5.1.1 How Fast?

• Rate equation


  Relates mathematically the rate of reaction to the concentration of the reactants
• Rate of reaction


  The change in concentration of a substance in unit time
• Unit of rate


  mol dm-3s-1
• Generalised rate equation


  r = k[A]m[B]n
• r


  Symbol for rate
• k


  Rate constant
• m, n


  Reaction orders
• Orders are usually integers 0,1,2
• Zero order


  Reaction is zero order with respect to that reactant, rate is independent of concentration
• First order


  Rate of reaction is directly proportional to the concentration of the reactant
• Second order


  Rate of reaction is proportional to the concentration of the reactant squared
• The total order for a reaction is the sum of the individual orders
• Calculating orders from initial rate data

  1. Plot initial rate vs concentration

  2. Gradient shows order
• The initial rate is the rate at the start of the reaction where it is fastest
• Calculating rate from concentration vs time graphs

  1. Draw tangent to curve

  2. Gradient of tangent is the rate

  
• Rate constant (k)


  Independent of concentration and time, constant at fixed temperature, increases with temperature
• Units of k


  • Depend on overall order of reaction
  • 1st order: s-1
  • 2nd order: mol-1dm3s-1
  • 3rd order: mol-2dm6s-1
• Calculating units of k

  1. Rearrange rate equation to get k as subject

  2. Insert units and cancel
• Continuous rate data


  1. Plot concentration vs time

  2. Calculate half-lives

  3. Constant half-lives = 1st order, increasing half-lives = 2nd order
• Deducing rate equation from initial rate data

  1. Compare experiments where only one reactant concentration is changed

  2. Determine order from effect on rate

  
• The overall rate equation is the product of the individual orders
• Calculating k from initial rate data

  1. Rearrange rate equation to get k as subject

  2. Plug in values from one experiment
• Increasing temperature


  Increases the rate constant k
• Arrhenius equation


  k = Ae-EA/RT, where A is a constant, R is gas constant, and EA is activation energy
• Arrhenius equation


  ln k is proportional to 1/T
• Y


  Must be second order
• Overall rate equation


  r = k [X] [Y]2
• The reaction is 3rd order overall and the unit of the rate constant =mol-2dm6s-1
• Calculating a value for k using initial rate data

  1. r = k [X] [Y]2

  2. k = r / ([X] [Y]2)

  3. k = 2.40 x 10–6 / (0.2 x 0.22)

  4. k = 3.0 x 10-4 mol-2dm6s-1
• k is the same for all experiments done at the same temperature
• Increasing the temperature


  Increases the value of the rate constant k
• Arrhenius equation


  k = Ae-EA/RT where A is a constant, R is gas constant and EA is activation energy
• Calculating activation energy from graph

  1. ln (Rate) vs 1/T

  2. Gradient = - EA/ R

  3. EA = - gradient x R
• The unit of EA using this equation will be J mol-1. Convert into kJ mol-1 by dividing 1000
• Techniques to investigate rates of reaction

  • Measurement of the change in volume of a gas
  • Titrating samples of reaction mixture
  • Colorimetry
  • Measurement of optical activity
  • Measurement of change of mass
  • Measuring change in electrical conductivity
• Reactions that can be measured by different techniques

  • H2O2(aq) + 2I- (aq) + 2H+(aq) 2H2O(l) + I2(aq)
  • HCOOCH3(aq) + NaOH(aq) HCOONa(aq) + CH3OH(aq)
  • (CH3)2C=CH2(g) + HI(g) (CH3)3CI(g)
  • BrO3–(aq) + 5Br –(aq) + 6H+(aq) 3Br2(aq) + 3H2O(l)
  • HCOOH(aq) + Br2(aq) 2H+(aq) + 2Br - (aq) + CO2(g)
  • CH3COCH3(aq) + I2(aq) → CH3COCH2I(aq) + H+(aq) + I–(aq)
  • CH3CHBrCH3 (l) + OH−(aq) CH3CH(OH)CH3 (l) + Br−(aq)
• Titration method


  1. Small samples removed from reaction mixture

  2. Quench reaction

  3. Titrate with suitable reagent
• Mechanism


  A series of steps through which the reaction progresses, often forming intermediate compounds
• Rate-determining step


  The slowest step that controls the overall rate of reaction
• Molecularity


  The number of moles of each substance in the slowest step