Rate Equations

• Rate of reaction is defined as the change in concentration of a substance in a given time. The units are mol dm-3 s-1.
• The activation energy is the minimum energy required to to start a reaction by the breaking of bonds (in the reactants).
• Increasing concentration increases the number of particles per unit volume so more frequent collisions so more successful collisions per unit time, so rate increases.
• Increasing pressure of a gas increases the number of particles per unit volume, so more frequent collisions, so more successful collisions in a given time, so rate increases.
• Increasing surface area of a solid increases the points of contact between the solid particles and the other reactant so more frequent collisions, so more successful collisions in a given time.
• Increasing temperature gives all the particles more energy so many more particles will have energy greater than or equal to Ea, so many more of the collisions will be successful, so more successful collisions per unit time, so the rate increases.
• A catalyst speeds up a reaction by providing an alternative reaction pathway with a lower activation energy, so more particles will have energy greater than or equal to Ea, so more of the collisions will be successful, so more successful collisions per unit time, so rate increases.
• A + B -> C + D

  Rate = k[A]^m [B]^m
• The overall order of a reaction is the sum of the order with respect to each reactant.
• The units of k for first order are s-1.

  The units of k for second order are mol-1 dm3 s-1.

  The units of k for third order are mol-2 dm6 s-1.

  The units of k for fourth order are mol-3 dm9 s-1.
• fold change in rate = fold change in [M]x
• fold change in rate = fold change in [known] x(known) * fold change in [M]x
• Rate-Concentration graphs:

  • zero order has no change in rate so is a straight horizontal line as rate is independent of [M]
  • 1st order is a straight line through the origin as it is a directly proportional relationship.
  • 2nd order is an exponential line. However, is the x axis is labelled [M]2, then it will look the same as the 1st order graph.
• Concentration-time graphs:

  • zero order - the gradient is constant at each point of the graph, so rate is constant (straight line down)
  • 1st order - gradient gets shallower (so rate gets shallower) so rate is dependent on [M]. Exponential line downwards.
  • 2nd order - same as first order graph but curve is steeper as [M] has a bigger effect on rate.
  • it is difficult to distinguish between 1st and 2nd order so plot a graph of 1/t vs [M].
• Continuous monitoring:

  • Start with known [A] and [B]. To ensure that concentration of only one changed during reaction (A), [B] should be much larger to ensure [B] is effectively constant so doesn't affect rate.
  • Determine [A] at different times during reaction by e.g. a titration, measuring the absorbance if there is a coloured soloution, measuring volume of gas produced, measuring pH if H+ is a reactant, or measuring the change in mass.
• Quenching is when a reaction may need to be stopped to allow the concentration to be measured. This can be achieved by placing the reaction mixture in an ice bath.
• Analysis of continuous monitoring:

  • plot graph of [] against time.
  • use graph to determine rate and [] at different times in the reaction.
  • plot rate-[] graph or compare how the rate and the [] change.
• The rate determining step is the slowest step in a reaction mechanism.
• Any step that occurs after the rate determining step will not affect the overall rate. So reactants involved in these later steps will not appear in the rate equation.
• The rate equation tells us the reactants (moles of reactants) involved in a reaction mechanism up to and including the rate determining step.