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Question

For the first order consecutive reaction :

Which of the following statement is incorrect ?

This question was previously asked in
MH SET 2025 Paper 2 Hindi Question Paper (15-Jun-2025)
The correct answer is

[B] is always greater than [C]

In a consecutive first-order scheme the intermediate B is formed from A and consumed to give C, so each species has a characteristic time profile. The question asks which description does not match.

"[B] is always greater than [C]" is the incorrect statement. B is an intermediate: it starts at zero, rises to a maximum, then falls back towards zero as it is converted onward. C is the final product: it starts at zero and rises monotonically towards the full initial amount of A. The two curves must therefore cross. At long times essentially all the material ends up as C while B has been consumed, so [C] greatly exceeds [B]. The claim holds only in the earliest part of the reaction, never "always".

"[A] decreases exponentially with time" is correct. A is consumed by a simple first-order step unaffected by anything downstream, so \([A] = [A]_0 e^{-k_1 t}\).

"[C] increases with an inverse exponential function" is correct in the sense meant — C follows a rising, saturating curve of the form \(1 - e^{-kt}\) terms, approaching \([A]_0\) asymptotically. Its curve is also sigmoidal at early times, showing an induction period while B accumulates.

"tmax depends on K1 and K2" is correct. Setting \(\frac{d[B]}{dt} = 0\) gives \(t_{max} = \frac{\ln(k_2/k_1)}{k_2 - k_1}\), which manifestly involves both rate constants.

Hence the incorrect statement is that [B] is always greater than [C].

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