To calculate the specific surface area of the activated carbon, we can use the Brunauer-Emmett-Teller BET equation. However, since we are assuming a monolayer of adsorbate, we can use the simpler Langmuir adsorption model.First, we need to find the number of moles of nitrogen gas adsorbed:n = mass / molar massn = 0.45 g / 28.02 g/mol molar mass of N2 n = 0.0161 molNow, we can use the ideal gas law to find the volume of nitrogen gas adsorbed at STP Standard Temperature and Pressure: 273 K and 1 atm :PV = nRTV = nRT / PV = 0.0161 mol 0.0821 L atm/mol K 273 K / 1 atmV = 0.361 LSince we know that nitrogen gas occupies a volume of 22.4 L/mol, we can find the surface area occupied by the adsorbed nitrogen gas:surface area = volume adsorbed / volume per mole * area per molearea per mole = 6.022 x 10^23 molecules/mol * 0.162 nm^2/molecule cross-sectional area of N2 area per mole = 9.76 x 10^4 m^2/molsurface area = 0.361 L / 22.4 L/mol * 9.76 x 10^4 m^2/molsurface area = 1.56 x 10^3 m^2Now, we can find the specific surface area by dividing the surface area by the mass of the activated carbon sample. However, the mass of the activated carbon sample is not provided. If you have the mass of the activated carbon sample, you can divide the surface area 1.56 x 10^3 m^2 by the mass to get the specific surface area in m^2/g.