For a reaction, activation energy $E_{a} = 0$ and the rate constant at 200 K is $1.6 \times 10^{6} s^{- 1}$ . The rate constant at 400 K will be [Given that gas constant, R = $8.314 J K^{- 1} {mol}^{- 1}$ ]

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$1.6 \times 10^{6} s^{- 1}$

$3.2 \times 10^{6} s^{- 1}$

$3.2 \times 10^{4} s^{- 1}$

$1.6 \times 10^{3} s^{- 1}$

answer is C.

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Detailed Solution

From Arrhenius equation

$\log \frac{k_{400}}{k_{200}} = \frac{E_{a}}{2 .303 R} [\frac{T_{2} - T_{1}}{T_{1} T_{2}}]$

$Since, given that E_{a} = 0 ∴ \log \frac{k_{400}}{k_{200}} = 0 = \log 1 \Rightarrow \frac{k_{400}}{k_{200}} = 1 So, k_{400} = k_{200} So rate constant at 400 K = 1.6 \times 10^{6} s^{- 1}$

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