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JEE MainChemistryChemical Kinetics

For a first order reaction, the Arrhenius equation is given as ₁₀ k = 14 - 1.25 10^4 T . If the half-life of the reaction is 6.93 10^5 s , the temperature at which the reaction occurs is ________ K . (Nearest integer)

Correct answer

625

Step-by-step solution

For a first order reaction, the rate constant k is related to the half-life t_ 1/2 by: k = 0.693 t_ 1/2 Substituting the given half-life: k = 0.693 6.93 10^5 = 10⁻⁶ s ⁻¹ Taking the base-10 logarithm of k : ₁₀ k = ₁₀(10⁻⁶) = -6 Substitute this value into the given Arrhenius equation: -6 = 14 - 1.25 10^4 T Rearranging the equation to solve for T : 1.25 10^4 T = 14 - (-6) 1.25 10^4 T = 20 T = 1.25 10^4 20 = 12500 20 = 625 K Answer: 625

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