Chapter 14 Chemical Kineticsp

• Factors that Affect Reaction rates

• Reaction Rates

• Concentration and Rate

• The Change of Concentration with Time

• Temperature and Rate

• Reactions Mechanisms

• Catalysis

Chemical Kinetics

I th t d f th t t hi h ti d l i i f tiIs the study of the rate at which reactions occur and also gives us information on how the reaction occurs (the Reaction Mechanism)

14 1 Factors that Affect Reaction Rates14.1 Factors that Affect Reaction RatesReaction rates depend on several factors

On a molecular level Reaction rates depend on the frequency with which molecules collide

14.2 Reaction Rates

Require a quantitative definition of the Reaction rate of a chemical reaction This is defined in terms of product(s) forming and reactant(s) disappearing per unit time

N2(g) + 3H2(g) → 2NH3(g)

This is the average rate, it doesn’t gives us an actual rate at a given moment in timee.g. Drive the 30km to the Ferries in 30 minutes was I driving 60km/hr all the way?

Gives information on the rate at a particular moment for this we plot the

Instantaneous Rate

Gives information on the rate at a particular moment, for this we plot the concentration of (product) with time and determine the slope at our time of interest

Reaction Rates and Stoichiometry

For the reaction plotted 1 mole of C4H9Cl forms 1 l f C H OH S t f d t f d1mole of C4H9OH. So rate of products formed is equal to the rate of disappearance of reactants.

What happens when this is not the case? e.g

2HI(g) →H2(g) + I2(g)

In this case the rate of appearance (formation) of H2 and I2 is equal, but the rate of HI disappearing is given bypp g g y

This leads to the generalisation that in a given reaction

aA + bB → cC + dD

How does the rate of reaction change as the concentration of (initial

14.3 Concentration and Rate

How does the rate of reaction change as the concentration of (initial reactants is changed)?For the reaction

NH4+(aq) + NO2

−(aq) N2(g) + 2 H2O(l)

The initial concentrations of both reactants are changed and the observed rate is measured

The rate law is expressed in the general form

R t k[A]m[B]n Wh k i th t t t (d d t )Rate = k[A]m[B]n Where k is the rate constant (depends on temp.) Big k characterizes fast reaction

m and n are the reaction orders with respect to the concentration of (A and B), Not stoichiometric coefficients must be determined experimentallyNot stoichiometric coefficients, must be determined experimentally

The exponents in a rate law indicate how the rate is affected by the concentration of each reactant, usually 0, 1 or 2

If m and n are both = 1 then the rate is first order with respect to [A] and first order with respect to[B].

So the rate law has an overall reaction order of 1+1 = 2, and the reaction is ,second order

Determining Rate Laws

F th R ti A + B → C + DFor the Reaction: A + B →   C + D

The experimentally data was tabulated as

Expt [A] M [B] M Init.Rate M s‐1Expt [A] M [B] M Init.Rate M s

1 0.1 0.1 0.001

2 0.1 0.2 0.002

3 0.2 0.1 0.004

So now we could find the value of k by substituting in our values from, say, expt. 1, starting with initial concentrations.g

The rate of a reaction depends on concentration.

The rate constant k does not, the rate constant is affected by temperature and a catalystcatalyst

Given a rate law we can calculate the rate of reaction using the rate constant and initial reactant concentrations.

Or given initial concentrations and initial rate we can calculate a rate law and the rate constant

14.4 The change in Concentration with Time

A rate law is an equation that tells us how a reaction rate depends on reactant concentrations.

But what if we are interested in how the reactant and product concentrations vary with time?

From a rate law we can calculate the rate of reaction using the rate constant and reactant concentrations. We now need an equation that allows us to determine the concentration of reactants and products at any particular time

First Order Reactions

Since ln[A]t/[A]o = ln[A]t - ln[A]o

W t thi ti i th f b iWe can get this equation in the form y = mx +c by re-arranging

We can test data to see if it fits this equation ….YES? Then first order

Sample exercise 14.7 Using the Integrated First order rate law

Second Order Reactions

Given the concentration of [A] at various times (t), tabulate to include ln[A] and 1/[A]1/[A]

Plot both vs. t, which gives the linear slope?

Half-Life

The half life of a reaction t is the time required for the concentration of a reactantThe half-life of a reaction t½ is the time required for the concentration of a reactant to reach half its original value

It is a convenient way of expressing how fast a reaction occurs

First Order Reactions

Half-Life

S d O d R ti

In contrast to first order reactions the half-life of second order reactions Does depend on the initial concentrations

Second Order Reactions

Summary of kinetics from an experimental perspective

The half-life of a second order reaction increases as the reaction progresses

Rate of reaction can be obtained from the rate law (if it is known)

Without the rate law, determine the rate of a reaction by

Use the initial rates if they are available (no products to affect the rate)

Determine the order of reaction

Use the initial rates if they are available (no products to affect the rate)

OR, Find the graph of the rate data that yields a straight line

OR,Test for constancy of the half-life

Substitute rate data into integrated rate laws to find the law that yields constant values for k, the rate constant

Time (s) [A] MTime (s) [A] M

0 Ao

t1 A1

t2 A2

t3 A3

Why is a reaction first or second order and why does increasing the temperature

14.5 Temperature and Rate

Why is a reaction first or second order and why does increasing the temperature speed up a reaction?

The Collision Model, explains what is happening on a molecular level

In a gas phase reaction there may be 1030 collisions per second, only a small number of collisions lead to reaction

The Molecules must also have sufficientThe Molecules must also have sufficient energy to react (breaking bonds)

The arrangement of atoms at the top of the energy barrier is the transition state

The Activation energy is the minimum amount of energy required to initiate a chemical reaction, (form the transition state)

Arrhenius developed a relationship between the Activation Energy and the rateArrhenius developed a relationship between the Activation Energy and the rate constant k

Determining the Activation Energy

Determining k at several different temperatures and plotting ln k vs. 1/T the Ea can be found from the slope Remember to plot T in Kelvin as the gas constant R has

it f J / l K !units of J / mol-K !

The Lower the Activation Energy, the faster the reaction

The higher the temperature the greater the proportion of molecules with KE ≥ Ea

14.6 Reaction Mechanisms

A reaction mechanism tells us the sequence of events that describes the process of forming products from reactants

The reaction may occur in a series of steps

The number of molecules participating as reactants in an elementary process is defined by the molecularity

The rate law can not generally be deduced from the overall balanced equation for a reaction as it depends on the rate law of the mechanism steps (Slowest)

Rate Laws for Elementary Reactions are determined by molecular proportions

For this elementary reaction (step 1 in a 2 step mechanism)

H2 + ICl → HI + HCl2 →

The rate Law is given as

Multi-step Mechanisms

A balanced chemical equation often occurs in a multi-step mechanism through a sequence of Elementary reactions

The sequence of Elementary reactions produces intermediatesq y p

One step is slower

Rate determining step

A valid mechanism must meet three criteria

Two types of Mechanisms

Mechanisms with a slow initial step

2NO2(g) + F2(g) → 2NO2F(g

Mechanisms with a fast initial step

If the slow step is not the first step, an intermediate is a reactant in the rate determining step

Example:

2NO(g) + Br2(g) →  2NOBr(g)

Has an experimentally determined Rate law of Rate = k[NO]2[Br2]

The proposed mechanism is:The proposed mechanism is:

NO(g) + Br2(g) NOBr2(g)

NOBr2(g) + NO(g) → 2NOBr(g)

k1

k-1

kBecause step 2 is the slow step the overall rate law is governed by that step

Rate = k2[NOBr2][NO]

k2

But NOBr2 is an unknown and unstable intermediate

Because the forward and reverse reactions occur faster than step 2 an equilibrium is established

In any dynamic equilibrium the rate of the forward reaction is equal to the rate of the reverse reaction sothe reverse reaction, so

When a fast step precedes a slow step, we can solve for the concentration of an intermediate by assuming that an equilibrium is established in the fast step

14.7 Catalysis

A catalyst increases the rate of a reaction (by lowering the Activation Energy), without being consumed in the reaction

Homogeneous Catalyst

Heterogeneous Catalyst

The reaction I3- (aq) + 2N3- (aq) → 3I- (aq) + 3 N2 (g) is catalyzed by CS2 (aq)

The mechanism is:

CS2 + N3- →  S2CN3

- SLOW

2S2CN3- + I3- → 2CS2 + 3N2 + 3I- FAST2S2CN3 + I3 →  2CS2 + 3N2 + 3I FAST

What is the rate law?

Heterogeneous Catalysts

Exist in a different Phase to the reactants

For example catalytic hydrogentation of alkenes with a Ni catalyst and Catalytic Converters.

Enzyme Catalysis

Substrate (yellow) binds to enzyme (purple) in an active site

Each enzyme catalyses aEach enzyme catalyses a specific reaction in the same way a key fits a given lock

The product is produced and theThe product is produced and the enzyme is unchanged.

An enzyme can increase a reaction rate up to 1018 times!reaction rate up to 10 times!

The product(s) leaving the active site is the rate determining step, once the products have left the psite can be filled by another substrate molecule