The rate constant for the reaction A B + C at 500 ~K is given as 0.004 ~s ⁻¹ . At what temperature will the rate constant become 0.014 ~s ⁻¹ ? E _ a for the reaction is 18.231 ~kJ .

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Correct answer: B. 700 K

The Arrhenius equation is given by ( k₂ k₁ ) = E_a R ( T₂ - T₁ T₁ T₂ ) . Given values are k₁ = 0.004 s ⁻¹ , T₁ = 500 K , k₂ = 0.014 s ⁻¹ , and E_a = 18.231 kJ/mol = 18231 J/mol . The gas constant R = 8.314 J K ⁻¹ mol ⁻¹ . Substituting the values into the equation: ( 0.014 0.004 ) = 18231 8.314 ( T₂ - 500 500 T₂ ) (3.5) = 2192.8 ( T₂ - 500 500 T₂ ) 1.25276 = 4.3856 ( T₂ - 500 T₂ ) 0.28565 = 1 - 500 T₂ 500 T₂ = 1 - 0.28565 = 0.71435 T₂ = 500 0.71435 700 K . Answer: 700 K

The rate constant for the reaction A B + C at 500 ~K is given as 0.004 ~s ⁻¹ . At what temperature will the rate constant become 0.014 ~s ⁻¹ ? E _ a for the reaction is 18.231 ~kJ .

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