Fraction of molecules The exponential term in the Arrhenius equation is equal to

Question

Fraction of molecules The exponential term in the Arrhenius equation is equal to the fraction of molecules, f, with kinetic energy greater than or equal to the activation energy: f=eEa/(RT) Most scientific calculators have an ex function as the second function of the LN button.

Part B)

A certain reaction with an activation energy of 115 kJ/mol was run at 455 K and again at 475 K . What is the ratio of f at the higher temperature to f at the lower temperature? Express your answer numerically using one significant figure. Hint: not 10

Explanation / Answer

f = e-Ea/RT

Activation energy, Ea = 115kJ/mol = 115 * 103 J/mol

Value of R = 8.314 JK-1mol-1

At 455K,

f455 = e-115000/(8.314*455) = e-30.4 =6.27*10-14 =0.627 * 10-13

At 475K,

f475 = e-115000/(8.314*475) = e-29.12 = 2.25*10-13

Ratio, f475/f455 = 2.25 * 10-13/0.627 * 10-13 = 2.25/0.627 = 3.58 = 3.6 (approx)

f475/f455 = 3 (to one significant figure)

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