Difference between First Order Reactions and Second Order Reactions

[Nathan Mariano 2G]

What is the difference between first-order reactions and second-order reactions? How does that change the value of n?

[Eva Guillory 2E]

https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Kinetics/Experimental_Methods/Methods_of_Determining_Reaction_Order has some useful descriptions to help differentiate them:

"In a first-order reaction, the reaction rate is directly proportional to the concentration of one of the reactants. First-order reactions often have the general form A → products."

"The simplest kind of second-order reaction is one whose rate is proportional to the square of the concentration of one reactant. These generally have the form 2A → products. A second kind of second-order reaction has a reaction rate that is proportional to the product of the concentrations of two reactants. Such reactions generally have the form A + B → products. An example of the former is a dimerization reaction, in which two smaller molecules, each called a monomer, combine to form a larger molecule (a dimer). "