John A. Schreifels

1
Chapter 14

• Rates of Reaction

2
Overview

• Reaction Rates
• Definition of Reaction Rates
• Experimental Determination of Rate
• Dependence of Rate on Concentration
• Change of Concentration with Time
• Temperature and Rate Collision and
  Transition-State Theories.
• Arrhenius Equation
• Reaction Mechanisms
• Elementary Reactions
• Rate Law and the Mechanism
• Catalysis

3
Reaction Rates

• Deal with the speed of a reaction and controlled
  by
• Proportional to concentrations of reactants
• Proportional to catalyst concentration catalyst
  a substance that increases the rate of reaction
  without being consumed in the reaction.
• Larger surface area of catalyst means higher
  reaction rate (more sites for reaction to take
  place).
• Temperature Higher temperature of reaction means
  faster.

4
Definition of Reaction Rate

• Reaction rate increase in concentration of
  product of a reaction as a function of time or
  decrease in concentration of reaction as a
  function of time.
• Thus the rate of a reaction is

• Rates are expressed as positive numbers. For the
  reaction in the graph we have

5
Reaction Rates and Stoichiometry

• A B ? C RC RA RB.
• A 2B ? 3C
• E.g.Calculate the rate of decomposition of HI in
  the reaction 2HI(g) ? H2(g) I2(g). Given
  After a reaction time of 100 secs. the
  concentration of HI decreased by 0.500 M.
• For the general reaction aA bB ? cC dD
• E.g. For the reaction 2A 3B ? 4C 2D
  determine the rates of B, C and D if the rate of
  consumption of A is 0.100 M/s.

6
Rate Laws and Reaction Order

• Rate Law an equation that tells how the
  reaction rate depends on the concentration of
  each reaction.
• Reaction order the value of the exponents of
  concentration terms in the rate law.
• For the reaction aA bB ? cC dD, the initial
  rate of reaction is related to the concentration
  of reactants.
• Varying the initial concentration of one reactant
  at a time produces rates, which will lead to the
  order of each reactant.
• The rate law describes this dependence R
  kAmBn where k rate constant and m and n are
  the orders of A and B respectively.
• m 1 (A varied, B held constant) gives R
  kA. Rate is directly proportional to A.
  Doubling A doubles R
• m 2 (A varied, B held constant) gives R
  kA2. The rate is proportional to A2.
  Doubling A quadruples R.
• E.g. Determine order of each reactant
• HCOOH(aq) Br2(aq) ? 2H(aq) 2Br?(aq)
  CO2(g) R kBr2
• E.g. The formation of HI gas has the following
  rate law R kH2I2. What is the order of
  each reactant?

7
Experimental Determination of a Rate Law First
Order

• Varying initial concentration of reactants
  changes the initial rate (usually all but one
  held constant) like one with two unknowns.
• Initial rate is the initial slope of the graph
  shown.
• As the initial concentration of that compound
  increases so does the rate.
• Initial rate vs. Ao plotted.
• If straight line then reaction is first order and
  slope is rate constant.
• Second order rate law determined in like manner.

8
Rate Law for All Reactants

• Order for all components done same way.
• E.g. Determine the reaction order for each
  reactant from the table.
• (aq)5Br?(aq)6H(aq)?3Br2(aq)3H2O(l)
  

Eg. 2 Determine the reaction orders for the
reaction indicated from the data provided. A
2B C ? Products.
9
Integrated Rate Law FirstOrder Reaction

• For a first order reaction, Rate ??A/?t
  kA or RA ?dA/dt kA.
• Use of calculus leads to
  or
• Allows one to calculate the A at any time after
  the start of the reaction.
• E.g. Calculate the concentration of N2O
  remaining after its decomposition according to
  2N2O(g) ? 2N2(g) O2(g) if its rate is first
  order and N2Oo 0.20M, k 3.4 s?1 and T
  780C. Find its concentration after 100 ms.
• Linearized forms
  or
• Plot lnA vs t.
• Slope of straight line leads to rate constant, k.
  
• E.g. When cyclohexane(let's call it C) is heated
  to 500 oC, it changes into propene. Using the
  following data from one experiment, determine the
  first order rate constant.

10
Half-Life First Order Reaction

• Half-life of First order reaction, t1/2
  0.693/k. the time required for the concentration
  of the reactant to change to ½ of its initial
  value.
• i.e. at t1/2 , A ½ Ao
• E.g. For the decomposition of N2O5 at 65 C, the
  half-life was found to be 130 s. Determine the
  rate constant for this reaction.

• For n half-lives t nt1/2 A 2-n Ao

11
SecondOrder Reactions Integrated Rate Law

• Rate law R kA2 and the integrated rate
  equation is
• Plot of vs. t gives a straight line with a
  slope of k.
• Half-life is
• E.g. At 330C, the rate constant for the
  decomposition of NO2 is 0.775 L/(mols). If the
  reaction is second-order, what is the
  concentration of NO2 after 2.5x102 s if the
  starting of concentration was 0.050 M?

12
Reaction Mechanisms

• Give insight into sequence of reaction events
  leading to product (reaction mechanism).
• Each of the steps leading to product is called an
  elementary reaction or elementary step.
• Consider the reaction of nitrogen dioxide with
  carbon dioxide which is second order on NO2
• NO2(g) CO(g) ? NO(g) CO2(g) Rate kNO22.
  
• Rate law suggests at least two steps.
• A proposed mechanism for this reaction involves
  two steps.
• NO3 is a reaction intermediate a substance that
  is produced and consumed in the reaction so that
  none is detected when the reaction is finished.
• The elementary reactions are often described in
  terms of their molecularity.
• Unimolecular One particle in elementary.
• Bimolecular 2 particles and
• Termolecular 3 particles

13
Rate Laws and Reaction Mechanisms

• Overall reaction order is often determined by the
  rate determining step.
• Use rate law of limiting step No intermediates!

2NO2(g) ? NO3(g) NO(g), R1 k1NO22 Slow
NO3(g) CO(g) ?NO2(g) CO2(g) R2 k2NO3CO Fast
NO2 CO ? NO CO2 Robs kNO22
E.g. Determine the rate law for the following
mechanism
14
Reaction Rates and Temperature The Arrhenius
Equation

• Rate (rate constant) increases exponentially with
  temperature.
• Collision theory indicates collisions every 10?9s
  10?10s at 25C and 1 atm.
• i.e. only a small fraction of the colliding
  molecules actually react.
• Collision theory assumes
• Reaction can only occur if collision takes place.
  
• Colliding molecules must have correct orientation
  and energy.
• Collision rate is directing proportional to the
  concentration of colliding particles.
• A B ? Products Rc ZAB
• 2A B ? Products Rc ZA2B, etc.
• Only a fraction of the molecules, p (steric
  factor), have correct orientation multiply
  collision rate by p.
• Particle must have enough energy. Fraction of
  those with correct energy follows Boltzmann
  equation where Ea
  activation energy, R gas constant and T temp.
  (Kelvin scale only please).
• This gives k Zpf

15
Transition State Theory

• Explains the reaction resulting from the
  collision of molecules to form an activated
  complex.
• Activated complex is unstable and can break to
  form product.

16
The Arrhenius Equation

• Summary
  where A frequency factor.
• Linear form .
• Plot ln k vs. 1/T the slope gives Ea/R.
• E.g. determine the activation energy for the
  decomposition of N2O5 from the temperature
  dependence of the rate constant.
• Two point equation sometimes used also
• E.g.2 Determine the rate constant at 35C for
  the hydrolysis of sucrose, given that at 37C it
  is 0.91mL/(molsec). The activation energy of
  this reaction is 108 kJ/mol.
• Rate constant increases when T2gtT1

k, s?1 Temp., C Temp., K
4.8x10?4 45.0 318.15
8.8x10?4 50.0 323.15
1.6x10?3 55.0 328.15
2.8x10?3 60.0 333.15
17
Catalysis

• Catalysts a substance that increases the rate of
  a reaction without being consumed in the
  reaction.
• Catalyst provides an alternative pathway from
  reactant to product which has a rate determining
  step that has a lower activation energy than that
  of the original pathway.
• E.g. Hydrogen peroxide and bromine
• 2H2O2(aq) ? 2H2O(l) O2(g).
• Mechanism is believed to be

1. Br2 red Br2(aq) H2O2(aq) ? 2Br?(aq) 2H(aq)O2(g)
2. Br? oxid 2H(aq)2Br?(aq)H2O2(aq) ? Br2(aq) 2H2O(l).
Overall 2H2O2(aq) ? 2H2O(l)O2(g)

• Notice that bromine is not consumed, even though
  it has participated in the reaction.

18
Homogeneous and Heterogeneous Catalysts

• Homogeneous catalyst catalyst existing in the
  same phase as the reactants.
• Heterogeneous catalysis catalyst existing in a
  different phase than the reactants.
• The previous section gave an example of a
  homogeneous catalyst since the catalyst Br2 was
  in the same phase as the hydrogen peroxide.
• The catalytic hydrogenation of ethylene is an
  example of a heterogeneous catalysis reaction
• ENZYMES (biological catalysts)
• They are proteins (large organic molecules that
  are composed of amino acids).
• Slotlike active sites. The molecule fits into
  this slot and reaction proceeds. Poisons can
  block active site or reduce activity by
  distorting the active site.

19
Steric Factor

• Molecules must have the correct orientation
  before a reaction can take place.

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