Question

Calculate the fraction of atoms in a sample of argon gas at 384K that have an energy of 10.7kJ or greater.

Answer 1

Apply Arrhenius equation here:
k = Ae^(-E_a/RT)
here we only want to look at the e^(-_Ea/RT) part.

I don't know if you have learned this but what the Arrhenius equation really means is:
k = pfZ where

p = fraction of collisions that occur with reactant molecules properly oriented
f = fraction of collisions having energy greater than the activation energy
Z = frequency of collisions

Now in the Arrhenius equation, p and Z have been combined to form A, and f is the part that says e^(-Ea/RT)

f = e^(-10.7 x 10^3 J/mol/(8.31 J/mol-K x 384 K))
f = 0.035

So the answer is 0.035 or 3.5%.