A graph of k versus 1 T is plotted for a chemical reaction, yielding a straight line that passes through the coordinates (2 10⁻³ K ⁻¹, 15) and (3 10⁻³ K ⁻¹, 5) . The activation energy for the reaction is ________ kJ mol ⁻¹ . (Nearest intege

Question

A graph of k versus 1 T is plotted for a chemical reaction, yielding a straight line that passes through the coordinates (2 10⁻³ K ⁻¹, 15) and (3 10⁻³ K ⁻¹, 5) . The activation energy for the reaction is ________ kJ mol ⁻¹ . (Nearest integer) (Given : R = 8.3 J K ⁻¹ mol ⁻¹ )

Quantrex Academy · Accepted Answer

Correct answer: 83

The Arrhenius equation is given by: k = A - E_a RT This represents a straight line equation y = mx + c , where y = k and x = 1 T . The slope of the line is m = - E_a R . Using the given coordinates (x₁, y₁) = (2 10⁻³, 15) and (x₂, y₂) = (3 10⁻³, 5) , the slope is: m = y₂ - y₁ x₂ - x₁ = 5 - 15 3 10⁻³ - 2 10⁻³ = -10 10⁻³ = -10^4 K Equating the slope to - E_a R : - E_a R = -10^4 E_a = 10^4 8.3 = 83000 J mol ⁻¹ Converting to kJ mol ⁻¹ : E_a = 83 kJ mol ⁻¹ Answer: 83

A graph of k versus 1 T is plotted for a chemical reaction, yielding a straight line that passes through the coordinates (2 10⁻³ K ⁻¹, 15) and (3 10⁻³ K ⁻¹, 5) . The activation energy for the reaction is ________ kJ mol ⁻¹ . (Nearest integer) (Given : R = 8.3 J K ⁻¹ mol ⁻¹ )

Correct answer

Step-by-step solution

More from Chemical Kinetics