reaction rate

• The concentration of reactants is another factor that affects reaction rate. Higher concentrations of reactants usually result in a faster reaction rate.
• Reaction rate: Changes in concentrations of reactants (or products) as a function of time
• Differential rate equation/ rate expression shows the relationship between the rate of disappearance of reactants and formation of products
• Rate law (@ rate equation): An equation that relates the rate of a reaction to the rate constant and the concentrations of the reactants raised to some powers
• Order of reaction: the sum of all the index or exponent or power of the reactants involved in the rate law
• Half-life: Time required for the concentration of a reactant to decrease to half of its initial concentration
• Collision theory:

  • Molecules of reactants must collide in order to form products
  • Products are formed only when effective collisions occur between molecules
• Effective collisions:

  • The colliding molecules must have a total kinetic energy equal to or greater than the activation energy, E a
  • Molecules collisions occur at the correct orientation
• Arrhenius equation: k = Ae^(-Ea/RT)
• Transition state theory: Explains the activation energy, E a as the energy required by reactant molecules to form the activated complex (transition state)
• Activated complex: temporary species formed by the reactant molecules as a result of the collision before they form the products
• • When temperature increases, average kinetic energy gain by molecules increases, number of molecules with energy equal or greater than Ea increases, frequency of effective collision between molecules increases, reaction rate increases
  • Catalyst:
  • When catalyst is added, provided alternative pathway which lowers Ea, frequency of effective collision between particles increases, reaction rate increases
  • Particle size:
• • Size of reacting particles decrease, total surface area exposed for reaction increases, more collisions between particles, frequency of effective collision increases, reaction rate increases
• Factors affecting reaction rate:

  • Concentration or pressure:
  • Concentration of reactant increases, more particles in the same volume, more collision between particles, frequency of effective collision increases, reaction rate increases
  • For gaseous reactants: Pressure increases, number of molecules per unit volume increases, frequency of effective collision between molecules increases, rate of reaction increases
  • Temperature:
• • With increasing temperature, average kinetic energy of the molecules increases, number of molecules with energy equal or greater than Ea increases, frequency of effective collision of molecules increases, rate increases
• Maxwell-Boltzmann distribution curve:

  • Shaded areas represent the number of molecules possessing kinetic energy equals or greater than activation energy, Ea
  • Only collisions of molecules with energy greater than Ea are able to react
  • At lower temperature T1, the fraction of energetic (and effective) collision is quite small
  • As the temperature increases, the distribution broadens and shifts towards higher energy
• Energy profile diagram showing the difference reaction in the presence of catalyst and without catalyst
• ARRHENIUS EQUATION: k: rate constant; R: universal gas constant (8.314 Jmol^(-1) K^(-1)); e: base of natural logarithm; T: absolute temperature (in K); Ea: activation energy; A: frequency factor

  • Higher T leads to larger k and increased rate; Larger Ea leads to smaller k and decreased rate
• Zero-order, First-order, Second-order Rate law (*for reaction: A → products):

  • Rate = k[A] 0
  • Rate = k[A]
  • Rate = k[A]^2
• Integrated rate law:

  • [A]=[A]o - kt
  • [A]=[A]o e^(-kt)
• Unit of rate constant: Mol L^(-1) s^(-1) or M s^(-1) or s^(-1) L mol^(-1) or M^(-1) s^(-1)
• Characteristic kinetic plot/linear plot to determine k:

  • [A] vs t
  • ln[A] vs t
  • 1/[A] vs t
• Half-life:

  • kAt_1/2 = 2
  • ln(t_1/2) = 1/k
• Graph rate:

  • Rate = k[A] 0
  • Rate = k[A]
  • Rate = k[A]^2
• Graph integrated law:

  • [A] = [A]o - kt
  • ln[A] = ln[A]o - kt
• Half-life (Graphical method):

  • t_1/2(I) = 1/2 t_1/2(II)
  • t_1/2(I) = t_1/2(II)
  • t_1/2(II) = 2 t_1/2(I)
• Example: metal-catalyzed and biochemical processes, radioactive reaction
• Comparison between k with different T:

  • ln(k1/k2) = (Ea/R)(1/T1 - 1/T2)
• ln([A]2/[A]1) = -Ea/R (1/T2 - 1/T1)