Question

if the decomposition of N2O5 has an activation energy of 103 kJ/mole and a frequency factor of 4.3 *10^13 s^-1. what is the rate constant for this decomposition at 20°C?100°C?

Answer 1

Arrhenus equation k = A e^-Ea/RT

where k = rate constant

A = frequency factor

Ea = activation energy

R= universal gas constant = 8.314 J/K/mol

T = temperature

Rate constant at 20oC :

k = A e^-Ea/RT

Given that T = 20^oC = 20 + 273 K = 293 K

A = 4.3x10¹³ s^-1

Ea = 103 kJ/mole = 103000 J/mol

Hence,

k = A e^-Ea/RT

   = ( 4.3x10¹³ s^-1)  e^{-(103000 J/mol/  8.314 J/K/mol x 293 K)}

   = 1.86 x 10^-5

k = 1.86 x 10^-5

Therefore,

rate constant at 20oC = 1.86 x 10^-5

Rate constant at 100oC :

k = A e^-Ea/RT

Given that T = 100^oC = 100 + 273 K = 373 K

A = 4.3 x 10¹³ s^-1

Ea = 103 kJ/mole = 103000 J/mol

Hence,

k = A e^-Ea/RT

   = ( 4.3 x 10¹³ s^-1)  e^{-(103000 J/mol/  8.314 J/K/mol x 373 K)}

   = 0.16

k = 0.16

Therefore,

rate constant at 100oC = 0.16