Consider the following reaction, the rate expression of which is given below $\mathrm{A}+\mathrm{B} \rightarrow \mathrm{C}$ rate $=k[\mathrm{A}]^{1/2}[\mathrm{B}]^{1/2}$ The reaction is initiated by taking 1 M concentration A and B each. If the rate constant (k) is $4.6 \times 10^{-2}\,\mathrm{s}^{-1}$, then the time taken for A to become 0.1 M is _____ sec. (nearest integer)

JEE Main · 2024 · 04 Apr 2024 · Shift 2 · Chemical Kinetics

Consider the following reaction, the rate expression of which is given below

A + B \to C

rate

= k [A]^{1/2} [B]^{1/2}

The reaction is initiated by taking 1 M concentration A and B each. If the rate constant (k) is

4.6 \times 1 0^{- 2} s^{- 1}

, then the time taken for A to become 0.1 M is _____ sec. (nearest integer)

Answer: 50

With

[A]_{0} = [B]_{0} = 1 M

and 1:1 stoichiometry,

[A] = [B]

at all times, so

r a t e = k [A]^{1/2} [B]^{1/2} = k [A]

: the reaction is pseudo-first-order in

A

k = \frac{2.303}{t} lo g \frac{[ A ] _{0}}{[ A ]} ⟹ 4.6 \times 1 0^{- 2} = \frac{2.303}{t} lo g \frac{1}{0.1} = \frac{2.303}{t}

t = \frac{2.303}{4.6 \times 1 0 ^{- 2}} \approx 50 s

JEE Main · 2024 · 04 Apr 2024 · Shift 2 · Integer answer