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NEET CHEMISTRYChemical KineticsEasy

Question

For a reaction, activation energy Ea=0E_a = 0 and the rate constant at 200 K200 \text{ K} is 1.6×106 s11.6 \times 10^6 \text{ s}^{-1}. The rate constant at 400 K400 \text{ K} will be [Given that gas constant, R=8.314 J K1 mol1R = 8.314 \text{ J K}^{-1} \text{ mol}^{-1}]

A

3.2×104 s13.2 \times 10^4 \text{ s}^{-1}

B

1.6×106 s11.6 \times 10^6 \text{ s}^{-1}

C

1.6×103 s11.6 \times 10^3 \text{ s}^{-1}

D

3.2×106 s13.2 \times 10^6 \text{ s}^{-1}

Step-by-Step Solution

According to the Arrhenius equation, the relationship between the rate constant (kk) and temperature (TT) at two different temperatures is given by lnk2k1=EaR[1T11T2]\ln \frac{k_2}{k_1} = \frac{E_a}{R} \left[ \frac{1}{T_1} - \frac{1}{T_2} \right] . Given that the activation energy Ea=0E_a = 0, the right side of the equation becomes zero. Therefore, lnk2k1=0\ln \frac{k_2}{k_1} = 0, which implies k2k1=e0=1\frac{k_2}{k_1} = e^0 = 1, or k2=k1k_2 = k_1 . This means the rate constant is completely independent of temperature when the activation energy is zero. Thus, the rate constant at 400 K400 \text{ K} will remain exactly the same as at 200 K200 \text{ K}, which is 1.6×106 s11.6 \times 10^6 \text{ s}^{-1}.

Exam Context & Concepts Covered

This question aligns with the NEET CHEMISTRY syllabus, specifically targeting concepts from Chemical Kinetics. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

CHEMISTRYChemical Kineticsreactionactivationenergyconstantconstant

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