Rates of chemical reactions

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					    13       Rates of Chemical
                 Reactions
    13.1   Rates of Chemical Reactions
    13.2   Expressions of Reaction Rates in Terms of
           Rates of Changes in Concentrations of
           Reactants or Products
    13.3   Methods of Measuring Reaction Rates
    13.4   Factors Affecting Reaction Rates


1
    Chemical Kinetics

    A study of
    (1)   reaction rates
    (2)   the factors affecting reaction rates
    (3)   reaction mechanisms
          (the detailed steps involved in reactions)




2
    Explosive reactions
        2H2(g) + O2(g)  2H2O(l)




3
    Vigorous reactions
    2K(s) + 2H2O(l)  2KOH(aq) + H2(g)




               Potassium reacts with
                  water vigorously
4
    Very rapid reactions
                 Formation of insoluble salts
                   +         −
                 Ag (aq) + Cl (aq) AgCl(s)




5
    Very rapid reactions
             Formation of insoluble bases
             Fe3+(aq) + 3OH−(aq) Fe(OH)3(s)




6
    Very rapid reactions
    Acid-alkali neutralization reactions
                      −
         H+(aq)   + OH (aq) H2O(l)




7
    Q.1
              +         −
           Ag (aq) + Cl (aq) AgCl(s)

           Fe3+(aq) + 3OH−(aq) Fe(OH)3(s)
                        −
           H+(aq)   + OH (aq) H2O(l)

     All involve oppositely charged ions




8
    Rapid or moderate reactions
    Displacement reactions of metals : -

     Zn(s) + 2Ag+(aq)  Zn2+(aq) + 2Ag(s)




9
     Rapid or moderate reactions
     Displacement reactions of metals : -

      Zn(s) + 2Ag+(aq)  Zn2+(aq) + 2Ag(s)

     Displacement reactions of halogens : -

      Cl2(aq) + 2Br(aq)  2Cl(aq) + Br2(aq)




10
     Slow reactions
     Fermentation of glucose
     C6H12O6(aq)  2C2H5OH(aq) + 2CO2(g)




11
     Slow reactions

       2MnO4(aq) + 5C2O42(aq) + 16H+(aq)
          2Mn2+(aq) + 10CO2(g) + 8H2O(l)




12
     Very slow reactions
     Rusting of iron
     4Fe(s) + 3O2(g) + 2nH2O(l)  2Fe2O3 · nH2O(s)




13
     Extremely slow reactions
                   +        2+
     CaCO3(s) + 2H (aq)  Ca (aq) + CO2(g) + H2O(l)

         Before corrosion        After corrosion




14
 Two Ways to Express Reaction Rates

     1. Average rate
     2. Instantaneous rate
        (rate at a given instant)




15
     Average rate of reaction
       Total change in amount of a product or a reactant
     
          Total time taken for the change to occur

         Amount is usually expressed in

           Concentration        mol dm−3
           Mass                    g

           Volume               cm3 or dm3

           Pressure               atm

16
Q.2 0.36 g of magnesium reacted with 50.0 cm3
    of 1.0 M hydrochloric acid to give 360 cm3 of
    hydrogen under room conditions.
    The reaction was completely in 90 seconds.

        Mg(s) + 2HCl(aq)  MgCl2(aq) + H2(g)



     (a) Average rate  0.36 g
                                4.0  10 g s
                                         3   1

                         90 s



17
Q.2 0.36 g of magnesium reacted with 50.0 cm3
    of 1.0 M hydrochloric acid to give 360 cm3 of
    hydrogen under room conditions.
    The reaction was completely in 90 seconds.

          Mg(s) + 2HCl(aq)  MgCl2(aq) + H2(g)


                        360 cm3
     (b) Average rate           4.0 cm3 s 1
                          90 s



18
     2.(c) Mg(s) + 2HCl(aq)  MgCl2(aq) + H2(g)
                               0.36 g
        No. of moles of Mg                 0.015 mol
                             24.3 g mol 1
         No. of moles of HCl  1.0 mol dm3  0.0500 dm3  0.0500mol

         Mg is the limiting reactant
         No. of moles of HCl reacted 2  0.015 mol  0.030 mol

         Decrease in concentration of HCl(aq) in 90 s
               0.030 mol
                         0.60 mol dm3
              0.0500 dm3
                        0.60 mol dm-3
         Average rate                 6.7  10-3 mol dm-3 s 1
                            90 s
19
     2.(d) Mg(s) + 2HCl(aq)  MgCl2(aq) + H2(g)

       Rate of reaction      Rate of reaction
                        = 2
        w.r.t. HCl(aq)       w.r.t. MgCl2(aq)

        Increase in concentration of MgCl2(aq) in 90 s
         1
          0.60 mol dm3  0.30 mol dm-3
         2
                       0.30 mol dm-3
        Average rate                 3.3  10-3 mol dm-3 s 1
                           90 s



20
     2. Instantaneous rate
     The rate at a particular instant of the
     reaction is called the instantaneous rate.

     For the chemical reaction
          aA + bB  cC + dD
     Instantaneous rate
        d[A] 1    d[B] 1   d[C] 1   d[D] 1
            ( )       ( )     ( )     ( )
         dt   a     dt b      dt c     dt d
                  [X] = molarity of X
21
     2. Instantaneous rate
     The rate at a particular instant of the
     reaction is called the instantaneous rate.

     For the chemical reaction
            aA + bB  cC + dD
     Instantaneous rate
        d[A] 1    d[B] 1   d[C] 1   d[D] 1
            ( )       ( )     ( )     ( )
         dt   a     dt b      dt c     dt d
     Units : mol dm3 s1, mol dm3 min1, mol dm3 h1…etc.
22
     Graphical Representation of Reaction
     Rates – Rate curves

     A rate curve is a graph plotting the amount of
     a reactant or product against time.




23
     Consider the reaction
              A              B   + C
          (reactant)       (product)




24
 At any time t, the instantaneous rate of the
 reaction equals the slope of the tangent to the
 curve at that point.
 The greater the slope, the higher the rate of the
 reaction.




25
     -ve slope of curve of reactant A
      [A]  with time




26
     +ve slope of curve of product B
      [B]  with time




27
 The rate at t0 is usually the fastest and is called
 the initial rate.
 The curve is the steepest with the greatest
 slope at time t0.




28
 The rate of the reaction gradually  as the
 reaction proceeds.

                           Flat curve
                            reaction completed




29
Q.3
 Concentration of product Z           X + Y  2Z


                                                   C
       (mol dm−3)




                                  B




                              A

30
                                             Time of reaction (min)
                    1 5.4 mol dm3
      Average rate                0.39 mol dm3 min 1
                    2     7 min

                                  X + Y  2Z
 Concentration of product Z



                                               C
       (mol dm−3)




                                  B




                              A

31
                                          Time of reaction (min)
 Concentration of product Z           X + Y  2Z


                                                       C
       (mol dm−3)




                                  B     Instantaneous rate at A
                                         1 (6.0 - 0.0) mol dm 3
                                         
                                         2    (1.6 - 0.0) min
                                         1.9 mol dm3 min1
                              A   1.6


32
                                                   Time of reaction (min)
 Concentration of product Z                   X + Y  2Z


                                    5.1                       C
       (mol dm−3)




                                          B     Instantaneous rate at B
                                                1 (5.1 - 2.7) mol dm 3
                              2.7               
                                                2    (3.0 - 1.0) min
                                                 0.6 mol dm3 min1
                               A

33
                                                          Time of reaction (min)
 Concentration of product Z           X + Y  2Z


                                                      C
       (mol dm−3)




                                  B    Instantaneous rate at C  0




                              A

34
                                                  Time of reaction (min)
Methods of Measuring Reaction Rates

     A. Physical measurements
       1. Continuous measurements
       2 Initial rate measurements
         (Clock reactions)
     B. Chemical measurements (Titration)



35
1. Continuous measurements
     Experiment is done in ONE take.
     The reaction rates are determined by
     measuring continuously a convenient property
     which is directly proportional to the
     concentration of any one reactant or product
     of the reaction mixture.

     Properties to be measured : –
     Gas volume / Gas pressure / Mass /
     Color intensity / Electrical conductivity
36
     1.1 Measurement of large volume changes

       Examples:
       (1) CaCO3(s) + 2HCl(aq)
                  CaCl2(aq) + H2O(l) + CO2(g)

       (2) Zn(s) + H2SO4(aq)
                   ZnSO4(aq) + H2(g)

       (3) 2H2O2(aq)  2H2O(l) + O2(g)
37
     1.1 Measurement of large volume changes




                       Temperature is
                       kept constant




        A typical laboratory set-up for measuring the
38
             volume of gas formed in a reaction
     Zn(s) + H2SO4(aq)  ZnSO4(aq) + H2(g)
     Volume of gas formed (cm3)




                                          dV
                                  slope      rate
                                          dt




39
                                          Time of reaction (min)
     Q.4
     (2) Zn(s) + H2SO4(aq)  ZnSO4(aq) + H2(g)
        H2(g) is sparingly soluble in water while
        CO2 is quite soluble in water.
      Volume
      of CO2
                                Rate 
                Rate 
                             Sigmoid curve



40
     1.2 Measurement of small volume changes
         - Dilatometry

                                Capillary tube




                                  Liquid phase reaction
                                  mixture

     CH3COOH(l) + CH3CH2OH(l)  CH3COOCH2CH3(l) + H2O(l)

41
     1.3 Measurement of mass changes
 CaCO3(s) + 2HCl(aq)  CaCl2(aq) + H2O(l) + CO2(g)




42
 The cotton wool plug is to allow the escape of CO2(g) but
 to prevent loss of acid spray due to spurting.
        stopwatch


                     cotton wool plug


     limestone pieces
                                    measured volume of
     of known mass
                                    standard
                                    hydrochloric acid

                                           electronic
                                           balance
43
      Zn(s) + H2SO4(aq)  ZnSO4(aq) + H2(g)

 CaCO3(s) + 2HCl(aq)  CaCl2(aq) + H2O(l) + CO2(g)
      Which reaction is more suitable to be followed
      by mass measurement ?

       Hydrogen is a very light gas.
      The change in mass of the reaction mixture
      may be very small.
      The electronic balance used in the school
      laboratory may not be sensitive enough to
      detect the small change.
 44
                        mfinal = total mass loss

     Loss of mass (m)                           dm
                                        slope      rate
                                                dt


                                                          time
     mfinal - mt




                            mfinal = mfinal – m0 (∵ m0 = 0)


                                     d[H ]
                             slope         =  rate 2
                                      dt

45                                                        time
     1.4 Colorimetry
     ∵ colour intensity  [coloured species]
                 d(colour intensity)
        rate  
                         dt




46
     H2O2(aq) + 2H+(aq) + 2I(aq)  I2(aq) + 2H2O(l)
     colour intensity  as reaction proceeds
     CH3COCH3(aq) + I2(aq)
          CH3COCH2I(aq) + H+(aq) + I(aq)

     Br2(aq) + HCOOH(aq)
           2H+(aq) + 2Br(aq) + CO2(g)

     2MnO4(aq) + 16H+(aq) + 5C2O42(aq)
          2Mn2+(aq) + 10CO2(g) + 8H2O(l)

     colour intensity  as reaction proceeds
47
48
     cuvettes




                A colorimeter
49
        Yellow
         light




     Yellow      Blue solution
     filter

     Complementary colours



50
                             Red  Cyan




     Pairs of opposite colours are complementary
     colours


51
                             Red  Cyan
                             Green  Magenta




     Pairs of opposite colours are complementary
     colours


52
                             Red  Cyan
                             Green  Magenta
                             Blue  Yellow

                                   CMYK

     Pairs of opposite colours are complementary
     colours


53
     When mixed in the proper proportion,
     complementary colours produce a neutral color
     (grey, white, or black).

54
                 I0       I




     I0 = intensity before absorption
     I = intensity after absorption




55
                           I0        I



                       I                               I 
     % transmittance     100%
                       I            Absorbance  log10  0 
                        0                              I


         If I = I0 ,                If I = 0 ,
         %T = 100%                  %T = 0%
         A = log101 = 0             A  log10  
         zero absorption            complete absorption
56
     A = bC
     Beer’s law




57
     Deviation at higher
 A   concentrations




                A calibration curve is first
                constructed for AC conversion




                                       C

58
 Q.5   [I2]

                      d[I2 ]
              slope          rate
                       dt


                                       time
         A

                       dA
               slope      rate
                       dt


59
                                       time
     1.5 Measurement of electrical
         conductivity

 Na+OH(aq) + CH3COOH(aq)  CH3COONa+(aq) + H2O(l)

        ∵ conducting mobility : OH > CH3COO

        ∴ conductivity  as the rx proceeds




60
     1.5 Measurement of electrical
         conductivity

         2MnO4(aq) + 16H+(aq) + 5C2O42(aq)
          2Mn2+(aq) + 10CO2(g) + 8H2O(l)

         ∵ total number of ions 
         ∴ electrical conductivity  as the rx proceeds




61
     1.6 Measurement of pressure changes

                      d(P )
              rate   T
                       dt
          PT = total pressure of the reaction
               mixture




62
 Q.6
     (i)    2NO(g) + 2H2(g)  N2(g) + 2H2O(g)
     (ii)   3H2(g) + N2(g)  2NH3(g)

     At fixed V and T, PT  n
     In both reactions,
     n  as the reactions proceed
      PT  as the reactions proceed


63
suction
flask

          dilute hydrochloric acid         pressure sensor



                        magnesium ribbon
                                             to data-logger
                                             interface and computer


          Mg(s) + 2HCl(aq)  MgCl2(aq) + H2(g)

 64
     A(g) + B(g)  products




65
     A chemical clock is a complex mixture of
     reacting chemical compounds in which the
     concentration of one or more components
     exhibits periodic changes.
     In cases where one of the reagents has a
     visible color, crossing a concentration
     threshold can lead to an abrupt color change in
     a reproducible time lapse.




66
     2. Initial Rate Measurements-Clock Reactions

     1. A set of experiments is done in which all
        reaction conditions but one are kept constant.
          2–           +
      S2O3 (aq)    + 2H (aq)  SO2(aq) + H2O(l) + S(s)

      Experiment     [S2O32(aq)] / M    [H+(aq)] / M
           1               0.10               1
           2               0.08               1
           3               0.04               1
           4               0.02               1

67
     2. Initial Rate Measurements-Clock Reactions
         2–          +
     S2O3 (aq)   + 2H (aq)  SO2(aq) + H2O(l) + S(s)
                                             yellow
                                           precipitate
     2. The time taken for the reaction to arrive at a
        particular point at the early stage of the
        reaction is measured.




68
 The beaker containing the reaction mixture is
 placed over a cross marked on a white tile.

69
 As more sulphur forms, the reaction mixture
 becomes more cloudy.
70
     The cross becomes more and more difficult to
     see and finally disappears.

71
           2–        +
     S2O3 (aq) + 2H (aq)  SO2(aq) + H2O(l) + S(s)
                                                yellow
                                              precipitate
 Average rate in the early stage
         Amount of S required to blot out the mark
     =
            Time taken to blot out the mark

     Since the amount of S required to blot out
     the mark is a constant,

     Average                  1
      rate     time taken to ‘blot out’ the mark
72
     Average                  1
      rate     time taken to ‘blot out’ the mark

 The average rate of reaction is inversely
 proportional to the time taken to ‘blot out’ the
 mark.

 The faster is the reaction, the shorter is the
 time taken for the mark to disappear.


73
                                 dS
              slope  initial rate 
                                 dt
                                          S
                   slope  average rate 
                                          t

amount of S


                           If S and t are small(early stage)

                                  dS ΔS
                                    
                                  dt Δt

                                                      time

74
     dS ΔS
            Since S is a constant
     dt Δt
     dS ΔS 1
         
     dt Δt t


75
     Initial rate  k[S2O32(aq)]x[H+(aq)]y

         Since HCl is in large excess,
         [H+(aq)]y  constant at the early stage

     Initial rate  k[S2O32(aq)]x[H+(aq)]y  k’[S2O32(aq)]x

                      ΔS 1
      Initial rate    
                      Δt t
        1          2
           k [S2O3 (aq)]x
             ''

        t

76
                                       Time taken (t)
             [S2O32(aq)]   [H+(aq)]                    1
     Expt.                              to mask the         / s1
                 (M)          (M)
                                          mark / s      t
       1        0.10           1            10

      2         0.08           1            13

      3         0.04           1            25

      4         0.02           1            50



77
 Q.7
       1
       t


             1 ''       2
                k [S2O3 (aq)] x

             t
           Linear  x = 1


                      [S2O32(aq)]
78
     Other Examples of Clock Reactions : -

     5I(aq) + IO3(aq) + 6H+(aq)  3I2(aq) + 3H2O(l)

     Small and fixed amounts of S2O32(aq) and starch are
     added to the reaction mixtures in all runs.
           I2(aq) + 2S2O32(aq)  2I(aq) + S4O62(aq)
           (fixed) (fixed)
           I2(aq)   +   starch  deep blue complex
           (excess)     (fixed)
     Time taken for the reaction mixture to turn deep blue
     is measured.
79
      Other Examples of Clock Reactions : -

     5I(aq) + IO3(aq) + 6H+(aq)  3I2(aq) + 3H2O(l)

     I2(aq) + 2S2O32(aq)  2I(aq) + S4O62(aq)
     (fixed) (fixed)
     I2(aq)   +   starch  deep blue complex
     (excess)     (fixed)

     By changing the concentration of any one of the
     reactants, deep blue colour will appear in different
     time lapses  a chemical clock !
                                        Halloween clock
80
      Other Examples of Clock Reactions : -

     5Br(aq) + BrO3(aq) + 6H+(aq)  3Br2(aq) + 3H2O(l)
         OH                            OH

                                 Br         Br


                  +     3Br2

      (fixed)          (fixed)
                                       Br



      Br2     +   methyl red  colourless
     (excess)         (fixed)


81
     Advantages of physical measurements

     1. Suitable for fast reactions.
     2. Small sample size
     3. More accurate than chemical method
        (titration)
     4. No interruption  continuous measurements
     5. Can be automated.



82
     Disadvantages of physical measurements

     1. More sophisticated
     2. More expensive
     3. More specific – only suit a limited number of
        reactions.




83
     B. Chemical Measurements (Titration Methods)


     1. Start a reaction with all reaction conditions
        but one fixed.
     2. Withdraw and quench fixed amounts of the
        reaction mixture at different times.




84
Quenching methods:
                           Temperature 
• Cooling the reaction mixture rapidly in ice.

• Diluting the reaction mixture with a
  sufficient amount of cold water or an
  appropriate solvent. Concentration 
• Removing one of the reactants or the
  catalyst (if any) by adding another
  reagent.
85
     B. Chemical Measurements (Titration Methods)


     1. Start a reaction with all reaction conditions
        but one fixed.
     2. Withdraw and quench fixed amounts of the
        reaction mixture at different times.
     3. Titrate the quenched samples to determine
        the concentration of one of the reactants or
        products.


86
                       H+ as catalyst
 CH3COCH3 + I2                          CH3COCH2I + HI

     Q.8

     The reaction is quenched by adding to it NaHCO3(aq)
     that removes the catalyst.
           HCO3(aq) + H+(aq)  H2O(l) + CO2(g)




87
                        H+ as catalyst
 CH3COCH3 + I2                           CH3COCH2I + HI

     Q.9

     Titrated with standard solution of Na2S2O3(aq) using
     starch as indicator (added when the end point is near)

                2                       2          
           2S2O3 (aq) + I2(aq)  S4O6 (aq) + 2I (aq)

     Colour change at the end point : deep blue to colourless




88
                        H+ as catalyst
 CH3COCH3 + I2                           CH3COCH2I + HI

     Q.10

      The excess S2O32(aq) would react with H+ to give a
      cloudy mixture with a pungent smell.

       S2O32(aq) + 2H+(aq)  S(s) + SO2(g) + H2O(l)




89
     Advantages of titrimetric method

     1. Only simple apparatus are required.
     2. Can be applied to a great variety of slow
        reactions.




90
     Disadvantages of physical measurements

     1. Not suitable for fast reactions.
       It takes time to withdraw samples and
       perform titration.
     2. Reactions are disturbed – NOT continuous
     3. Time consuming – NOT automated




91
     Factors Affecting
      Reaction Rates


92
     Collision Theory


                              No reaction

      Sufficient K.E.
      Incorrect orientation




93
     Collision Theory


                            No reaction

      Correct orientation
      Insufficient K.E.




94
     Collision Theory




     Sufficient K.E.
     Correct orientation

              Effective collision
95
     Collision Theory


                  Activation energy




     Bond breaking and bond forming occur at the
     same time
     Ea < B.E.(s) of the bond(s) to be broken

96
     Collision Theory


                  Activation energy




      Higher Ea
       more K.E. required for effective collision
       slower reaction

97
     Collision Theory


                  Activation energy




      Lower Ea
       less K.E. required for effective collision
       faster reaction

98
     Collision Theory


                  Activation energy




      Rate of reaction depends on Ea which in turn
      depends on the nature of reactants.
      E.g. K is more reactive than Mg

99
 Factors Affecting Reaction Rates

      concentration    particle size

       pressure         catalyst

      temperature         light



100
 Effect of concentration
      •   e.g. Reaction between Mg and HCl




101
 Effect of concentration

                           (a) 2.0 M HCl
                           (b) 1.0 M HCl
                           (c) 0.5 M HCl
                           Reaction rate:
                           (a) > (b) > (c)


102
 Effect of concentration

                     Time for reaction to
                     complete: t1 < t2 < t3

                     Higher [HCl(aq)]
                      Faster reaction




103
      [X] 
       Reactant particles are more crowded
       Collision frequency 
       Number of effective collisions 
       Reaction rate 




104
 For the reaction    aA + bB  cC + dD


               Rate  k[A]x[B]y
      where x and y are the orders of reaction
      with respect to A and B
      k is the rate constant
      units  mol dm3 s1/(mol dm3)x+y




105
 For the reaction    aA + bB  cC + dD


               Rate  k[A]x[B]y
      x and y can be  integers or fractional

      x  y is the overall order of reaction.

      x, y can ONLY be determined experimentally.




106
 Effect of pressure
 Only applicable to reactions involving gaseous
 reactants.




107
      Pressure 
       Reactant particles are more crowded
       Collision frequency 
       No. of effective collisions 
       Rate of reaction 




108
  Effect of temperature

      Applicable to ALL reactions




109
      T
       K.E. of particles 
       Collision frequency  (minor effect) and
        No. of particles with K.E. > Ea  (major effect)
       No. of effective collisions 
       Rate of reaction 




110
Rate

       Rate of reaction 
       exponentially with temperature
                           Ea
             Rate  e     RT


       In general, a 10oC  in T
       doubles the rate.


         T / C
111
      Effect of particle size

      For a fixed volume of solid,
      Smaller particle size  greater surface area




112
      CaCO3(aq) + 2H+(excess)  CaCl2(aq) + H2O(l) + CO2(g)


                                        Rate involving
                                        powdered solid
                                        reactant is higher


                                        Reason: higher
                                        chance of contact
                                        between reactant
                                        particles

113
      Q.11




             0.5 g powder
                       0.5 g granule




114
      Effect of Catalyst
      A catalyst is a substance that alters the rate
      of a chemical reaction by providing an
      alternative reaction pathway with a different
      activation energy.
      A positive catalyst speeds up a reaction by
      providing an alternative reaction pathway
      with a lower Ea.

      A negative catalyst slows down a reaction
      by providing an alternative reaction pathway
      with a higher Ea.
115
      Effect of Catalyst

      Catalysts remain chemically unchanged at the
      end of reactions.




116
                 MnO2 as catalyst
      H2O2(aq)                      2H2O(l) + O2(g)

            Physical measurement




117
                                    MnO2 as catalyst
                         H2O2(aq)
      Volume of gas formed (cm3)                       2H2O(l) + O2(g)




118                                                Time of reaction (min)
      Titrimetric method (Q.12)
                 MnO2 as catalyst
      H2O2(aq)                      2H2O(l) + O2(g)

      Pipette samples at different times
      Remove MnO2(s) by filtration
      Titrate with MnO4(aq)/H+(aq)

      5H2O2(aq) + 2MnO4(aq) + 6H+(aq)
                  2Mn2+(aq) + 8H2O(l) + 5O2(g)
119
       Q.13


[H2O2]


              Without MnO2




              With MnO2


                 time
 120
      Effect of light

      Light with specific frequency (E  h) can
      provide sufficient energy to break a particular
      chemical bond in a reactant leading to a
      photochemical reaction.

                      h
        Br – Br                Br + Br
        C6H14 + Br  C6H13 + HBr
                       C6H13Br…
121
      Autocatalysis

      Catalysis in which the product acts as the
      catalyst of the reaction

      2MnO4(aq) + 16H+(aq) + 5C2O42(aq)
                  2Mn2+(aq) + 10CO2(g) + 8H2O(l)

      CH3COCH3(aq) + I2(aq)
                  CH3COCH2I(aq) + H+(aq) + I(aq)

122
      Q.14


[MnO4]      Rate 


                      Sigmoid curve

                      Rate 




                               time
123
      The END




124
13.1 Rates of Chemical Reactions (SB p.5)

                                                      Back


        In a chemical reaction, a total of 0.18 g of carbon
        dioxide gas is given out in 1 minute at room
        temperature. What is its average rate in mol s–1 for that
        time interval?
                                                                  Answer
                                             0.18 g
         Number of moles of CO2 =
                                    (12.0  16.0  2) g mol - 1

                                = 0.0041 mol
                        0.0041mol
         Average rate =
                           60 s

                     = 6.83 × 10–5 mol s–1
  125
13.1 Rates of Chemical Reactions (SB p.5)




        In the uncatalyzed decomposition of hydrogen
        peroxide solution into water and oxygen at room
        conditions, the volume of oxygen given out in 20
        hours is 5 cm3. What is its average rate in mol s–1 for
        that time interval?
             2H2O2(l)  2H2O(l) + O2(g)
        (Molar volume of gas at room temperature and
        pressure= 24.0 dm3 mol–1)
                                                  Answer

  126
13.1 Rates of Chemical Reactions (SB p.5)

                                               Back




                                         5 cm3
          Number of moles of O2   =
                                    24 000 cm3 mol 1
                                  = 2.08 × 10–4 mol
                                   2.08  10 -4 mol
                    Average rate =
                                   (20  60  60) s
                                  = 2.89 × 10–9 mol s–1




  127
13.1 Rates of Chemical Reactions (SB p.6)




        The change in concentration
        of reactant X in a chemical
        reaction is illustrated in the
        graph on the right.




  128
13.1 Rates of Chemical Reactions (SB p.6)




        With the use of the graph, calculate
        (a)   the initial rate of the reaction;
        (b)   the average rate for the time interval from
              the 1st to the 2nd minute;
        (c)   the instantaneous rate at the 3rd minute.

        (Give your answers in mol dm–3 min–1.)

                                                 Answer

  129
13.1 Rates of Chemical Reactions (SB p.6)




                                        (a) Initial rate
                                            =   Slope of the tangent
                                                to the curve at t0
                                            = (0.100  0.160) mol dm 3
                                                     (1.2  0) min

                                            = -0.05 mol dm-3 min-1




  130
13.1 Rates of Chemical Reactions (SB p.6)




                                        (b) Average rate

                                              (0.080  0.110) mol dm 3
                                            =
                                                     (2  1) min


                                            = -0.03 mol dm-3 min-1




  131
13.1 Rates of Chemical Reactions (SB p.6)

                                                Back


                                        (c) Instantaneous rate at the
                                            3rd minute
                                            =    Slope of the tangent to
                                                 the curve at the 3rd
                                                 minute
                                            = (0.046  0.077) mol dm
                                                                     3


                                                    (3.5  2) min

                                            = -0.021 mol dm-3 min-1




  132
13.1 Rates of Chemical Reactions (SB p.8)




  (a) In the hydrolysis of an ester at a constant temperature
      of 398 K, the concentration of the ester decreases from
      1 mol dm–3 to 0.75 mol dm–3 in 4 minutes. What is its
      average rate in mol dm–3 s–1 for that time interval?

                                                  Answer
        (a) Average rate at 398 K
            = –(1 – 0.75) mol dm-3  (4  60) s
            = –0.001 04 mol dm-3 s-1




  133
13.1 Rates of Chemical Reactions (SB p.8)




  (b) The graph on the right shows the
      change in concentration of
      a reactant in a chemical reaction.




  134
13.1 Rates of Chemical Reactions (SB p.8)




 With the use of the graph above, calculate
 (i)    the initial rate of the reaction;
 (ii)   the average rate for the time interval from the 20th to
        the 30th second;
 (iii) the instantaneous rate at the 10th second.

                                                    Answer


  135
13.1 Rates of Chemical Reactions (SB p.8)

                                                         Back


                                                    -3
        (i)   Initial rate = (0.02 - 0.01) mol dm
                                    (0  10) s
                          = -1  10-3 mol dm-3 s-1

        (ii) Average rate = (0.009 - 0.006) mol dm -3
                                  (20  30) s
                            = -3  10-4 mol dm-3 s-1

                                   (0.018 - 0.013) mol dm -3
        (iii) Instantaneous rate =
                                           (0  10) s
                                  = -5  10-4 mol dm-3 s-1

  136
13.2 Expressions of Reactions Rates in Terms of Rates of Changes in
     Concentrations of Reactants or Products (SB p.10)

                                                Back

        Haemoglobin (Hb) binds with carbon monoxide
        according to the following equation:
                        4Hb + 3CO  Hb4(CO)3
        Express the rate of the reaction in terms of the rate of
        change in concentration of any one of the reactants or
        the product.
    The rate of the reaction is expressed as:
                                                          Answer
                      d [Hb 4 (CO)3 ]   1 d [Hb]   1 d [CO]
             Rate                             
                            dt          4   dt     3    dt

  137
13.2 Expressions of Reactions Rates in Terms of Rates of Changes in
     Concentrations of Reactants or Products (SB p.10)

                                                     Back

   Express the rate of the following reaction in terms of the
   rate of change in concentration of any one of the reactants
   or the product.
                       2H2(g) + O2(g)  2H2O(l)
                                                                   Answer

                    1 d [H2 O(l)]    1 d [H2 (g)]    d [O 2 (g)]
             Rate =                             
                    2     dt         2 dt                dt




  138
13.3 Methods of Measuring Reaction Rates (SB p.11)




        Alkaline hydrolysis of ethyl ethanoate (an ester) using
        sodium hydroxide solution is represented by the
        following equation:
        CH3CO2CH2CH3(l) + NaOH(aq)
                      CH3CO2Na(aq) + CH3CH2OH(aq)
        The rate of the reaction can be followed by titrating
        small volumes of the reaction mixture with standard
        dilute hydrochloric acid at successive five-minute
        intervals.


  139
13.3 Methods of Measuring Reaction Rates (SB p.11)




        (a) Suggest a method to quench the reaction mixture
            so that the concentration of sodium hydroxide
            solution can be determined accurately. Explain
            briefly why this method can be used.
                                                               Answer
          (a) The reaction mixture can be quenched by pipetting a
              sample of the reaction mixture into a conical flask
              containing ice water. The cooling and dilution of the
              reaction mixture decrease the reaction rate sufficiently for
              chemical analysis.


  140
13.3 Methods of Measuring Reaction Rates (SB p.11)




        (b) Explain why the change in concentration of
            sodium hydroxide solution but not that of ethyl
            ethanoate is measured in order to determine the
            rate of the above reaction.
                                                            Answer
         (b) Sodium hydroxide is a strong alkali that reacts with strong
             mineral acids almost instantaneously. Therefore, the
             titration of sodium hydroxide solution and dilute
             hydrochloric acid provides accurate experimental results.



  141
13.3 Methods of Measuring Reaction Rates (SB p.11)

                                                          Answer
        (c) Explain which option, A or B, is a reasonable set of
            experimental results for the above titration.
                                Option A
            Time after mixing (min) Volume of HCl added
                                        at the end point (cm3)
                       5                          10
                       10                            8
                                 Option B
            Time after mixing (min)     Volume of HCl added
                                        at the end point (cm3)
                        5                            8
                       10                            10
  142
13.3 Methods of Measuring Reaction Rates (SB p.11)




         (c) Sodium hydroxide is a reactant of the hydrolysis. As the
             reaction proceeds, the concentration of sodium hydroxide
             in the reaction mixture decreases with time, and hence
             the amount of dilute hydrochloric acid used in the titration.
             Thus, option A is a reasonable set of experimental results.




  143
13.3 Methods of Measuring Reaction Rates (SB p.11)




        (d) Name a suitable indicator for the titration.

                                                       Answer
           (d) Methyl orange / Phenophthalein




                                                Back



  144
13.3 Methods of Measuring Reaction Rates (SB p.13)




        A student recorded the following experimental results
        for the reaction of zinc and dilute hydrochloric acid.
                Zn(s) + 2HCl(aq)  ZnCl2(aq) + H2(g)

        Time    0.0   1.0 2.0 3.0    4.0   5.0       6.0 7.0 8.0    9.0
        (min)
   Volume        0    15   26   33    38    40       41   42   42   42
   of H2(g)
  produced
    (cm3)

  145
13.3 Methods of Measuring Reaction Rates (SB p.13)




        (a) Plot a graph of volume of hydrogen gas produced
            against time.
                                                     Answer
           (a)




  146
13.3 Methods of Measuring Reaction Rates (SB p.13)




        (b) Describe the change in the rate of the reaction
            using your graph in (a).
                                                              Answer
            (b) As shown in the graph in (a), the volume of hydrogen
                gas given out at the beginning of the reaction (e.g. in
                the time interval between the 1st and the 2nd minute) is
                greater than that near the end of the reaction (e.g. in
                the time interval between the 6th and the 7th minute).
                Therefore, the rate of the reaction decreases with time.




  147
13.3 Methods of Measuring Reaction Rates (SB p.13)




        (c) Explain how you can measure the initial rate of the
            reaction graphically.
                                                               Answer

           (c) The initial rate can be found by determining the slope of
               the tangent to the curve at time zero.




  148
13.3 Methods of Measuring Reaction Rates (SB p.13)

                                                   Back

        (d) Determine graphically the rate of the reaction at
            the 5th minute. State the unit.
                                                              Answer
           (d) From the graph in (a),
               rate of reaction
               = slope of the tangent to the curve at the 5 minute

                 (46  34) cm3
               =
                   (8  2) min
               = 2 cm3 min-1


  149
13.3 Methods of Measuring Reaction Rates (SB p.15)

                                                Back


  Suggest an experimental method for determining the rate
  of each of the following reactions:
  (a) S2O82–(aq) + 2I–(aq)  2SO42–(aq) + I2( aq)
  (b) CH3COOCH3(aq) + I2(aq)
                                    CH3COOCH2I(aq) + HI(aq)
  (c) 2MnO4–(aq) + 5C2O42–(aq) + 16H+(aq)
                   2Mn2+(aq) + 10CO2(g) + 8H2O(l) + H+(aq)

     (a) Colorimetric measurement / titration          Answer
     (b) Colorimetric measurement
  150(c) Colorimetric mesurement / titration
13.4 Factors Affecting Reaction Rates (SB p.17)




             Explain why sawdust burns explosively in pure
                       oxygen but slowly in air.
                                                         Answer
         A higher concentration of oxygen increases
         the rate of combustion.



                                                  Back



  151
13.4 Factors Affecting Reaction Rates (SB p.21)




  (a) List THREE factors that affect the rate of a chemical
      reaction.
                                                       Answer
         (a) Concentration of reactants / pressure /
             temperature / surface area / catalyst /
             light (any 3)




  152
13.4 Factors Affecting Reaction Rates (SB p.21)




  (b) The figure below shows the laboratory set-up for
      measuring the change in mass of the reaction mixture
      with time in the course of the reaction:
        CaCO3(s) + 2HCl(aq)  CaCl2(aq) + H2O(l) + CO2(g)




  153
13.4 Factors Affecting Reaction Rates (SB p.21)




  A certain mass of calcium carbonate was added to 50 cm3 of
  2.0 M hydrochloric acid at 20°C. Carbon dioxide was
  allowed to escape and the mass of the reaction mixture was
  measured at regular time intervals. The results were
  expressed as the loss of mass with respect to time. The
  experiment was carried out with one change of condition at
  a time:
  (i) using 1.0 M hydrochloric acid in place of 2.0 M
      hydrochloric acid.
  (ii) carrying out the reaction at 30°C.
  (iii) using powdered calcium carbonate of the same mass.
  154

				
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