[A] → [B] Reactant Product If formation of compound [B] follows the first order of kinetics and after 70 minutes the concentration of $[\mathrm{A}]$ was found to be half of its initial concentration. Then the rate constant of the reaction is $\mathrm{x} \times 10^{-6} \mathrm{~s}^{-1}$. The value of x is $\_\_\_\_$. (Nearest Integer)

JEE Main · 2022 · 27 Jul 2022 · Shift 2 · Chemical Kinetics

[A] → [B]
Reactant Product

If formation of compound [B] follows the first order of kinetics and after 70 minutes the concentration of

[A]

was found to be half of its initial concentration. Then the rate constant of the reaction is

x \times 1 0^{- 6} s^{- 1}

. The value of x is

____

.
(Nearest Integer)

Answer: 165

For a first-order reaction, the half-life is related to the rate constant by:

t_{1/2} = \frac{0.693}{k}

Given:

t_{1/2} = 70

minutes =

70 \times 60 = 4200

seconds

k = \frac{0.693}{4200} = \frac{0.693}{4200}

s⁻¹

k = \frac{6930}{42000} \times 1 0^{- 6}

s⁻¹

k = 165 \times 1 0^{- 6}

s⁻¹

Therefore, x = 165

JEE Main · 2022 · 27 Jul 2022 · Shift 2 · Integer answer