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Define half life of a reaction, Show that for a first order reaction half life is independent of initial concentration. |
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Answer» Solution :Half life of a REACTION is defined as the TIME REQUIRED for the reactant CONCENTRATION to reach one half of its initial value. For a first order reaction, the half life is a constant i.e., it does not depend on the initial concentration. The rate constant for a first order reaction is given by, `k=(2.303)/(t)log""([A_(0)])/([A])` at `t=t_((1)/(2)),[A]=[A_(0)]//2` `:. k=(2.303)/(t_(1//2))log""([A_(0)])/([A_(0)]//2)` `k=(2.303)/(t_(1//2))log(2)` `k=(2.303xx0.3010)/(t_(1//2))=(0.6932)/(t_(1//2))` `t_(1//2)=(0.6932)/(k)` |
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