Question

The activation energy for a reaction is changed from 184 kJ/mol to 59.3 kJ/mol at 600. K by the introduction of a catalyst. If the uncatalyzed reaction takes about 2653 years to occur, about how long will the catalyzed reaction take? Assume the frequency factor A is constant and assume the initial concentrations are the same

Answer 1

Arrhenius equation is

rate constant, k= Ae^-Ea/RT

A = frequency fsctor

Ea = Activation energy

R= gas constant , 8.314J/K mol

T = Temperature in Kelvin , 600K

Arrhenius equation for the reaction without catalyst

k1 = A e^-Ea1/RT

= Ae-184kJ/mol/(0.008314kJ/mol × 600K )

= A e^-36.89

Arrhenius equation for the reaction with catalyst

k2 = Ae^-Ea2/RT

  = A e^{- 59.3kJ/mol/(0.008314kJ/mol × 600K)}

  = A e^{- 11.89}

^{divide k1 by k2}

k1/k2 = e^-36.89/e^-11.89

take ln on both side

ln(k1/k2) = -36.89 + 11.89

ln(k1/k2) = - 25

2.303log(k1/k2) = -25

log(k1/k2) = - 10.855

k1/k2 = 1.396×10^-11

k2 = 7.163×10¹⁰ × k1

Initial concentrations are same

So,

the reaction with catalyst is 7.163×10¹⁰ fold faster than reaction without catalyst

Therefore,

Time would take for the catalysed reaction = 2653yr/7.163×10¹⁰ = 3.704× 10^-8 year = 0.01947 minute