Chemical KineticsAP Chem

Area of chemistry that deals with rates or speeds at which a reaction occurs

The rate of these reactions are affected by several factors

Chemical Kinetics

Describing Rates

time

propertyobservableRate

Such as:ConcentrationColorBubblesTemppH

Whatever is appropriate:HoursMinutesSeconds

Candle Wax Example

Describing Rates

Collisions cause reactions!◦ Breaking of bonds directly linked to rate◦ Must overcome repulsion of electron clouds

Also correct orientation sometimes needed

◦ Example: Chalk dropping

Collision Theory

Concentration of reactants◦With gases, pressure used instead

Temperature at which the reaction occurs

The presence of a catalystSurface area of solid or liquid reactants

Factors Affecting Rates of Reaction

Demo: ◦ Chalk + 1 M HCl / Chalk + 1 M Acetic Acid

Prediction? Factor?

◦ Chalk + 1 M HCl / Chalk + 6 M HCl Prediction? Factor?

◦ Chalk + 1 M HCl (Room Temp) / Chalk + 1 M HCl (Heated) Prediction? Factor?

Factors Affecting Rates

Speed of reaction or reaction rate is the time over which a change occurs

Consider the reaction A BReaction rate is a measure of how quickly A is consumed or B is produced

Average Reaction Rates

Average rate of reaction can be written:

This is a measure of the average rate of appearance of B

Average Reaction Rates

t

BmolesrateAverage

)(

Average rate can also be written in terms of A:

This is the rate of disappearance of A (equal to B only negative)

Average Rates can only be positive

Average Reaction Rates

t

AofmolesrateAverage

)(

Start with one mole of A at time zero, measure amounts of A and B at given time intervals

Average Reaction Rates

Data for Reaction A B

Average Reaction Rate

Moles A Moles B

When mole ratios of equations are not 1:1 For the reaction:

Rates and Stoichiometry

aA + bB cC + dD

Example◦ If the rate of decomposition of N2O5 in a reaction

vessel is 4.2 x 10-7 M/s, what is the rate of appearance of NO2 and O2

2 N2O5(g) 4 NO2(g) + O2(g)

Rates and Stoichiometry

Consider the reaction between butyl chloride and water:

Instantaneous Rate of Reaction

C4H9Cl(aq) + H2O(l) C4H9OH(aq) +HCl(aq)

t

ClHCrateAverage

94

Using the curve created from the data, we can determine the instantaneous rate for any given point on the curve

Recall: slope is rise over run!

Instantaneous Rate of Reaction

Analogy: Distance between Fall River and Norton is 29.7 mi along a certain route. It takes Mr. N 30 minutes to get to school. His average rate is 59.4 mph.

But at t = 15, Mr. N’s instantaneous rate is 95 mph, and at t = 1 Mr. N’s instantaneous rate is 25 mph.

Instantaneous Rate vs. Average Rate

Increasing concentration of reactants gives increasing rate

Decreasing rates of reactions over time is typical◦Due to decreasing concentration of reactants

Concentration and Rates

Rates of a reaction can be related to concentrations with a rate constant (k)

For reaction:

Rate laws are defined by reactant (not product) concentrations

Rate Laws

yx BAkRate aA + bB cC + dD

For the rate law expression:

The overall order of reaction is the sum of the powers (x + y)◦ However, rate with respect to [A] is only x

Reaction Order

yx BAkRate

In most rate laws reaction orders are 0, 1, or 2◦ Can be fractional or negative at times◦ Most commonly 1 or 2

Reaction orders are determined experimentally, and do not necessarily relate to coefficients of a balanced equation

Reaction Order

Example:What is the overall order of reaction for the reaction below?

CHCl3(g) + Cl2(g) CCl4(g) + HCl(g)

Rate= k [CHCl3][Cl2]1/2

A.) ½B.) 2C.) 3/2D.) 2/2

Reaction Order

Zero order for a reactant means concentration changes have no effect on reaction rate◦Example: Drinking

1st order means concentration changes give proportional changes in reaction rate◦Double the concentration, double the rate

Meaning of Reaction Order

2nd order rate law, increasing in concentration results in a rate increase equal to the concentration increased to the second power◦Example: Double conc. = 22 = 4 (rate increase) Triple conc. = 32 = 9 (rate increase)

Meaning of Reaction Order

The units for the rate constant depend on the order of the rate law

Units of Rate Constant (k)

Zion)concentratof(units

rate of unitsconstantrateofUnits

constant rate of units/

ZM

sM

Z = overall order of reaction

Rate Law Overall Order Units of Rate Constant (k)

Rate = k Zero M/s (M s-1)

Rate = k [A] First 1/s (s-1)

Rate = k [A][B] Second 1/M s (M-1 s-1)

Rate = k [A]2[B] Third 1/M2 s (M-2 s-1)

What is the unit for the rate constant for the reaction below?

CHCl3(g) + Cl2(g) CCl4(g) + HCl(g)

Rate= k [CHCl3][Cl2]1/2

A.) M½/sB.) M/sC.) M2/sD.) M-1/2/s

Units of Rate Constant (k)

A particular reaction was found to depend on the concentration of the hydrogen ion. The initial rates varied as a function of [H+] as follows:

[H+] (M) 0.0500 0.100 0.200Initial rate(M/s) 6.4x10-7 3.2x10-7 1.6x10-7

What is the order of the reaction in [H+] A.) 1 B.) 2 C.) -1 D.) -1/2

Determining Order of Reactants from Experimental Data

Rate Data for the Reaction Between F2 and ClO2

[F2] (M) [ClO2] (M) Initial Rate (M/s)

0.10 0.010 1.2 x 10-3

0.10 0.040 4.8 x 10-3

0.20 0.010 2.4 x 10-3

Determining Rate Law by Experimental Data

What is the rate law expression for the reaction?

Rate law tells how rate changes with changing concentrations at a particular temperature

We can derive equations that can give us the concentrations of reactants or products at any time during a reaction (instantaneous)◦ These are known as integrated rate laws

Concentration and Time

Rate = k Using calculus, the integrated rate law is:

[A]t is concentration of reactant at time t [A]0 is initial concentration of reactant

Integrated Zero Order Reactions

0][ AktA t

This has the same form as the general equation for a straight line

Graphically, the slope is equal to -k

Integrated Zero Order Reaction

bxmy

0][ AktA t

Separate equations can be derived relating to time required for reactants to decrease to half of initial concentration (aka half-life or t1/2)

When t = t1/2, [A]t is half of [A]0 ([A]t =[A]0/2)

Half-life (t1/2) for Zero Order

Rate = k [A] Using calculus, the integrated rate law

becomes:

This equation is of the general equation for a straight line (like before)

Integrated First Order Reaction

0t AlnAln tk

Note that only the second graph is used so that the slope can be determined

Also, y-intercept is ln [A]0

Graph of Int. First Order

Example2N2O5(g) 4NO2(g) + O2(g)

The decomposition of dinitrogen pentoxide is a 1st order reaction with a rate constant of 5.1 x 10-4 s-1 at 45ºC. If initial conc. is 0.25M, what is the concentration after 3.2 min.?

Int. First Order Reaction

Example #22N2O5(g) 4NO2(g) + O2(g)

The decomposition of dinitrogen pentoxide is a 1st order reaction with a rate constant of 5.1 x 10-4 s-1 at 45ºC. How long will it take for the concentration of N2O5 to decrease from 0.25M to 0.15M?

Int. First Order Reaction

For first order reactions:

Note it is independent of concentration! This is used to describe radioactive decay

and elimination of medications from the body

Half life for First Order Reactions

kt

693.02/1

Rate = k [A]2

Using calculus, the integrated rate law becomes:

Just like the previous two, this equation is of the general equation for a straight line

Int. Second Order Reaction

0][

1

][

1

Akt

A

Unlike first order, second order does depend on initial concentrations:

Half Life of Second Order Reaction

0][

1

Ak

Summary

Ways to find Rate Constant or Reaction Order

Conc. Vs. Time (Graphically)k = slope

Rates vs. Conc. (Exp. Data/Rate Laws)

Half-life expressions

Most reactions increase in rate with increasing temperature

This is due to an increase in the rate constant with increasing temperature

Relationship between Temperature & Rate

Minimum amount of energy required to initiate a chemical reaction◦ Varies from reaction to reaction

This is the kinetic energy required by colliding molecules in order to begin a reaction◦ Remember, even with sufficient KE, orientation is

still important

Activation Energy, Ea

Activation energy must be enough to overcome initial resistance for a reaction to take place

Activation Energy, Ea

Diagram can be used to determine if reaction is exothermic (- ∆H) or endothermic (+∆H)

Activated complex (or transition state) is the arrangement of atoms at the peak of the Ea barrier◦ Unstable and only

appears briefly

Activation Energy Diagram

The relationship between rate and temperature was non-linear

Reaction rate obeyed an equation based on 3 factors:1. Fraction of molecules that possess Ea

2. # of collisions per second3. Fraction of collisions with proper orientation

Observations made by Arrhenius

k = the rate constant R = gas constant (8.314 J/mol*K) T = Absolute temperature (K) Ea = the activation energy A = frequency factor

◦ A is mostly constant with variations in temperature

Arrhenius Equation

RTEaek /A

Taking the natural log of both sides gives a formula in straight line form:

Graph of ln k versus 1/T will be a straight line with a slope of –Ea/R and a y-intercept of ln A

Arrhenius Equation

ART

Ek a lnln

In order to compare different rates at different temperatures the equation can be rearranged:

Arrhenius Equation

122

1 11ln

TTR

E

k

k a

Example◦ The rate constant of a first order reaction is 3.46 x

10-2 s-1 at 298 K. What is the rate constant at 350 K if the activation energy is 50.2 kJ/mol?

k1 = 3.46 x 10-2 s-1 k2 = ?

T1= 298 K T2 = 350 K

Arrhenius Equation

Example

KKJ

molK

mol

kJ

k

s

298

1

350

1

314.8

2.5010x46.3ln

2

1-2

4

2

1-2

1098.4314.8

5020010x46.3ln

xJ

molK

mol

J

k

s

01.310x46.3

ln2

1-2

k

s

0493.10x46.3

2

1-2

k

s

2

1-2

0493.

10x46.3k

s

k2 = 0.702 s-1

The process by which a reaction is broken down into multiple step reactions◦Chemical equations only show beginning and ending substances

◦Can show in detail bond breaking and forming and structural changes that occur during a reaction

Reaction Mechanisms

Elementary steps◦Processes that occur in a single event or

step, are elementary processes. Can determine rate laws from elementary

steps, unlike overall reactions◦Particles collide with sufficient energy

and proper orientation for reaction to occur

◦These are the small step reactions in which an overall reaction occurs

Reaction Mechanisms

Often times chemical reactions are a result of multiple steps not shown by the overall equation

The above rxn below 225 °C occurs as 2 elementary steps

Multistep Mechanisms of Rxn

)(2)()()(2 gggg CONOCONO

1st step◦ 2 NO2 molecules collide

2nd step◦ The NO3 then collides with CO and transfers an O

The elementary steps must add to result in the overall chemical equation

Multistep Mechanisms of Rxn

)()(3)(2)(2 gggg NONONONO

2(g)2(g)(g)3(g) CONOCONO

Every reaction is made up of a series of elementary steps

Rate laws reflect the relative speeds of these steps

The rate law of an elementary step is directly related to its molecularity◦ This is the number of molecules that participate

as reactants

Rate Laws of Elementary Steps

Unimolecular = 1st order (Aproduct)◦Rate =k[A]

Bimolecular = 2nd order (A+B prod)

◦Rate= k[A][B]

Common Elementary Step Reactions

Rate Laws for all Elementary Steps

Most reactions involve multiple steps Often one step is much slower than the

other The Rate Determining Step (RDS) is the

slowest step in the reaction The slowest step of a multi-step reaction

determines the overall rate of reaction!

Rate Determining Step

Good things to know/determine:◦ Steps must add up to overall reaction◦ Identify Catalyst

Consumed at first, regenerated later (not in overall)◦ Identify Intermediates

Produced and then consumed later◦ Each step has a rate law

Depends on number of reactants◦ Rate Determining Step => slowest step

Reaction Mechanisms

Example:◦ What is the rate law of the following multi-step

reaction?

Rate Determining Step

)()(3)(2)(21:1step ggk

gg NONONONO

2(g)2(g)(g)3(g) CONOCONO:2step 2 k

)(2)()()(2: gggg CONOCONOOverall

slowfast

As a general rule catalysts change the rate of reaction by lowering the Ea

Usually this is done by giving completely different mechanism for the reaction◦This lowers the overall Ea

Catalysts

Catalysts