The rate constants for the first order reaction are $x$ s $^{- 1}$ at $300$ K and $y$ s $^{- 1}$ at $320$ K. Calculate the activation energy of the reaction.
$[R = 8.314$ J K $^{- 1}$ mol $^{- 1}$ and $y / x = 4]$

Question

The rate constants for the first order reaction are x s − 1 at 300 K and y s − 1 at 320 K. Calculate the activation energy of the reaction. [ R = 8.314 J K − 1 mol − 1 and y / x = 4 ]

TestHub · Accepted Answer

Using the Arrhenius equation: lo g ( k 1 ​ k 2 ​ ​ ) = 2.303 R E a ​ ​ ( T 1 ​ T 2 ​ T 2 ​ − T 1 ​ ​ ) Given k 1 ​ = x at T 1 ​ = 300 K and k 2 ​ = y at T 2 ​ = 320 K, with x y ​ = 4 . lo g ( 4 ) = 2.303 × 8.314 E a ​ ​ ( 300 × 320 320 − 300 ​ ) 0.602 = 19.147 E a ​ ​ ( 96000 20 ​ ) 0.602 = 19.147 E a ​ ​ ( 4800 1 ​ ) E a ​ = 0.602 × 19.147 × 4800 E a ​ = 55327 J mol − 1 ≈ 55.34 kJ mol − 1 Answer: 55.34 kJ.

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