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  • In this problem, we're given the concentration of a reactant inside of a porous catalyst

  • 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.

In this problem, we're given the concentration of a reactant inside of a porous catalyst

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