sphere for three different catalysts. Same diameter, but the concentration profiles are

significantly different, and the question is, which one of these catalysts is going

to react the largest amount of reactant in a given time? It's the same reaction, and

we also require to indicate any assumptions. So there's not really sufficient information

to answer this. We can make some assumptions, and depending on which assumptions we make,

we can end up with different answers. So one assumption is that the rate constant is the

same. Well if we make this assumption, then it's easy to determine that catalyst 1 reacts

the most, because the amount that reacts is going to be the rate constant times the concentration

inside the catalyst, and since the concentration is changing we integrate over the volume of

the catalyst. Each catalyst has the same volume, so if the rate constant is the same, the one

with the highest concentration is going to have the highest rate, and so that's catalyst

1. The other extreme would be to assume that the diffusivities are the same for each of

the catalysts. This means the rate constants are different, and now the catalyst with the

highest rate is going to be catalyst 3 because the gradient, diffusivity times the change

in concentration of A with respect to radius evaluated at the external surface, evaluated

here, for how much is diffusing into the catalyst because whatever diffuses in reacts. If the

diffusivity is the same then the one with the largest gradient, which is catalyst 3

has the largest gradient here, and therefore the most is diffusing in, and so this would

say the k3 is larger than k2, larger than k1, and therefore the most that reacts now

is in catalyst 3. So you can see, just from these concentration gradients comparing different

catalyst, we need more information to reach a conclusion as to which is reacting the most

material per time.