Half Life And Lifetime Flashcards
What is meant by half life?
This is how long it takes for the concentration of a reactant to drop to half of the initial value
What is meant by the term lifetime?
This is how long it takes for the concentration of a reactant to drop to 1/e of the initial value
How can you determine half life for a first order reaction?
1st order: [A]t=[A]oe^-kt The half life is the time for [A]t= [A]o/2 Sub this in: 1/2[A]o=[A]oe^-kt1/2 1) cancel out [A]o 2) remove e by ln 3) rearrange to find t1/2= ln2/k
How do you know if the order of a reaction is 1st order from half life
Since the half life
T1/2=ln2k does not contain [A]o, it does not depend on initial conc and so half life is constant
In each successive period of time, the concentration of A falls to half its value at the start of the period
How can you determine lifetime for a 1st order reaction
1st: [A]t= [A]oe^-kt Lifetime is the time taken for [A]t=[A]o/e Substitute to get: 1/e[A]o=[A]oe^-kt 1) cancel out [A]o 2) ln to get rid of e 3) rearrange to get t=1/k
How can you determine half life for a second order reaction
2nd: 1/[A]t= 1/[A]o +2kt
Substitute in: [A]t= 1/2[A]o
1) cancel down and rearrange to get:
T1/2= 1/2k[A]o
How do you know if a reaction order is 2nd from half life
The half life gets longer as the concentration of the reaction falls
How can you determine lifetime for a 2nd order reaction
1st: 1/[A]t= 1/[A]o +2kt Lifetime is the time taken for [A]t=[A]o/e Substitute to 1) cancel out [A]o 2) ln to get rid of e 3) rearrange to get t=e-1/ 2k[A]o
How can you determine half life for a zero order reaction?
0: [A]t= [A]o- kt Substitute in: [A]t= 1/2[A]o You get : [A]o/2 = [A]o -kt1/2 Rearrange and cancel to get: T1/2= [A]o/ 2k
How do you know if a order is zero order from its half life?
Within two half lives, all of the reactant is gone
What is the zero order half life equation?
t1/2= [A]o/2k
What is the 1st order half life equation?
t1/2= ln2/k
What is the 2nd order half life equation?
t1/2= 1/2k[A]o
How do you draw a line of best fit
1) get data into format to get a straight line
2) plot points
3) find average for x and y
4) mark this point- line of best fit goes through it
Half points should lie below and half above
y=mx +c
