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