To calculate the surface area of the activated carbon powder, we can use the Brunauer-Emmett-Teller BET theory, which relates the amount of gas adsorbed to the surface area of the adsorbent. In this case, we are given the volume of nitrogen gas adsorbed, the temperature, and the pressure. We can use the following steps to find the surface area:1. Convert the volume of nitrogen gas to moles using the ideal gas law.2. Calculate the number of nitrogen molecules adsorbed.3. Multiply the number of nitrogen molecules by the cross-sectional area of a nitrogen molecule to get the surface area.Step 1: Convert the volume of nitrogen gas to molesPV = nRTWhere:P = pressure 1 atm V = volume 12 mL = 0.012 L n = moles of nitrogen gasR = ideal gas constant 0.0821 L atm / K mol T = temperature 77 K n = PV / RTn = 1 atm * 0.012 L / 0.0821 L atm / K mol * 77 K n 0.0019 molesStep 2: Calculate the number of nitrogen molecules adsorbedNumber of molecules = moles * Avogadro's numberNumber of molecules = 0.0019 moles * 6.022 x 10^23 molecules/molNumber of molecules 1.14 x 10^21 moleculesStep 3: Multiply the number of nitrogen molecules by the cross-sectional area of a nitrogen moleculeSurface area = Number of molecules * Cross-sectional area of a nitrogen moleculeSurface area = 1.14 x 10^21 molecules * 0.16 nm/moleculeSurface area 1.82 x 10^21 nmThe surface area of the given sample of activated carbon powder is approximately 1.82 x 10^21 nm.