Lec 03 Jan 9 Fri

# Lec 03 Jan 9 Fri - (ii First-order reactions(14-5 1.8 Rate...

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(ii) First-order reactions (14-5): Rate depends on reactant concentration 1 [A] d[A] = k d t Now integrate: 1 [A] [ A ] o [ A ] d[A] = k d t 0 t Get: ln [A] - ln [A] o = – k t OR: How do you know that the data is for 1st order reaction ? ln[A] Intercept : ln [A] o slope = - k Time (s) Plot of ln[A] vs t is linear for first-order reactions. ln [A] = ln [A] o k t Integrated rate law for 1 st order reactions 1.8 Half-life for first order reactions : ln [A] [A] o = k t ln 1/2[A] o [A] o = k t 1/2 ln 1 / 2 ( ) = k t 1/2 ln 2 ( ) = k t 1/2 t 1/2 = ln 2 k = 0.693 k About natural logarithms: ln (say “lawn”) log x = y, so x = 10 y ln x = y, so x = e y (e base of ln = 2.718…) Rate = d A [ ] dt = k A [ ] 1 (optional info!)

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Example : Radioactive technetium ( 99m Tc) is used clinically because of its short half-life [a metastable 99m Tc, decays to 99 Tc emitting γ radiation]. (1) If the decay rate constant is 0.116 h
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Lec 03 Jan 9 Fri - (ii First-order reactions(14-5 1.8 Rate...

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