half-life (t1/2) - time needed for concentration of reactant to drop to 1/2 or original value 

• fast reaction >> short half-life
• t1/2 = -ln (1/2) / k = 0.693 / k for 1st-order reactions (no dependence on initial concentration)
• t1/2 = 1 / k[A]0 for 2nd-order reactions (dependence on initial concentration)

Find the half-life of a substance that decomposes by 20% after 5 years. 

• 0.8 = (1)(1/2)5/x
• ln(0.8) = 5/x ln(1/2)
• ln(0.8) / ln(1/2) = 5/x
• x = 5 ln(1/2) / ln(0.8)
• 15.5 years

Find the age of a piece of wood whose carbon-14 count is 35/min, when a new piece of wood has a count of 125/min.  

• Given:
  • half life of carbon-14 = 5715 years
  • ln[A]t = -kt + ln[A]0
  • [A]t = 35
  • [A]0 = 125
  • t1/2 = -ln (1/2) / k
• 5715 = -ln(1/2) / k
• k = -ln(1/2) / 5715 = 0.00012
• ln(35) = -(0.00012)t + ln(125)
• ln(35) - ln(125) = -(0.00012)t
• t = (ln35 - ln125) / -0.00012
• 10608 years

Find the half life of a substance if 95% of it disappears after 10 years.  

• 0.05 = (1/2)10/x
• ln (0.05) = 10/x (ln(1/2))
• ln (0.05) / ln (1/2) = 10 / x
• x = 10 ln(1/2) / ln(0.05)
• 2.3 years

collision model - based on kinetic-molecular theory

• shows effects of both temperature/concentration on molecular level
• assumes that molecules must collide to react w/ each other
• not all collisions lead to reactions
• orientation factor - molecules need to be in a certain position to react when colliding