To calculate the thickness of a monolayer of gas adsorbed on the surface of a solid using the BET theory, we need to know the specific surface area of the solid, the volume of gas adsorbed at standard pressure, and the cross-sectional area of the adsorbed gas molecule.Given:Specific surface area A = 100 m/gVolume of gas adsorbed V = 10 mL/g = 0.01 L/g converted to liters We also need to know the cross-sectional area of the adsorbed gas molecule. For simplicity, let's assume the gas is nitrogen N2 , which is commonly used in BET experiments. The cross-sectional area of a nitrogen molecule is approximately 0.162 nm.First, we need to find the number of moles of gas adsorbed per gram of solid. We can use the ideal gas law for this:PV = nRTWhere:P = pressure 1 atm, standard pressure V = volume of gas adsorbed 0.01 L/g n = number of moles of gasR = ideal gas constant 0.0821 L atm/mol K T = temperature 298 K, room temperature Rearranging the equation to solve for n:n = PV / RTn = 1 atm 0.01 L/g / 0.0821 L atm/mol K 298 K n = 0.000407 mol/gNow, we can calculate the number of gas molecules adsorbed per gram of solid N :N = n Avogadro's numberN = 0.000407 mol/g 6.022 10 molecules/molN = 2.45 10 molecules/gNext, we can find the total surface area occupied by the adsorbed gas molecules S :S = N S = 2.45 10 molecules/g 0.162 nm/moleculeS = 3.97 10 nm/gNow, we can calculate the thickness of the monolayer t using the specific surface area A and the total surface area occupied by the adsorbed gas molecules S :t = S / At = 3.97 10 nm/g / 100 m/g 10 nm/m converted m to nm t = 3.97 nmSo, the thickness of a monolayer of gas adsorbed on the surface of the solid using the BET theory is approximately 3.97 nm.