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A reversible reaction occurs when reactants form products and the products (with the aid of reactant(s)) is able to revert back to the reactants (both chemical reactions can occur, for example let's say O2+2H2->2H2O is reversible, water can be separated to form oxygen gas and hydrogen gas and vice versa). In an irreversible reaction, the reaction only goes in one direction (say the same example given above was irreversible, water could not convert back into O2 gas and H2 gas.
Two things that whether or not a system is reversible can affect is entropy and work done on the environment. In the case of a reversible process, Delta S system = -Delta S surrondings. This is not the case with an irreversible process.
For the calculations for work, it is affected in the formulas for irreversible expansion and reversible expansion. For irreversible expansion, work is equal to negative pressure times delta V while reversible expansion is equal to negative nRT times the natural log of V2 over V1.
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