For the first order reaction `AtoB`, the time taken to reduce to `1//4` of initial concentration is 10 min. The time required to reduce to `1//16` of initial concentration will be

Options

A. 10 min
B. 20 min
C. 4.46 min
D. 2.24 min

Answer

B

Explanation

`10 K=2.303"log"(1)/(1-(1)/(4))=2.303 "log"(4)/(3)`
`tk=2.303"log"(1)/(1-(1)/(16))=2.303"log"(16)/(15)`
`(1),(2)(t)/(10)=(("log"16)-("log"15))/(("log"4)-("log"3))=(0.028)/(0.125)`
`rArrt=(0.28)/(0.125)min=2.24min`