The Brunauer-Emmett-Teller BET theory is used to calculate the surface area of porous materials, such as activated carbon. In this case, we are given the mass of the activated carbon sample, its monolayer adsorption capacity, and its BET surface area.First, we need to find the mass of the adsorbed monolayer. To do this, we multiply the mass of the activated carbon sample by its monolayer adsorption capacity:Mass of monolayer = mass of activated carbon monolayer adsorption capacityMass of monolayer = 0.5 g 80 mg/gSince 1 g = 1000 mg, we need to convert the mass of the activated carbon to mg:Mass of monolayer = 500 mg 80 mg/g = 40000 mgNow that we have the mass of the adsorbed monolayer, we can calculate the total surface area of the activated carbon sample. To do this, we multiply the mass of the activated carbon sample by its BET surface area:Total surface area = mass of activated carbon BET surface areaTotal surface area = 0.5 g 900 m/g = 450 mSo, the total surface area of the activated carbon sample is 450 m.