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In a reversible reaction, we are assuming that it is happening so slowly that no heat is lost to the surroundings. Therefore, the total change in entropy of the universe for a reversible reaction will be equal to zero, whereas the total change in entropy of the universe for an irreversible reaction will be greater than zero. The change in entropy of the two systems though, regardless of whether they are reversible or irreversible will be the same because entropy is a state variable.
To add on to that, it should be noted that reversible reactions have provide the maximum amount of work where as irreversible reactions provide substantially less since there is energy loss to heat, friction, etc.
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