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# Reaction rate

By Cynthia Watkins,2014-08-14 09:06
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Reaction rate

Reaction rate

A. Definition:

amount of reactant reacted Reaction rate = time interval

[tan]react = limt0t

dreact[tan] = dt

amount of product producedReaction rate = time interval

[]product = limt0t

dproduct[] = dt

2;；e.g. 2HaqSOaqHOlSsSOg()()()()();?，?;;2322;dH[]31+reaction rate = mol dm s of H consuming dt2dSO[]23231reaction rate = mol dm s of consuming SO23dt

dP[]SO21reaction rate = Pa s of SO forming 2dt

dms1reaction rate = g s of S forming dt

Consider the following reaction:

2 A + B ?， AB 2

dAB[]dA[][]dB2 ；？；？22dtdtdt

dAB[]1dA[][]dB2 ；？；？2dtdtdt

This is important to specify which species is taken in the rate expression, since the rate can be different for different species. Ususally the rate of the reaction is defined as follow:

1Reaction rate = rate of change of [A] 2

= rate of change of [B]

= rate of change of [AB] 2

B. Collision theory:

1. The reaction occurs when particles collide. 2. The more the collisions, the faster the reaction is. 3. In order to occur a reaction, the molecules need a minimum energy (activation energy/threshold energy), below which a

collision cannot be successful, particles bounce apart again without reacting.

4. Increasing temperature increases the kinetic energy of particles.

This causes

(i) collision would be more frequent;

(ii) more particles have an energy higher than the activation energy.

Number of collision with energy higher than Ea EaRT= Total number of collision ~e

Reaction rate / page 1

C. Factors affecting the reaction rate:

1. concentration

2. temperature

3. pressure (for gas only)

4. surface area (for solid only)

5. catalyst

6. light

D. Concentration effect

Incresaing concentration means crowding of particles and decreasing the distance of collision.

concentration collision frequency reaction rate

1. Rate equation (rate law):

Ex. In the kinetic study of the following reaction:

(g) ?， CO (g) + NO (g) CO (g) + NO22

the initial concentrations of the reactants and the initial reaction rates are determined in a number of experiments. 333 1Experiment Initial [CO] mol dm Initial [NO] mol dm Initial rate mol dms 2

1 0.10 0.10 0.015

2 0.20 0.10 0.030

3 0.40 0.10 0.060

4 0.10 0.20 0.030

5 0.10 0.30 0.045

From experiment 1, 2 and 3, reaction rate ? [CO]

From experiment 1, 4 and 5, reaction rate ? [NO] 2

reaction rate ? [CO] [NO] 2

dNO[] reaction rate = = k[CO] [NO] 2dt311 where k is called the rate constant, its unit is dm mol sin this experiment;

and the above expression is called the rate equation (rate law) of the reaction;

the rate order of the reaction is 2.

(a) First order reaction (Unimolecular reaction):

For the elementary step: A (g) ?， X (g)

dA[] ；？kA[]dt

[]AtdA[] ？；kdt(([]A0o[]A

ln[A] ln[A] = kt o

Rate ln[A]

[A] Time

slope = k slope = k

Examples of the (a) First order reaction:

CH CH33

CH?C?Cl + OH ?， CH?C?OH + Cl S1 33N

CHCH 3 3

rate = k [(CH)CCl] 332262224 RaRnHe?，?;88862

rate = k [Ra]

Half-life : The time taken for half of the reactant to be converted to the product. t1

2

For radioactive decay is known as first order reaction.

Assume t = 0 Initial concentration = [A] 0

1 t = concentration = [A] t0122

Rate equation for the first order reaction : ln[A] ln[A] = kt o

Reaction rate / page 2

1 ln[A]= k ln[A]to0 122

ln 2 = k t1

2

ln.20693 = t1kk2

(b) Second order reaction (Bimolecular reaction):

For the elementary step: 2 A (g) ?， X (g)

dA[]2 ；？kA[]dt

[]AtdA[] ？；kdt((2[]A0o[]A

11 ；？kt[][]AA01Rate [A]

2 [A] Time

slope = k slope = k Examples of the second order reaction: CH?Cl + OH ?， CH?OH + Cl S2 33N rate = k [CH?Cl][ OH] 3

2 NO ?， 2 NO + O 222 rate = k [NO] 2

(c) Zeroth order reaction:

For the elementary step: A (g) ?， X (g)

dA[]0 ；？kA[]dt[]At []Akdt？；(([]A0o

[A] [A] = kt 0

Rate [A]

[A] Time

slope = 0 slope = k Example of the Zeroth order reaction: Reaction involves solid catalyst.

2 HI ?， H + I22

rate = k

Technique to determine the rate order: (a) Method of initial rate: 2；;Disappearance the cross in the reaction SOaqHaqHOlSOgSs()()()()();?，2?;;2322Decolorization of methyl red in the reaction

；；; 5633BraqBrOaqHaqBraqHOl()()()()();;?，?;322

(b) Method of excess reactant:

Refer the experiment in TAS to find the rate order of the reaction.

CHCOCH (aq) + I (aq) ?， CHCOCHI (aq) + HI (aq) 33232

Reaction rate / page 3

(c) Plotting a graph of log(rate) against log [A] log (1/time)

For a reaction: A + B ?， X + Y

By means of initial rate method, let [B] >> [A] n Assume rate = k [A]

log (rate) = log k + n log [A]

Slope = n

Intercept = log k

log [A]

2. Reaction mechanism:

Reaction mechanism is the term used to describe the detailed step by step pathway of chemical reactions by which reactants

are converted to products.

Consider the following typical mechanism. To begin with, consider the relatively simple reaction of nitrogen oxide with

hydrogen to give nitrogen and water. The reaction is

2 NO (g) + 2 H (g) ?， N (g) + 2 HO (g) 222

The rate is found experimentally as follow:

dNO[]2 ；？kNOH[][]2dt

The stoichiometry is not the same as the molecularity of the reaction. It can be explained by the following mechanism.

(1) 2 NO (g) + H (g) ?， N (g) + HO (g) (slow) 2222

(2) HO (g) + H (g) ?， 2 HO (g) (fast) 2222

Overall: 2 NO (g) + 2 H (g) ?， N (g) + 2 HO (g) 222

The overall reaction rate is determined by the slowest step (1) is called the rate-determining step.

dNO[]2Reaction rate = ；？kNOH[][]2dt

Activated complex I

Energy

Activated complex II

Ea1

Ea 2

N (g) + HO (g) + H (g) 2222

(Intermediate)

2 NO (g) + H (g) H 2

N (g) + 2 HO (g) 22

Reaction Profile

Ex. Consider the reaction A (g) + B (g) ?， AB (g) + B (g) 2

Experimental findings show that the rate of formation of AB is proportional to the concentration of B and the 2

concentration of a certain substance C but does not vary with the concentration of A.

(a) Deduce the rate law for this reaction.

(b) Suggest the reaction mechanism for this reaction.

(c) What might be the function of C? Why is it not written in the overall equation?

Difference between activated complex and intermediate: Activated complex Intermediate

It is meta-stable. It is very unstable.

It may be isolated. It cannot be isolated.

Its structure may be deduced. Its structure is usually unkown.

E. Pressure effect (for gas only)

Pressure Collision frequency Reaction rate

F. Surface area effect (for solid only)

Surface area Collision frequency Reaction rate

G. Temperature effect

(1) Temperature Kinetic energy Collision frequency

(2) Temperature Kinetic energy Number of particles have energy higher than Ea,

the collisions are more effective. Arrhenius equation:

Reaction rate / page 4

EaRT kAe

where k is the rate constant of a rate equation,

Ea is the activation energy of the reaction, 11R is the gas constant (8.314 J mol K),

T is the absolute temperature.

e = 2.7183

EaAltermative form I: lnlnkA？；RT

The activation energy of a reaction can be determined by plotting a graph of ln(rate) against 1/T.

ln(rate)

Ea slope？；R

Ea= R(slope)

Alternative form II: 1/T

Ea At temperature T: ？？？？？？？？？？？？？？？？？？？？？？？？？？？(1) lnlnkA？；11RT1

Ea At temperature T: ？？？？？？？？？？？？？？？？？？？？？？？？？？？(2) lnlnkA？；22RT2

kE111a (1)-(2): ln()()？；；kRTT212

Remarks:

Raising 10C of temperature, the reaction rate becomes nearly double for most chemical reactions. T

10 (By approximation) kk？~221

where k is the rate constant at TC, 22

k is the rate constant at TC, 11

T = T T 21

*Arrhenius equation: EaRT kzpe

H. Catalyst effect

Catalyst gives an alternative pathway requiring less (more) activation energy in a reaction.

Energy

with negative catalyst

(activated complex) without catalyst

with positive catalyst

(product)

(reactant)

Reaction Coordinate

Reaction rate / page 5

Definition of Catalyst:

A substance, which is unchanged chemically at the end of the reaction, but changes the rate of a reaction. Kinds of catalysts:

(a) Positive catalyst: the catalyst increases the reaction rate, e.g. manganese(IV) oxide for hydrogen peroixde. (b) Negative catalyst: the catalyst decreases the reaction rate, e.g. preservatives to prevent spoilage, vitamin C for fruit

browning.

Characteristic of catalyst:

(a) Rate changed depends on the amount of the catalyst.

(b) It is selective to a special reaction.

(c) Mass and chemical properties do not change, but physical appearance may be changed. (d) Small amounts of a certain impurities may oison” a catalyst. Usually reactants must be purified before using a expensive catalyst, e.g. arsenic oxide for platinum in contact process.

(e) Many catalysts are transition metals, e.g. iron for Haber process, nickel for preparation of Town gas from naptha. (f) There are two types of catalysts:

(i) homogeneous catalyst (same physical state with all reactants)

e.g. sulphuric acid is a homogeneous catalyst in esterification.

COOH (l) + HOCHCH (l) ?， CHCOOCHCH (l) + HO (l) CH3233232

the catalyst and all reactants have the same physical state.

(ii) heterogeneous catalyst (different physical states with one of reactant)

e.g. nickel is a heterogeneous catalyst in the hydrogenation of alkene.

HC=CH (g) + HH (g) ?， CHCH (g) 2233

Reactants are gaseous but catalyst is a solid.

(g) Enzyme is an organic catalyst in living cells.

Reaction mechanism of catalytic effect:

(a) Homogeneous catalyst: (Intermediate Formation)

Consider the decomposition of methanoic acid:

HCOOH (aq) ?， HO (l) + CO (g) 2

The reaction is a simple reaction which has one elementary step only, its energy diagram is shown as following.

rate = k[HCOOH] ???????a standard first order reaction

Consider the decomposition of methanoic acid with hydrogen ion as catalyst:

Reaction rate / page 6

The catalysed reaction involves the following mechanism:

O

?fast;;COHCOOHHH;；[]H Step 1: (K

H

O

?

slow;;CO[][]H；?，HHCOHO??；？;Step 2: 2k1

H

fast;;Step 3: []HCOCOH；？?，??;k2;HOverall: HCOOHCOHO?，?;2

Rate equation:

From step 1: Forward reaction rate = Backward reaction rate + Forward reaction rate = k[HCOOH][H] 11+ Backward reaction rate = k[HCOOH] 112++ k[HCOOH][H] = k[HCOOH] 11112;kHCOOH[]112 K？？;kHCOOHH[][]11;; [][][]HCOOHKHCOOHH2;Step 2 is the rate determining step, the overall reaction rate = kHCOOH[]12;= kKHCOOHH[][]1+The reaction rate involves [H] though it is used as a catalyst.

(b) Heterogeneous catalyst: (Adsorption mechanism) Consider the contact process: Pt 2 SO (g) + O (g) ?，? 2 SO (g) 223

O=O O O

O=S ?O O S ? O

Activated site

The reaction involves that the solid catalyst absorbs the reactants SO and O on its surface. If the number of activated sites is 22

limited compared with [SO] and [O], the The reaction rate depends on the number of activated sites on the surface of the 22

solid catalyst.

~ rate = k[activated sites]

= k

The reaction becomes zero order with respect to the concentration of reactants.

Light:

Light is a form of energy. If the wavelength of the light is appropriate, it may cause the breaking of bonds in the original

molecules such that the reaction may then take place quickly. indark..e.g. H (g) + Cl (g) ?，?? no observable change 22h?，?H (g) + Cl (g) 2 HCl (g) explosion 22

Reaction rate / page 7

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