The BET Brunauer-Emmett-Teller surface area is a widely used parameter to characterize the surface area of porous materials. To calculate the BET surface area, we can use the following formula:BET surface area = Amount of physisorbed nitrogen / Monolayer coverage Surface areaGiven the amount of physisorbed nitrogen N is 4.2 mol/g, the monolayer coverage M is 16.2 mol/m, and the surface area S is 500 m/g, we can plug these values into the formula:BET surface area = 4.2 mol/g / 16.2 mol/m 500 m/gBET surface area = 0.259259259 500 m/gBET surface area 129.63 m/gTherefore, the BET surface area of the mesoporous silica is approximately 129.63 m/g.