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What is Half-Life time of a reaction ?Derive the equation of Half -Life time(t_((1)/(2))) for zero order reaction. |
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Answer» Solution :Half-LIFE time:The half-life of a reaction is the time in which the concentration of a reactant is reduced to one half of its intial concentration it is called half life and REPRESENTED as `(t_((1)/(2)))` . To derive `t_((1)/(2))` EQUATION of zero -order reaction: For a zero order reaction,rate constant (k) is given by following equation . `k=([R]_(0)-[R])/(t)`.........(a) Where t=half life time =`t_((1)/(2))`.....(i) `[R]_(0)` =The concentration of reactant at t=0 time....(ii) [R]=The concentration of reactant at `t_((1)/(2))` time =`(1)/(2)` initial concentration `[R]_(0)` `therefore [R]=(1)/(2)[R]_(0)`......(iii) Put these value in (a) `k=([R]_(0)-(1)/(2)[R]_(0))/(t_(1)/(2))` `therefore k=(1[R]_(0))/(2xxt_((1)/(2)))` and `t_((1)/(2))=([R]_(0))/(2k)` (half life of zro ordr reaction) It is clear that `t_((1)/(2))` for a zero order reaction is directly proportional to the inital concentration of the reactants and iversely proportional to the rate constant. |
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