Disperse
late Middle English: from Latin dispers- ‘scattered’, from the verb dispergere, from dis- ‘widely’ + spargere ‘scatter, strew’.
wiktionary
From French disperser, from Latin dispersus, past participle of dispergere(“to scatter abroad, disperse”), from dis-(“apart”) + spargere(“to scatter”); see sparse.
etymonline
disperse (v.)
late 14c., dispersen, "to scatter, separate and send off or drive in different directions," from Latin dispersus, past participle of dispergere "to scatter," from dis- "apart, in every direction" (see dis-) + spargere "to scatter" (see sparse). The Latin word is glossed in Old English by tostregdan. Intransitive sense of "to separate and move apart in different directions without regularity" is from 1520s. Of clouds, fears, etc., "to dissipate," 1560s (transitive), 1590s (intransitive). Related: Dispersed; dispersing.