Quick doubt about catalysis modeling

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The discussion centers on the relationship between the partial pressure of oxygen (O2) raised to the 1/2 power and its role in the formation of PSO3 in catalysis modeling. Participants express confusion over how to accurately represent pressures of reactants and products when they are raised to different exponents. The author of the referenced material appears to have made an approximation that lacks clear explanation, leading to frustration among readers. The specific chemical reaction being studied is not explicitly stated but involves the conversion of O2 in the context of catalysis. Overall, the conversation highlights the challenges in understanding catalysis modeling and the need for clearer explanations in educational materials.
Est120
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reading J M Smith "Chemical engineering kinetics" there is a part in the book that i can't really understand
how does the partial pressure of oxygen (O2) that is raised to the (1/2) power "magically" combines to give PSO3? , i know that at constant Temperature you can pretty much express pressures between reactants and products using conversion but still you won't be able to factorize because they are raised to different exponent number, i think the author made an approximation but as usual they never explain anything, this book really sucks tbh lol
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