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Derive the relationship between half life and rate constant for first order reaction. |
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Answer» In first order reaction, the concentration of reactants. Depends upon the first power of concentration of reactants. From the integrated rate equation for a first order reaction with rate constant, k, concentration at any time, t is expressed as, `A to B` The half-time of a reaction is defined as the time required to reduce the concentration of the reactant to half of its initial value. It is denoted by the symbol `t_(1//2).` Thus, For first order reaction, we know that `k=1/tln""([A]_(0))/([A])` at half life of reaction, `t=t_(1//2)and [A]-[A]_(0//2)` So, `k=(1)/(t_(1//2))ln""([A]_(0))/([A]_(0))` `impliest_(1//2)=(0.693)/(k)` Since k is a constant for a given reaction at a given temperature and the expression lacks any concentration term. So, half-time of a first order reaction is independent of initial concentration of reactant. |
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