time taken for first order rxn, 2 reduce initial conc. by factor of 1/4 is 10min.if the conc. is reduced to 1/16 then the time required is?

Let initial concentration = Ao
Concentration after 10 minutes, A = Ao/4
Equation for first order reaction:
k = 2.303tlogAoAk = 2.30310logAoAo/4k = 0.2303 log 4k = 0.1386min-1

Now,
Concentration after time t = Ao/16
t = 2.3030.1386logAoAo/16t = 16.616 log 16 t = 20 minutes

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