefficient • Unit of rate constant k • M-p s-1 or 1/(Mp s) • p = (m+n) – 1 • Rate depends on reactant conc…k does not depend on reactant conc.**Rate = k[A][B]**• What happens to the rate if we… • Double conc of A (everything else the same)? • Double conc of B (everything else the same)? • Triple conc of A and double conc of B? • Order of A? B? Overall?**Rate = k[A]2[B]**• What happens to the rate if we… • Double conc of A (everything else the same)? • Double conc of B (everything else the same)? • Triple conc of A and double conc of B? • Order of A? B? Overall?**Rate = k[A]0[B]3**• What happens to the rate if we… • Double conc of A (everything else the same)? • Double conc of B (everything else the same)? • Triple conc of A and double conc of B? • Order of A? B? Overall?**Rate = k[A]m[B]n**• Two ways to determine the rate law • Initial rate method • Can have many reactants • Graphical Method • Can only have one reactant • Solving a rate Law: • Need to determine the orders of the reactants • Need to determine the rate constant k**Change in Conc. with time**• So far, we have considered rate based on the change in concentration and rate constants. • Using calculus, we can convert these same equations to more useful forms. • This is the graphing method to determining the order of a reaction. • Specific for only one reactant: [A]**Rate Laws**• Differential Rate Law: • Expressed how rate depends on concentration. • Integrated Rate Law • Integrated form of the differential. Has specific variables.**Zero Order Reaction**• Rate only depends on the rate constant…not on the concentration of A • Differential: • Integrated:**First Order Reaction**• Rate only depends on the rate constant and on the concentration of A • Differential: • Integrated:**First Order**Plot of [A] vs. t Plot of ln[A] vs. t**Second Order Reaction**• Rate only depends on the rate constant and on the square concentration of A • Differential: • Integrated:**Second Order**Plot of ln[A] vs. t Plot of 1/[A] vs. t**Usefulness of the Integrated Rate Laws**[A]t = -kt + [A]0 • We can know the concentration at any time point for a given reaction. • We can determine the order of a reaction. • We can determine the half life of a reaction.**Determining the Order**[A]t = -kt + [A]0 • This tells us that a plot of concentration of A vs time will yield a straight line. • Because this is the zero order rate equation, a plot of [A] vs. t will yield a straight line. y = mx + b**Determining the Order**• First Order: ln[A]t = -kt + ln[A]0 • A plot of ln[A] vs. t will give a straight line. • Second Order: • A plot of 1/[A] vs. t will give a striaght line.**Half life, t1/2**• The time required for the concentration of a reactant to reach one-half its value: • [A]t1/2 = ½[A]0 • This is a convenient way to describe the rate of a reaction. • A fast reaction will have a short half life.**Derivation: t1/2 of First Order**ln[A]t = -kt + ln[A]0**Summary**** Note: The half life of a first order says that it does NOT depend the concentration of the reactant A. So, the concentration decreases by ½ each regular time interval, t1/2.**A first order reaction has k = 6.7 x 10-4 s-1.**• How long will it take for the conc to go from 0.25M to 0.15M? • If the initial conc is 0.25M, what is the conc after 8.8 min?**A first order reaction has [A] = 2.00M initially. After 126**min, [A] = 0.0250M. • What is the rate constant k? • What is the half life?**A second order reaction has k = 7.0 x 10-9 M-1s-1.**• If the initial conc is 0.086M, what is the conc after 2.0 min?**A first order reaction has t1/2 = 35.0 sec.**• What is the rate constant k? • How long would it take for 95% decomposition of the reactant?**A first order reaction has a half life of 19.8 min. What is**the reaction rate when [A] = 0.750M?**Collision Model**• Based on Kinetic Molecular Theory • Molecules must collide to react • Greater the collisions, greater the rate • As concentration increases, rate increases • As temperature increases, rate increases**Orientation**• Most collisions do not lead to reactions • Molecular orientation of collision is important**Still not enough**• Usually, a collision in the correct orientation is still not enough to cause a reaction. • Kinetic energy of a collision must cause bonds to break. • For a reaction to occur, there must be enough kinetic energy to be greater than some energy. • Activation Energy, Ea, is the minimum energy required to initiate a reaction.**Transition State**• Transition state is also called the activated complex • High energy intermediate state • The activation energy represents the higher energy state of the transition state ‡ A A B B A A + B B A B + A B