Subtitles section Play video Print subtitles 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.