The integrated rate equation for a first order reaction is given by
k=t2.303loga−xa
Where
k=Rateconstanta=initialconcentrationofthereactantsa−x=concentrationofreactantsleftaftertime,t.
k=52.303log0.0010.1=54.606=0.9212min−1
Hence, the rate constant of the given reaction is 0.9212min−1