Question

What is the surface area of a sample of activated carbon if 10 mL of nitrogen gas (at a temperature of 25°C and a pressure of 1 atm) is adsorbed onto 0.1 g of the carbon with a monolayer capacity of 0.5 mL/g?

Answer 1

To calculate the surface area of the activated carbon, we need to first determine the volume of nitrogen gas adsorbed as a monolayer on the carbon.Given:- Volume of nitrogen gas adsorbed = 10 mL- Mass of activated carbon = 0.1 g- Monolayer capacity = 0.5 mL/gFirst, we need to find the volume of nitrogen gas adsorbed as a monolayer:Volume of nitrogen gas adsorbed as a monolayer = mass of activated carbon  monolayer capacity= 0.1 g  0.5 mL/g= 0.05 mLNext, we need to find the surface area of the activated carbon using the Brunauer-Emmett-Teller  BET  equation:Surface area  A  =  V_mono  N_A  A_N2  /  mass of activated carbon Where:- V_mono is the volume of nitrogen gas adsorbed as a monolayer  0.05 mL - N_A is Avogadro's number  6.022  10^23 molecules/mol - A_N2 is the cross-sectional area of a nitrogen molecule  0.162 nm First, we need to convert the volume of nitrogen gas adsorbed as a monolayer from mL to moles. We can use the ideal gas law equation  PV = nRT  for this conversion:n = PV / RTWhere:- P is the pressure  1 atm - V is the volume  0.05 mL = 0.00005 L - R is the ideal gas constant  0.0821 L atm/mol K - T is the temperature  25C = 298 K n =  1 atm  0.00005 L  /  0.0821 L atm/mol K  298 K n = 2.03  10^-6 molNow we can calculate the surface area of the activated carbon:A =  2.03  10^-6 mol  6.022  10^23 molecules/mol  0.162 nm  /  0.1 g A = 2.01  10^18 nm/gSo, the surface area of the activated carbon is approximately 2.01  10^18 nm/g.