A first order reaction has a half-life of 60 min and an initial rate of 4.0x10^-3 M min^-1. Find its rate after 150 min, in units of 10^-4 M min^-1 (two decimals; ln 2 = 0.693).

JEE Advanced levelNumerical answerDifficulty 3 of 3ck052

A first order reaction has a half-life of $60 min$ and an initial rate of $4.0 \times 1 0^{- 3} M mi n^{- 1}$ . Find its rate after $150 min$ , in units of $1 0^{- 4} M mi n^{- 1}$ (two decimals; $ln 2 = 0.693$ ).

Numerical answer type, answer in 10^-4 M min^-1, tolerance 0.02.

For first order, rate

= k [A]

, so the rate decays with the same half-life as the concentration (here

k = 0.693/60 = 0.01155 mi n^{- 1}

[A]_{0} = 0.346 M

). Since

150/60 = 2.5

half-lives, rate

= 4.0 \times 1 0^{- 3} \times (1/2)^{2.5} = 4.0 \times 1 0^{- 3} \times 0.17678 = 7.07 \times 1 0^{- 4} M mi n^{- 1}