For the reaction, a → b, the rate constant is 0.0208 m-1 sec-1. how long would it take for [a] to decrease from 0.100 to 0.0450 m?

First, assume the order of the given reaction is n, then the rate of reaction i.e.

where, dx is change in concentration of A in small time interval dt and k is rate constant.

According to units of rate constant, the reaction is of second order.

  (second order formula)

Put the values,

t= 587.9 s

Hence, time taken is 587.9 s