Multiphase reactors, in which a bubble stream exists, are widely used in chemical and energy engineering industry To design these reactors the phase interface has to be calculated. The interface can be reduced to the size distribution of the bubbles, and only by much work may this size distribution be calculated together with the balanced equations of coalescence and the occurrence of decomposition of each bubble fraction, This paper gives these balanced equations with the aid of a simplifying analytical approximation, The result is only one balanced equation either for the average bubble volume or the specific phase interface, In the first part of the paper above only the specific phase interface and the size distribution of the bubbles in the column with regard to low gas contents and pure liquids with law viscosities are calculated, Big bubbles and gas plugs are not considered.