For a reaction with rate = k[A]^n the initial rate is 6.4x10^-3 M s^-1 at [A] = 0.50 M and 8.0x10^-4 M s^-1 at [A] = 0.125 M. The initial rate at [A] = 0.0625 M is

JEE Advanced levelSingle correct optionDifficulty 3 of 3ck026

For a reaction with rate $= k [A]^{n}$ the initial rate is $6.4 \times 1 0^{- 3} M s^{- 1}$ at $[A] = 0.50 M$ and $8.0 \times 1 0^{- 4} M s^{- 1}$ at $[A] = 0.125 M$ . The initial rate at $[A] = 0.0625 M$ is

The concentration falls by 4 and the rate by 8, so

4^{n} = 8

and

n = 1.5

. Going from 0.50 M to 0.0625 M is a fall by a factor 8, so the rate falls by

8^{1.5} = 22.63

6.4 \times 1 0^{- 3} /22.63 = 2.83 \times 1 0^{- 4} M s^{- 1}