The invention relates to a method and apparatus for safely producing hydrogen peroxide by injecting dispersed minute bubbles of hydrogen and oxygen into a rapidly flowing liquid medium. The liquid medium can contain either a water-soluble organic compound, a water-insoluble organic compound, a combination of a water-insoluble organic compound with water, liquid carbon dioxide or supercritical carbon dioxide. The minute bubbles are surrounded by the liquid medium of sufficient volume for quench cooling any explosive reaction between the hydrogen and oxygen. The present invention also relates to reactors with internal catalyst structures and reactors that have a circular path, both of which may be used to produced hydrogen peroxide.