Rates of reaction

• Rate = delta Y / delta X
• Continuous monitoring:

  • The continuous monitoring method allows data to be collected throughout the course of reaction
  • Allowing data to be plotted on a concentration-time graph
  • For coloured solutions colorimetry allows the measurement of absorption of light passing through it
  • A calibration curve made from known concentrations can be used to determine the concentration at a given time
  • The light needs to pass through a coloured filter to control the wavelength of the light being used
• Order of reaction:

  • The order attributed to a reagent identifies the effect changing its concentration has on the rate of a reaction
  • If the concentration of a reagent is doubled and :-
  • the rate remains constant = zero order
  • the rate doubles = first order
  • the rate quadruples = second order
• The rate equation:

  • The relationship between the rate & order of reactants is shown in a rate equation: rate = k x[A]^a[B]^b
  • rate = moldm^-3
  • k = rate constant
  • [A] = concentration of the reagent in moldm-3
  • ^a = order of reagent
  • The overall order is the sum of the individual orders
• The rate constant:

  • The rate constant, k, is a constant of proportionality & reflects the ease that a reaction takes place
  • Large value of k results in a greater rate of reaction
  • However the value of k:-
  • is different for different reactions
  • varies according to temperature
  • higher temperatures = large value of k = faster rate
  • for every 10 degrees Celsius increase the rate of reaction roughly doubles
• The rate constant units:

  • To determine the units of the rate constant,
  • rate = moldm^-3s^-1
  • [] = moldm^-3
  • k = rate / [A]^a[B]^b
• • orders multiply the units of concentrations
  • [A]^2 = moldm^-3 x moldm^-3 = mol^2dm^-6
  • Multiplying reactant concentrations add the units
  • [A][B] = moldm^-3 x moldm^-3 = mol2dm^-6
• Orders from experimental results:

  • Orders of reaction must be determined experimentally by monitoring how a physical quantity changes over time
  • Orders can't be found directly from the chemical equation
  • The initial rate is the instantaneous rate at the beginning of an experiment when t=0
• Concentration- time graphs:

  can be used to determine:

  • rate : from the gradient
  • order: from the shape
• Zero order:

  • straight line with a negative correlation
  • rate is constant i.e: not affected by the concentration
• First order:

  • Downward curve
  • Rate is decreasing i.e: affected by the concentration
  • second order is similar but starts steeper and tails off slowly
• Initial rate:

  • The initial rate is determined from a tangent taken from t=0.
  • The value calculated from this tangent is an approximation, but reliable when the reaction is less than 15% complete
• Half -life:

  • The half - life (t1/2) of a reaction is the time it takes for the concentration to decrease by half
  • First order reactions have a constant t1/2 an exponential decay --> 2nd order don't
• Determining rate constant:

  k can be determining for a first order reaction by using:

  1. Rate i.e: tangent --> rate = k[A]
  2. Half-life (as first orders have exponential relationships) --> k= ln2/ t1/2
• Rate - concentration graphs:

  • zero order : rate = k[A]^0 --> rate if reaction is tangent constant ( y-intercept = rate), rate = k
  • first order: rate = k[A] --> rate of reaction is directly proportional to concentration
  • second order: rate = k[A]^2 --> k can't be determined from this graph unless it is replaced as rate against concentration squared. This will then generate a directly proportional line
• Many reactions have mechanisms that require more than one step to complete.

  Step 1: C2H4 + HX --> C2H5+ + X- (slow step)

  Step 2: C2H5+ + X- --> C2H5X (fast step)
• The slowest step is the one determines the overall rate of reaction, the rate - determining step i.e: the step with the greatest activation energy
• Not all reactants are involved in the rate - determining step and the particle numbers won't match the balanced equation
• There is a direct relationship between the order & the rate determining step, as order relates to moles involved.

  • zero order = not involved
  • first order = 1 mole of reactant
  • second order = 2 moles of reactant
• • As temperature increases, the rate increases & the value of the rate constant k will also increase
  • For many reactions each 10 degrees Celsius in temperature doubles the rate constant & doubles the rate of the reaction
• • Increasing temperature shifts the Boltzmann distribution to the right, increasing the proportion of particles that exceed the activation energy Ea
  • As the temperature increases particles move faster & collide more frequently
  • To react particles must also collide with the correct orientation
• • With increasing temperature, increasing frequency of collisions is comparatively small compared with the increase in proportion of molecules that exceed Ea from the shift in the Boltzmann distribution. So the change in rate is mainly determined by Ea.
• The Arrhenius equation:

  • The Arrhenius equation is an exponential relationship between the rate constant k and the temperature T
  • k = Ae^-Ea/RT
• • The exponential factor e^-Ea/RT represents the proportion of molecules that exceed Ea and that have sufficient energy for a reaction to take place
  • The pre-exponential term ( frequency factor) A takes into account the frequency of collisions with the correct orientation
  • This term does increase slightly with temperature as the frequency of collisions increasing but is essentially constant over a small temperature range.
  • The frequency factor essentially gives the rate if there were no activation energy
• Logarithmic form of the Arrhenius equation:

  • This form of the equation allows Ea & A to be determined graphically
  • ln k = - Ea/RT + ln A