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A pseudo first order reaction is actually a higher order reaction in which the concentrations of all the reactants except one is super high. This way, only the change in concentration of one reactant will be significant and you can solve for its concentration as if it was a real first order reaction.
A pseudo first order reaction is just another way of saying a second order reaction but under more ideal conditions in order to simplify your calculations. If the concentration of one reactant is in great excess, you may assume that it is constant, allowing it to be ignored so that the rate therefore relies solely on the concentration of the other reactant. This allows you to treat more complicated second order reactions as if they were first order reactions.
A regular first order reaction is just what it is. A pseudo first order reaction means that the reaction is not actually first order because there are other reactants whose concentration will affect the rate of reaction. However, we can calculate what is the order of reaction for a certain reactant by making the other reactants have a very large concentration. After plotting the graph of [A] against t, we can see that the reaction is first order with respect to A.
Dr. Lavelle gave an example in class that really helped me understand this. He said that if a person has a million dogs, and gives a few away, that person will still have about a million dogs. The number doesn't realllllyyy change. Similarly, for a pseudo-first order reaction, one of the other reactant's concentration will be so much higher than the one you are studying that, over time, as A (the one you are observing) concentration changes, the others don't really. It makes the math and analysis easier for more complex reactions.
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