A plot of k versus 1 T (where T is temperature in Kelvin) for a chemical reaction yields a straight line passing through the points (3 10⁻³ K ⁻¹, -4) and (4 10⁻³ K ⁻¹, -10) . The activation energy of the reaction is ________ kJ mol ⁻¹ . [Gi

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A plot of k versus 1 T (where T is temperature in Kelvin) for a chemical reaction yields a straight line passing through the points (3 10⁻³ K ⁻¹, -4) and (4 10⁻³ K ⁻¹, -10) . The activation energy of the reaction is ________ kJ mol ⁻¹ . [Given: R = 25 3 J K ⁻¹ mol ⁻¹ ]

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Correct answer: 50

The Arrhenius equation is given by: k = A - E_a RT The plot of k versus 1 T is a straight line with slope m = - E_a R . Using the given points (x₁, y₁) = (3 10⁻³, -4) and (x₂, y₂) = (4 10⁻³, -10) , the slope is: m = y₂ - y₁ x₂ - x₁ = -10 - (-4) 4 10⁻³ - 3 10⁻³ m = -6 1 10⁻³ = -6000 K Equating the slope to - E_a R : - E_a R = -6000 E_a = 6000 R = 6000 25 3 J mol ⁻¹ E_a = 2000 25 = 50000 J mol ⁻¹ Converting to kJ mol ⁻¹ : E_a = 50 kJ mol ⁻¹ Answer: 50

A plot of k versus 1 T (where T is temperature in Kelvin) for a chemical reaction yields a straight line passing through the points (3 10⁻³ K ⁻¹, -4) and (4 10⁻³ K ⁻¹, -10) . The activation energy of the reaction is ________ kJ mol ⁻¹ . [Given: R = 25 3 J K ⁻¹ mol ⁻¹ ]

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