For the thermal decomposition of a gaseous compound, the plot of ₁₀ k versus 1 T yields a straight line with a slope of -6.0 10^3 K . What is the activation energy ( E_a ) for this reaction? [Given: R = 8.314 J K ⁻¹ mol ⁻¹ and 2.303 8.314 = 19.15 J K ⁻¹ mol ⁻¹ ]

Step-by-step solution

According to the Arrhenius equation: k = A e^ -E_a / RT Taking logarithm to the base 10 on both sides: ₁₀ k = ₁₀ A - E_a 2.303 RT Comparing this with the equation of a straight line y = mx + c , the slope m of the plot of ₁₀ k versus 1 T is given by: m = - E_a 2.303 R Given that the slope is -6.0 10^3 K : - E_a 2.303 R = -6.0 10^3 E_a = 6.0 10^3 2.303 R Substituting the given value of 2.303 R = 19.15 J K ⁻¹ mol ⁻¹ : E_a = 6.0 10^3 19.15 J mol ⁻¹ E_a = 114900 J mol ⁻¹ = 114.9 kJ mol ⁻¹ Answer: 114.9 kJ mol ⁻¹