Rate equations

• Rate equations is an equation that relates the concentrations of substances involved in a reaction ( only the reactants and catalyst are involved)
• Rate = k [A]^m [B]^n

  K is the rate constant

  m is the order of reaction in respect of A

  n is the order of reaction in respect to B

  m+n = overall order of reaction

  Units for rate is moldm^-3 s^-1 (moles/dm per second)
• What does the graph of a zero-order reaction look like?

  • The graph is a straight line.
  • The rate remains constant regardless of concentration.
• Zero order

  Changing the concentration has no effect on the rate of reaction

  So it's not included in the rate equation

  Graph would be straight
• 1st order

  Changing the concentration would change the rate proportionally e.g. if concentration doubles then rate also doubles.

  It's represented in a rate equation as simply [X] or [X]^1
• 2nd order

  Changing the concentration, changes the rate proportionally squared e.g. if concentration doubles then rate of reaction is times by 4

  Represented in a rate equation as [X]^2
• How to work out rate equation questions

  1. Identify pairs of experiments where only one concentration is changed
  2. Take note on effect of what is happening to the two concentrations and the effect on the rate
  3. Decide if it's 0, 1st or 2nd order for that species/compound
  4. Write rate equation
  5. Calculate rate constant with units
• What is the term for the step in a multi-step reaction that is the slowest?

  Rate determining step
• Why is it unlikely for all three reactant particles to collide at the same time in some reactions?

  Because reactions occur in a small number of steps involving intermediates
• What is the significance of the rate determining step in a multi-step reaction?

  • It is the slowest step in the reaction mechanism.
  • It controls the overall rate of the reaction.
  • Steps after it do not affect the rate of reaction.
• How do steps occurring after the rate determining step affect the rate of reaction?

  They do not affect the rate of reaction and will not appear in the rate equation
• Rate determining step examples

  A + B + C --> Y + Z

  Step 1) A+B -> D (1st intermediate) Fast

  Step 2) D -> E ( 2nd intermediate) Slow

  Step 3) E+C -> Y+Z Fast

  So step 2 is the rate determining step so only step 1 and step 2 would affect the rate. So rate = [A] [B] it wouldn't include D because it's a product
• Arrhenius equations

  K = Ae^-(EA/RT)

  K is the rate constant ( units vary per reaction )

  A is the A constant ( units same as k)

  e is exponential button on the calculator

  EA is the activation energy ( units is Jmol-¹ )

  R is the gas constant

  T is temperature measured in Kelvin
• Arrhenius equation

  As Ea becomes larger, then k becomes slower so a larger Ea means a slower rate while increasing temperature would increase k so a this would be a faster rate
• Rearranging the arrhenius equation by using log


  Would cause the equation to look like lnK = lnA - Ea/RT

  which can be used as a y = mx + c equation
• Calculating the rate order

  1. If there is an experiment that doesn't stay the same there's is two methods to calculate the order
  2. 1st way is to create another experiment in between the reaction e.g. in the diagram 2.5 is created
  3. For the reaction you don't know the order you leave the same number, the reaction you do know number it the number where it changes
  4. Calculate what should happen to the rate
  5. Then compare it with the next experiment so the reaction you do know doesn't change and calculate wt happens to the rate

  
• Overall order of reaction is just all the orders added together e.g. for Rate = [A]^2 [B] the overall order is 2+1 which is 3