Half Life: time it takes for the reactant concentration to decrease to one half its initial value (t½) .
Value of “t” when [A]t = (½) [A]0
So ln (½) = -kt → 0.693 = kt → t½ = 0.693 / k
Simply: t½ = 0.693 / k
The half life of a first order reaction is independent of initial concentration:
Example:
*SO2Cl2 decomposes in a first order reaction to produce SO2 and Cl2. What is the half life if the rate constant at a given temperature is 2.20 x 10-5 s-1 ?
t½ = 0.693 / k
t½ = 0.693 / 2.20 x 10-5 s-1
t½ = 3.15 x 104 s
*How long would it take for 75% of the SO2Cl2 to decompose?
75% is half of the initial concentration plus half of the concentration left over after the first half life, so it is two times the half life.
Second Order Half Life:
t½ = 1 / k[A]0
This time, the half life depends on initial concentration and each subsequent half life becomes larger as time progresses.
Zeroth Order Half Life:
t½ = [A]0 / 2k
Again, the half life is dependent upon initial concentration of the reactant, but instead of becoming larger as the reaction progresses, as a zeroth order reaction proceeds, each half-life gets shorter.
Graphing of Kinetic Data:
It is possible to determine the order of a reaction by graphical plotting of the data for a particular experiment.
If you plot the data for ln[A]t on the vertical axis against time “t” on the horizontal axis, a first order reaction will give you a straight line.
If you plot the data for 1 / [A]t on the vertical axis against time “t” on the horizontal axis, a second order reaction will give you a straight line.
If a curved line results for either graph, the reaction order is not the one that matches that graph.
An organized explanation of the key points in the chapter thus far is found in Table 13.2, pg 544.
Collision Theory: (3 Stooges Universe)
Three things must happen between objects before there is a reaction:
1. Objects must “hit” (Collision).
2. Must collide with enough energy to break bonds (Activation Energy = Ea).
3. Objects must smack into each other the right way (Orientation).
Example:
O=N + Cl ̶ Cl → [O=N ̶ Cl···Cl]ǂ
This ǂ symbol denotes a highly unstable, activated state that quickly falls apart to
O=N ̶ Cl + Cl
Notice the orientation of N to Cl. If O smacked into Cl:
N=O + Cl ̶ Cl → No Reaction
Nitrogen must collide with Chlorine, not Oxygen in order for a reaction to occur here.
Enzymes function the same way:
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