7.4.3   Kinetics

 

Experimental study of the rate of a reaction with variation of reactant concentration.

 

Rates of  reaction

There is a wide diversity in the rates of chemical reactions.  Many take place rapidly e.g. precipitation, explosions, neutralisation, others take place at moderate speeds e.g. zinc + dilute sulphuric acid, and some are very slow e.g. iron rusting.  All chemical processes occur at a definite rate under a particular set of conditions.

 

The rates of chemical reactions can be determined by measuring the decrease in concentration of reactants, or the increase in concentration of products, with time.  There are a number of methods which can be used to follow the progress of a reaction, all of which depend on the detection of some physical change which takes place as the reaction proceeds.  Suitable methods include;

 

1.      Measuring the volume of gas evolved (or consumed) at intervals using a gas syringe e.g. for CaCO3 (s) + HCl(aq)

2.      Measuring the electrical resistance of a solution.

3.      Measuring the change in colour of a solution with a colourimeter.

4.      Removing samples (aliquots) from the reacting mixture and titrating.

 

Measurements of this type do not give the reaction rate directly but only the concentration of reactants or products at a particular time.  The rate of reaction for any particular concentration of reactant can be obtained by drawing a tangent at the appropriate point on the curve of a concentration/ time graph and determining the gradient. 

As the rate of reaction is constantly changing it is usually quoted in terms of the initial reaction rate.

 

 


                        [A]I

 

 

 

Concentration

[A]T

 

 

          

 

 


           T1          T2                                Time

 

Rate of reaction = rate of change of concentration = gradient

 

Gradient = [A]I – [A]T

                   T2 – T1

 

Simple rate equation in the form: rate = k[A]x[B]y with indices either zero or integral; the rate constant and order of reaction. (Integrated rate equations are not required).

 

Rate Equations

The rate of a reaction is measured as the rate at which reactants disappear or the rate at which products appear i.e. the change in concentration per unit time.  The exact relationship between the rate of reaction and the concentrations of reactants and products in any particular reaction can only be determined experimentally.  The rate of reaction can be found by measuring the concentration of reactants or products at regular intervals during the course of the reaction.  A concentration/ time graph can then be plotted.

 

 


[reactant]                                              [product]

 

 

 

 

 

                        Time                                                     Time

 

As the reactants are consumed during the reaction, the reaction rate decreases as the reaction proceeds.  The rate of reaction is directly proportional to the rate of disappearance of reactants.

For a general reaction

aA  +  bB                                       cC

the rate of formation of C (or the rate of disappearance of A and B) is proportional to the powers of the concentrations of A and B.

 

i.e.        Rate = k[A]x[B]y

 

This expression is called the rate equation where

k is the rate constant

x is the order of reaction with respect to A

y is the order of reaction with respect to B

x + y is the overall order of reaction.

 

Example 1

H2(g)  +  I2(g)                   2HI(g)

In this reaction we can see that H2 and I2 will disappear at the same rate but HI will be formed at twice this rate.  From experiment it can be determined that

Rate  =  k[H2]1[I2]1

The reaction is 1st order with respect to hydrogen and 1st order with respect to iodine

and 2nd order overall.

 

 

Units of the rate constant

 

These will be determined by the rate equation and will change for different reactions.

1st order           rate = k[A]

                        mol dm-3 s-1 = k x mol dm-3

k = mol dm-3 s-1  =  s-1 

                              mol dm-3

 

2nd order          rate = k[A] [B]

                        mol dm-3 s-1 = k x mol dm-3  x mol dm-3

                        k =        mol dm-3 s-1           =   mol dm-3 s-1    =    mol-1 dm3 s-1                               

                              mol dm-3  x  mol dm-3          mol2 dm-6

 

Determining the order of reaction

The order of reaction with respect to any reactant can be found by inspection of the experimental data linking concentration of reactants and the rate of reaction.

 

Example 2

For the thermal decomposition of ethanal (CH3CHO) at 800K the following data was determined.

[CH3CHO]

mol dm-3

Rate of decomposition of CH3CHO

mol dm-3 s-1

0.100

9 x 10-7

0.200

3.6 x 10-6

0.400

1.44 x 10-5

 

(a) Deduce the rate equation for the reaction.

When the concentration doubles the rate increases by four times.          

Rate = k[CH3CHO]2

 

(b)    Calculate the rate constant k for this equation at 800K giving its units.

Rate = k[CH3CHO]2

From the table

 

9 x 10-7 = k[0.100]2

k =       9 x 10-7            =          9 x 10-5 mol-1 dm3 s-1

            1 x 10-2

Units

k = mol dm-3 s-1            =          mol-1 dm3 s-1

      mol2 dm-6

 

 

(c)     Calculate the rate of decomposition at 800K at the instant when

[CH3CHO] = 0.25 mol dm-3.

            Rate = k[CH3CHO]2

            = 9 x 10-5 mol-1 dm3 s-1 x (0.25) mol2 dm-6

            = 5.625 x 10-6 mol dm-3 s-1

 

 

 

 

Example 3

2H2(g)  +  2NO(g)                                           2H2O(g)  +  N2(g)

 

Initial [NO]

Initial [H2]

Initial rate

6 x 10-3

1 x 10-3

3.19 x 10-3

6 x 10-3

2 x 10-3

6.36 x 10-3

6 x 10-3

3 x 10-3

9.56 x 10-3

1 x 10-3

6 x 10-3

0.48 x 10-3

2 x 10-3

6 x 10-3

1.92 x 10-3

3 x 10-3

6 x 10-3

4.3x 10-3

 

 

(a)    Deduce the rate equation.

 

 

 

 

 

 

 

 

By inspection

Rate µ [H2]1         

Rate µ [NO]2

Rate = k[NO]2[H2]1

(b)    What are the value and units for the rate constant?

 

Rate = k[NO]2[H2]1

3.19 x 10-3 = k[6 x 10-3]2[1 x 10-3]

k = 3.19 x 10-3        =  3.19 x 10-3 

      [6 x 10-3]2[1 x 10-3]      3.6 x 10-8

=  8.86 x 104

 

Units  =    mol dm-3 s-1      =  mol-2 dm6 s-1

  (mol dm-3)2 (mol dm-3)

 

 

 

 

 

Relationship between the rate equation and mechanism. (Limited to the alkaline hydrolysis of primary and tertiary alkyl halides).

 

Reaction Mechanisms

Chemical equations show the reactants taking part and the products formed but can say nothing about what takes place during this change.  Most reactions take place in a series of distinct steps called a reaction mechanism.

A reaction mechanism can only be worked out from the rate equation for a reaction, not from the stoichiometric equation.

 

Rate Determining Step

Most chemical reactions are more complicated than the equation for the reaction would imply.  For example, a reaction with more than three reacting species is unlikely to take place in a single step, as the probability of  three particles colliding and reacting instantaneously is extremely small.  Only the concentrations of those reactants taking part in the slowest step appear in the rate equation. The rate of the slowest step is the limiting factor for the rate of reaction as a whole and is known as the rate determining step.

If the change

                        A  +  C                                    D

Proceeds by the mechanism

                        A                     B          slow, rate determining step

                        B  +  C             D         fast

The rate at which D is formed will depend on the rate at which A produces B, not on how quickly B reacts with C.  The rate equation would be of the form

                        Rate = k[A]x

 

Molecularity

The term molecularity is used to indicate the number of reacting species taking part in the rate determining step.

If one molecule is involved in bond cleavage during the rate determining step the process is said to be unimolecular.

                        AB                   A  +  B

 

If two molecules are involved the process is bimolecular.

                        AB  +  C                      A  +  BC

 

Molecularity must be a whole number.

 

 

Hydrolysis of alkyl halides

 

             R-X  +    OH-                            R-OH  +  X-  

 

Kinetic studies indicate that there are two mechanisms depending on whether the alkyl halide is primary or tertiary.

 

Primary

By experiment it is found that

Rate = k [R-X] [OH-]

 

The reaction is first order with respect to both the hydroxide and halogenoalkane.

This suggests that the slow rate determining step is bimolecular.

 

CH3CH2Br  +  OH-                              CH3CH2OH  +  Br-

 


CH3                                      CH3             -                            CH3

 


HO-                  C       Br                    HO      C          Br                       HO   C   +    Br-

 


       H      H                                 H       H                                        H    H                                                                                                                   

 

Tertiary

Rate = k[R-OH]

 The reaction is first order with respect to the halogenoalkane and zero order with respect to hydroxide

This suggests that the slow rate determining step is unimolecular.

 

(CH3)3CBr  +  OH-                              (CH3)3COH  +   Br-

 

The following mechanism has been proposed.

Step 1 

               CH3                                                             CH3

 


                                      SLOW

CH3      C        Br                                             CH3     C+        +  Br-

                                rate determining step

 

              CH3                                                              CH3

 

Step 2

 

                CH3                                                               CH3

                                                FAST

CH3         C+      +   OH-                                  CH3       C         OH

 


                CH3                                                                CH3

 

 

 

 

Qualitative effect of temperature on rate constants and its relationship to activation energy.  Simple graphical interpretation in terms of molecular kinetic energies.  Simple collision theory.

 

For any reaction it is found that the rate constant k and the activation energy Ea are related by the equation

                                    k = A x e-Ea/RT

 
Collision theory

Collision theory is based on the idea that reactions occur when particles collide. However not every collision results in reaction.  Reaction will only occur if the collision has a certain minimum value of energy called the activation energy, Ea, which is characteristic for each reaction. Some reactions require that the particles collide with the correct orientation to one another so that particles possess the correct collision geometry.  Such collisions are said to be activated.

 

Reaction rate = collision frequency x fraction of activated particles

 

 

 

 


                                                          Ea

Energy                     reactants

 


                                                                                products

                                                                                   

 

                                                Reaction co-ordinate

 

The observed increase in reaction rate is due to the number of particles which possess sufficient energy to overcome the activation energy barrier Ea.

 

If collision energy < Ea – no reaction

   collision energy  ³ Ea  - reaction occurs

 

 

Qualitative explanation of the effects of concentration, temperature and catalysis on rate of reaction in terms of the distribution of molecular kinetic energies and activation energy, where appropriate

 

 

 

 

 

 


Energy                                           Ea       intermediate

                        reactants

 

 

                                                                                                            products

 

 


                                    Reaction co-ordinate

 

STEP 1            reactants                       intermediate      (SLOW)

This step proceeds slowly as reactant bonds are broken and the activation energy barrier Ea is overcome.  This is the rate determining step which governs the overall rate of reaction.

 

STEP 2            intermediate                  products           (FAST)

This step proceeds rapidly as there is only a small activation energy barrier to overcome.

 

 

Concentration

 

Temperature

The rates of most chemical reactions increase dramatically for only small increases in temperature.  For many gaseous reactions the reaction rate is approximately doubled by a rise in temperature of about 10 oC.  The observed increase in reaction rate with temperature rise is not simply due to an increase in the average velocity of the particles resulting in a greater number of collisions per second. (A 10 oC rise results in an increase in  collision frequency of only about 1-2%). 

The increase in reaction rate is due to the increased number of particles which possess the activation energy. This is because the proportion of activated molecules increases rapidly