Question

The activation energy for a particular reaction is Ea = 13.40 kJ. What percentage of the molecules are at or above the activation energy at 500.0 K?

Answer 1

Solution :-

Given data

Activation energy Ea = 13.40 kJ * 1000 J / 1 kJ = 13400 J

Temperature = 500.0 K

% of molecules above activation energy = ?

Following formula is used to calculate the fraction of molecules above the activation energy

Fraction of molecules above activation energy = e^(-Ea/RT)

Where R = 8.314 J per K. mol , T= kelvin temperature , Ea = activation energy

Now lets put the values in the formula

Fraction of molecules above activation energy = exp^{(- 13400 J / 8.314 J per K. mol * 500.0 K)}

                                                                                                          = 0.0398

Now lets convert this fraction to the percentage

0.0398 * 100 % = 3.98 %

Therefore at 500.0 K molecules above the activation energy are 3.98 %