JEE Main · 2025 · 03 Apr 2025 · Shift 1 · Chemical Kinetics

In a reaction

A + B \to C

, initial concentrations of

A

and

B

are related as

[A]_{0} = 8 [B]_{0}

. The half lives of

A

and

B

are 10 min and 40 min . respectively. If they start to disappear at the same time, both following first order kinetics, after how much time will the concentration of both the reactants be same?

(A)60 min
(B)80 min
(C)20 min
(D)40 min✓ Correct

Answer: (D)

Solution

For a first-order reactant the concentration decays as

[X]_{t} = [X]_{0} e^{- k t}

with

k = \frac{ln 2}{t _{1/2}}

, so

k_{A} = \frac{ln 2}{10}

and

k_{B} = \frac{ln 2}{40}

. Equal concentrations require

[A]_{0} e^{- k_{A} t} = [B]_{0} e^{- k_{B} t}

, and with

[A]_{0} = 8 [B]_{0}

this becomes

8 = e^{(k_{A} - k_{B}) t}

, giving

ln 8 = (k_{A} - k_{B}) t

. Substituting,

3 ln 2 = ln 2 (\frac{1}{10} - \frac{1}{40}) t = ln 2 \cdot \frac{3}{40} t

, so

3 = \frac{3}{40} t

. The two concentrations become equal after

t = 40

min.

JEE Main · 2025 · 03 Apr 2025 · Shift 1 · Single correct option

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JEE Main · 2025 · 03 Apr 2025 · Shift 1 · Chemical Kinetics

Solution

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