Kinetics

• Whats kinetics?


  The study of the rate of chemical reactions
• What factors affect the rate of chemical reactions?

  Temperature, concentration, pressure, catalysts.
• What is an SN1 reaction dependent on?

  Conc of substrate
• What is the rate of reaction?

  The rate of change of conc of a species with respect to time
• If you're measuring the rate of converting A into B what would be the equation and how would you calculate it?

  Plot a graph of conc against time of both conc of A and B. Draw a tangent and calculate the change in conc and change in time = gradient

  A is being used up so its conc will decrease over time, value will be negative. So you need to put a - in front of the equation so you get a positive value, as the rate of reaction is always a positive quantity.

  𝑣A = −( d[A]/dt)

  For B, you're forming B, so its conc will always increase and be positive, so need for negative sign

  𝑣B = d[B] /dt

  
• What are the units for rate?

  mol dm-3 s -1 (or mol L-1 s -1 )
• What's the rate law?

  Rate law is an equation that relates the rate of a chemical reaction to the concentration of reactants.

  v=k[A]m[B]n

  k= rate constant depends on specific temp and reaction

  m & n = orders of reaction with respect to the reactants A & B.
• What does the order mean?

  The order tells us how the rate of the reaction changes when the concentration of a specific reactant changes.

  • If m=1 , the rate is directly proportional to the concentration of A. This means if you double the concentration of A, the reaction rate will also double.
  • If n=1, the rate is also directly proportional to the concentration of B.

  1+1 =2

  The overall order is second-order meaning the rate of reaction depends on the conc of both A & B
• What does it mean for a reaction to be 2nd order?

  • If you double the concentration of A, the rate will double.
  • If you double the concentration of B, the rate will also double.
  • But, if you double both A and B, the rate will increase by a factor of 4 : 2×2=4
• What's the isolation method?

  This method involves using a large excess of one reactant to effectively "ignore" its concentration, making the reaction appear to depend on the concentration of just one reactant.

  For example, if you use a large excess of B the the rate of reaction will only depend on A

  v=k′[A]m
• What does K represent in the isolation method?

  Pseudo-first-order rate constant where k′ is modified to account for the effects of B as this is in excess.

  The reaction is 2nd order but it's made to behave like a first-order reaction
• How do you determine m in the isolation method?

  Measure the inital rate of the reaction at different conc of A.

  Once you've determined m you repeat the process but now keep A in excess to determine n for B.

  Pick 2 experiments and find the relationship between conc and the rate of A.

  • Ratio of rates between Experiment 2 and Experiment 1:

  0.080/0.020 = 4

  Ratio of concentrations:

  0.20/0.10 = 2

  v0​=k[A]m

  4= 2^m

  m=2 : second order

  
• Whats a zero-order reaction?

  if the rate of reaction does NOT depend on the concentration(s) of any of the reactant(s).
• What's a first order reaction?

  if the rate of reaction depends upon the concentration of only one species raised to the first power
• What would be the integrated rate law for a first order reaction?

  [A]𝑡 = [A]0𝑒−𝑘𝑡  

  [A]t = concentration of A at time t,

  [A]0 = initial concentration of A

  k = rate constant

  t = elapsed time.

  If you're converting reactant A into a product then the conc of A decreases exponentially with time.

  This form of the integrated rate law allows us to predict the concentration of A at any time after the start of the reaction.   
• What would be the logarithimc version?

  ln[A]𝑡 = ln[A]0 − 𝑘t

  This is useful for determining the time required for the concentration of A to reach a certain value

  This form of the integrated rate law will give a straight line if

  ln [A]t is plotted against t.

  A straight line has the form y = a + bx.

  a = value of ln [A]0, from which the initial concentration of A can easily be determined,

  b = –k, easily allowing determination of the rate constant.  

  
• If you are given a set of data that show how the concentration of a substance varies with time and you plot ln [A]t versus t, if the points fall along a straight line then what does that mean?

  that demonstrates that the reaction is first-order with respect to that substance.
• How would you measure the rate of a first-order reaction?

  Measuring the reactants half-life
• What is half-life?

  This is the time taken for the concentration of the reactant to fall to half of its original value.

  The half-life (t½) is a constant and is independent of concentration for a first-order reaction. When t = t½ the value of [A]t will be half of [A]0 :

  𝑡½ = ln 2 /k
• What units does k have in a first-order reaction?

  time-1
• What's a second-order reaction?

  one in which the rate of the reaction depends upon the concentration of one species raised to the second power (i.e. the concentration squared).

  A + A → products

  𝑣A = − d[A]/ d𝑡 = 𝑘[A]^2

  Integrated:

  1 /[A]𝑡 = (1 /[A]0 )+𝑘t
• What's the difference between integrated and normal rate law equation?

  • Rate law tells us how fast the reaction is happening at a specific moment.
  • Integrated rate law helps us predict what the concentration of a reactant will be at a given time.
• Determine the half life if the gradient of this graph is –0.101 min-1 ?

  Half-life: t_½=ln⁡2/k=ln⁡2/0.101= 6.86 min.

  
• The concentration of a reactant, A, was monitored over time and the following data obtained:  

  Demonstrate graphically that this reaction follows first-order kinetics with respect to A?

  If its first-order the graph should be a straight line.

  Take log of (a) and plot that on the x-axis 

  And time on y- axis 

  Then plot to get the gradient which will give you K 

  K will give you a negative number so you have to do -K to get a positive value

  
• . A first-order reaction has a half-life of 200 s. If the initial concentration of the reactant is 25 mm, determine the concentration of the reactant after 10 min.

  3.13um

  
• The metabolism of a drug follows first order kinetics, with a rate constant of 0.02 min-1. If the initial concentration of the drug in blood plasma is 18 ng/mL, how long will it take for the drug’s concentration to fall to 5% of its original value?


  150mins

  
• How would you represent graphically that a reaction is second order?

  If a reaction is second-order, plot a graph of 1/[A]t  against t will give a straight line.

  
• What's a second-overall reaction?

  the rate of the reaction depends upon the concentration of both reactant species each raised to the first power (i.e. first-order with respect to each reactant).

  
• How would you represent graphically that a reaction is a second-overall reaction?

  If a reaction is second-order overall, a plot a graph which will give a straight line through the origin.

  
• With second-order overall reactions what do we assume?

  That the initial conc of reactants A and B are different
• What happens if the initial conc of a second overall equation are the same?

  the concentrations of A and B will be identical at all times during the reaction as they are decreasing at the same rate

  Therefore cannot use the integrate rate law equation as it'll just equal to 0.

  You can use the isolation method where having one reactant in excess so its concentration remains essentially constant as it hardly changes at all throughout the reaction.

  
• Determine the overall order for this reaction:

  2NO + Cl2 → 2NOCl  ?

  𝑣 = 𝑘[NO]2[Cl2]  

  No = 2nd order with respect to NO

  Cl2 = 1st order with respect to CL2

  2+1 =3 - 3rd order overall

  Units:

  
• Determine the overall order of reaction for C4H9Br + OH = C4H9OH + Br - the rate of reaction is only determined by C4H9Br?

  1st order

  𝑣 = 𝑘[C4H9Br]  

  Units:

  
• Determine the overall order of reaction of C3H7Br + OH = C3H7OH + Br, if rate of reaction is determined by C3H7Br + OH?

  2nd overall

  𝑣 = 𝑘[C3H7Br][HO−]  

  
• The reaction between nitric oxide and chlorine is second-order with respect to nitric oxide. Using the data provided, demonstrate graphically that this is the case and determine the initial concentration of nitric oxide and the rate constant for the reaction?

  Second-order reactions should give a straight line.

  You plot 1/ [A]t concentration against time.

  The inital conc is is the intercept and if you do 1/ inital conc of NO it'll give you 0.099mM.

  
• Why does increasing the temperature increase the rate of reaction?

  The probability of collisions taking place is increased as the molecules move faster. Also, there's a greater probability that the colliding molecules will have sufficient energy for the collision to result in a successful reaction and have more energy to overcome the activation barrier.
• How is the relationship between the rate of reaction and temperature represented?

  By Arrhenius equation:

  K= rate constant

  A= pre-exponential factor ( same units as k)

  Ea = activation energy (Jmol-1)

  R = gas constant (8.3145 J K-1 mol-1)

  T= absolute temperature (0 oc = 273.15k)

  
• What does the pre-exponential factor represent?

  The total frequency of collisions
• Whats the logarithmic version of the arrhenius equation?

  By plotting ln k against 1/T and this should give a straight line.

  Gradient = − Ea/R, which you can calculate Ea.

  Because of how the values of 1/T that will equal 0 so it will reach infinity , so it's best to pick a point on the line (not a plotted one).

  Use y= a +bx to calculate the intercept of a

  
• The rate constant for the decomposition of ethanal was measured at a range of different temperatures. Use the data in the table to determine the pre-exponential factor and the activation energy of this reaction.  

  9.83 X 10^11 dm3 mol-1 s-1