# Effect of a catalyst on the rate of reaction

Submitted by Haneen on Thu, 04/05/2007 - 23:35

The decomposition of NH3 to N2 and H2 was studied on two surfaces:

Surface  E a (kJ/mol)
W            163
Os          197

Without a catalyst, the activation energy is 335 kJ/mol.

How many times faster is the reaction at 275. K on the W surface compared with the reaction with no catalyst present? Assume the frequency factor A is the same for each reaction.

set up a ratio of the Arrhenius equations and solve for the ratio of rate constants.

How can we set up a ratio if the concentration is unknown? even if it was the same, won't that affect the ratio? I tried to solve it ignoring the concentration and it didn't work.

To solve this, use Arrhenius equation in the form

k = A e -Ea/RT

the rate of the reaction is proportional to the rate constant , k

you need a ratio of the k's with and without the catalyst

kw/o catalyst = Aw/o catalyst e -Ea[sub]w/o catalyst[/sub]/RT

kw/ catalyst =A w/ catalyst e -Ea[sub]w/ catalyst[/sub]/RT

(w/ mean with and w/o means without)

ok since the problem said A w/o = A w/  (A is proportionaly to the frequency of collisions)

when we take the ratio of  kw/ / kw/o  the A term will cancel

so you have

kw/ catalyst = e -Ea[sub]w/ catalyst[/sub]/RT
_______      ________________________________
kw/o catalyst =  e -Ea[sub]w/o catalyst[/sub]/RT

Plug in your numbers and it will give you how many times the catalyst reaction is.