Question

1) The speed constant for the second order reaction in the gas phase

It varies with the temperature according to the table below. Calculate the activation energy for the process, according to Arhhenius' equation

Answer 1

41.7 kJ/mol

Step-by-step explanation:

ln(k) = ln(A) − Eₐ/(RT)

Pick any two points. I'll choose 100°C and 400°C.

When T = 100°C = 373 K, k = 1.10×10⁻⁹ L/mol s:

ln(1.10×10⁻⁹) = ln(A) − Eₐ/(R × 373)

When T = 400°C = 673 K, k = 4.40×10⁻⁷ L/mol s:

ln(4.40×10⁻⁷) = ln(A) − Eₐ/(R × 673)

Subtract the two equations and solve:

ln(4.40×10⁻⁷) − ln(1.10×10⁻⁹) = -Eₐ/(R × 673) + Eₐ/(R × 373)

5.991 = 0.00120 Eₐ/R

Eₐ/R = 5013.4

Eₐ = 41700 J/mol

Eₐ = 41.7 kJ/mol