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Half-Life, Collision Model

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
Subject: 
Chemistry
Subject X2: 
Chemistry

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