Reaction kinetics

• Define the rate of reaction

  How quickly the reactants are turned into products
• What are the two equations for the rate of reaction?

  Amount of reactant used up/ time taken

  
  

  Amount of product formed/ time taken
• How can we express A+B-->C as a singles step (elementary reaction)?

  k[A][B]

  
  

  Rate has the units: mol dm^-3 s^-1

  
  

  k - rate constant, which encompasses the temperatre and collision frequency.

  
  

  [A] - the molar concentration of reagent A
• What happens when it's not an elementary step, like A+2B--> C?


  More complicated.

  
  

  k[A]^m[B]^n

  
  

  m- the order of the reaction with respect to A

  n- the order of the reaction with respect to B

  m+n- the overall order of the reaction
• How can the orders of reagents be found?

  Experimentally, not through stoichiometry
• How can you find the rate of reaction at a particular time, on a graph?

  Draw a tangent at that line and find the gradient of the line
• What are the three methods of finding the order of the reaction/reactant?

  - Graphical method

  - Initial rates method

  - Isolation method
• Graphical method

  Find the rate at various points and then you plot a graph of rate versus time.
• What does zero order mean?

  The rate is not affected by the concentration of this reactant, [A]^0

  
  

  Concentration v/s time - decreasing linear graph

  
  

  Rate v/s time - a horizontal line

  
• What does first order mean?

  The rate is directly proportional to the concentration of the species, ie [A]

  
  

  Concentration v/s time - decreasing less curvy exponential graph

  
  

  Rate v/s time- an increasing linear graph

  
• What does second order mean?

  The rate is proportional to the square of the concentration of this reactant, ie [A]^2

  
  

  Concentration v/s time - decreasing more curvy exponential graph

  
  

  Rate v/s time- an increasing exponential graph

  
• Initial rates method

  Find the rate of reaction by changing the initial rates of reagents and compare how the rate differs.
• How do you use the initial rates method?

  - Find two experiments where only one of the reagents' concentration changes.

  - Compare how the concentration changes with how the rate changes.

  - If the concentration increases by x and the rate doesn't change, the order of the reactant is zero.

  - If the concentration increases by x and the rate changes by x, the order of the reactant is first.

  - If the concentration increases by x and the rate changes by x^2, the order of the reactant is second.

  - Repeat for the other reagents.
• Isolation method


  Use a large excess of reactants except the reactant under investigation, so that their concentrations remain virtually constant

  
  

  If we have the reactantion A+B--> C+D with the rate law, rate =k[A][B].

  
  

  We set [A]>>[B] so that the rate law can now be written rate=k-observed [B]^n.

  
  

  k-observed=k[A]^m

  
  

  We can make this approximation since the value of [A] doesn't change within experimental error ans allows us to study B directly
• What are the units for k when the overall order of reaction is one?

  s^-1
• What are the units for k when the overall order of reaction is two?


  mol^-1 dm^+3 s^-1
• How do you find the fraction of molecules with the activation energy?

  e^(-Activation energy/RT)

  
  

  R- gas constant

  T- temperature
• Why is finding the fraction of molecules with the activation energy unitless?

  All the units of the components of the equation cancel out each other.
• What is the equation to find k?

  k=Ae^(-Activation energy/RT)

  
  

  lnk=lnA -Ea/RT

  
  

  A- Arrhenius factor

  k - rate constant

  Ea- activation energy

  R- gas constant

  T- temperature
• How do you find the activation energy and the Arrhenius factor without using the equation?

  Plot ln k v/s 1/T

  
  

  A- is the y intercept

  
  

  Activation energy is the gradient times by R
• What is the rate determining step?

  The slowest step in a multi-step reaction
• What does the rate equation take account of?

  Takes account of the slowest step and every step before it.
• A+B-->X (slow)

  
  

  A+X--> D (fast)

  Overall rate - k[A][B]

  
  

  X is an intermediate which does not appear in the overall chemical equation.

  
  

  X can be isolated as they are local energy minima.

  
  

  Maxima energy points - transition points and can't be isolated.
• What is the rate equation for this mechanism?

  
  

  H2 +2NO -->N2O +H20 (Slow)

  
  

  N2O+H2--> H2O +N2 (Fast)

  Rate=k[H2][NO]^2
• What is the rate equation for this mechanism?

  
  

  H2+ICl-->HI +HCl(slow)

  
  

  HI+ICl-->I2+HCl(fast)

  Rate = k{H2][ICl]
• What happens if it's like this:

  
  

  A+B-->X (fast)

  A+X-->D (slow)

  First step: rate =k1[A][B]

  Second step= k2[A][X]

  [X]=k1[A][B]

  k1k2[A][A][B]

  
  

  Overall: k[A]^2[B]
• 2NO-->N2O2 (fast)

  N2O2+O2-->2NO2 (slow)

  Rate= [NO]^2[O2]