Question

Using the thermodynamic interpretation of the Arrhenius equation, the pre-exponential factor can be expressed as: A =- sed as: A - koT - EAST Use this equation to determine a value for the largest possible rate constant for a reaction is at 300 K, which you would get if Gibbs free energy of activation AG# = 0 and the entropy of activation ASF = 0. From your answer, how long does it take for a single reaction event to occur?

Answer 1

Given

kyT AS elka

k = Ae^-E_a/RT

T = 300 K

$\Delta$S^# = 0

k_b = 1.38 x 10^-23 m² kg s^-2 K^-1

h = 6.626 x 10^-34 m² kg s^-1

The maximum rate constant is required to be found

k is maximum when enery of activation, E_a = 0,

Using these values we get,

A = 1.38 x 10^-23 x 300/6.626 x 10^-34 s^-1

= 6.25 x 10¹² s^-1

maximum rate constant, k_max = A =  6.25 x 10¹² s^-1 = collision frequency

Therefore time taken for collision = 1/collision frequency = 1/6.25 x 10¹² s

= 1.6 x 10^{-13 s}

Therefore, time required for a single event = 1.6 x 10^-13 s