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Pseudo rate laws are useful in finding the overall rate law when a reaction has multiple reactants with changing concentrations. What this allows is to assume that the concentrations of the other reactants do not change, so the reaction appears as a first order.
To find the overall rate of reactions with multiple reactants, one needs to use experimental data to find the rate law (and thus the order of each reactant). To do this, we make the concentration of all except one reactant so that we can assume constant concentration while observing how only one reactant influences the reaction. If we attain a 1st order when looking at the experimental data, we call it a pseudo-1st order (if it is another order it would be psuedo n order) because we create an artificial system to determine the order thus we don't have 100% assurance that it is truly a 1st order (or n order) reaction.
When working with pseudo-1st order rate laws, it's also important to note that the order(n) is usually determined by looking at linear plots of [A] vs t (n=0), ln([A]) vs t (n=1), and (1/[A]) vs t (n=2). Whichever one is linear tells you which order the reaction is.
I found this link that really helped me with this topic. https://chem.libretexts.org/Core/Physic ... _reactions
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