1.

Show that is the half life period of a first order reaction is independent of then initial concentration of the reactant.

Answer»

For first order reaction, equation of rate constant is K =  \(\frac{2.303}{t}\) log \(\frac{a}{a-x}\)

Where a = initial concentration of reactant 

When half of the reaction is completed, x = \(\frac{a}{2}\)

a - x = a - \(\frac{a}{2}\) = \(\frac{a}{2}\) 

putting t = t1/2 in the equation, we get 

k = 2.303/ t1/2 \(\Big(\frac{a}{a/2}\Big)\) = 2.303/ t1/2 log 2 = 0.693/k 

This shows half-life is independent from initial concentration of reactant 



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