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A chemical reaction was carried out at \( 300 \mathrm{K} \) and \( 280 \mathrm{K} \). The rate constants were found to be \( K_{1} \) and \( K_{2} \) at \( 300 \mathrm{K} \) and \( 280 \mathrm{K} \) respectively. Then which of the following is true?

1. \( K_{1}=4 K_{1} \)
2. \( K_{2}=2 K_{1} \)
3. \( K_{2}=0.25 K_{1} \)
4. \( K_{2}=0.5 K_{1} \)

Correct answer: \( K_{2}=0.5 K_{1} \)

Solution

For most reactions, the rate constant increases with temperature according to the Arrhenius equation. Since 280 K is lower than 300 K, the rate constant at 280 K must be smaller than at 300 K, matching the given relation.

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