If you are bringing peace or calm to a state of unrest, you are pacifying the situation. Just think of the transformation a squalling baby undergoes when a pacifier is placed within his mouth, and you will remember the power of the verb to pacify.
If you work to establish peace in a certain location between factions at war, then you are working to pacify a country or region. The U.N. has specially trained workers, called peace keepers, who go into to trouble spots to try to pacify rebellions factions and restore order. Or, one can pacify a disgruntled crowd: "The store manager attempted to pacify the restless crowd of shoppers by promising the popular out-of-stock item would soon be back on the shelves."