halflife

# halflife - • 5715 =-ln(1/2 k • k =-ln(1/2 5715 =...

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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: o half life of carbon-14 = 5715 years o ln[A]t = -kt + ln[A]0 o [A]t = 35 o [A]0 = 125 o t1/2 = -ln (1/2) / k
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Unformatted text preview: • 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...
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