We know that adding a catalyst provides an alternative pathway with lower activation energy. My concern is how would the amount of catalyst change that? For example experimentally if I increase the amount of catalyst from 10mol% to 20mol% then the reaction would be faster. But what affect would it have on the rate-constant and the half-life of the reaction?
The effect of a catalyst is indeed to lower the activation energy of the reaction providing an alternative path for it to occur. This means that as long as the amount of catalyst is limiting step of the reaction kinetics, increasing the amount of catalyst will increase the velocity, the rate constant. After a certain amount of catalyst is available which exceeds the stoichiometric amount of reactive species involved, parts of it will remain "unused" in the bulk and you will stop seeing an increase in the rate constant.
About the half-life of the reaction. Consider, for example a homogenous first order irreversible reaction: You know that its half-life = ln2/K K is the rate constant, dependent on temperature, ionic strength, surface area of reactant, available energy, presence of catalyst.
Which depends upon temperature, ionic strength, available energy, presence of catalyst. The k term explicit the dependency of the rate constant of the temperature: K = k. e^-E/RT E is the activation energy, R is the gas constant, K is the frequency factor, and T is the temperature. So K ( rate constant ) depends on temperature and activation energy.
If you increase K, you decrease the half-life.
Your question: "But what affect would it have on the rate-constant and the half-life of the reaction?" demonstrates that your understanding of catalytic processes is naive. The reaction mechanism of a catalytic process is commonly rather complex. The dependence of the kinetics of a substrate consumption in a catalytic reaction is not predictable.
What system do you mean. What is the catalyst? What does it mean 10 mole %? Is 1/10 of the substrate mixture in moles a catalyst? In homogeneous catalysis, the reaction rate and t1/2 depends on the catalyst concentration. At low concentrations, the relationship: r = f(ccat) can be linear, with larger concentrations not. But start with specifying the system. Regards,
I agree with Yuri and Miroslaw that more information is needed to properly answer this question. I assume from the term half-life that you probably have a single reactant being consumed by a first order irreversible reaction and your question is what happens if you keep the feed rate the same but increase the concentration of the catalyst. In some cases (but not always) this will increase the amount of reaction that takes place. I hope this helps. We could all probably help more if you clarify the question.
One could write a lot and guess a lot more, but let's wait what the questioner will write. Regards,
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