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 165 kJ/mol was run at 555 K and again at 575 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.

Explanation / Answer

Using the equation given above,

f = e^(-Ea/RT)

ln(f2/f1) = Ea/R[1/T1 - 1/T2]

with,

Ea = 165 kJ/mol

R = gas constant

T1 = 555 K

T2 = 575 K

f2/f2 = ratio fraction f at higher to lower temperature

we get,

ln(f2/f1) = 165,000/8.314 [1/555 - 1/575]

(f2/f1) = 3.5

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