To calculate the enthalpy of adsorption of nitrogen gas on the surface of activated charcoal, we can use the Langmuir adsorption isotherm equation and the Clausius-Clapeyron equation.The Langmuir adsorption isotherm equation is given by: = P * K / 1 + P * K where is the fractional coverage of the surface, P is the equilibrium pressure of nitrogen, and K is the Langmuir adsorption constant.The Clausius-Clapeyron equation is given by:ln K = -H_ads / R * 1/T + Cwhere H_ads is the enthalpy of adsorption, R is the gas constant 8.314 J/mol*K , T is the temperature in Kelvin, and C is a constant.First, we need to find the fractional coverage of the surface. Since the surface area of the charcoal is given as 1200 m^2/g, we can assume that the surface is fully covered when 1 g of nitrogen is adsorbed. The molar mass of nitrogen N2 is 28 g/mol. Therefore, the maximum amount of nitrogen that can be adsorbed on the surface is:1 g / 28 g/mol = 0.0357 molNow, we can calculate the number of moles of nitrogen adsorbed at the given equilibrium pressure 8.5 x 10^-3 atm :n = P * V / R * TAssuming a volume of 1 L 0.001 m^3 for simplicity:n = 8.5 x 10^-3 atm * 0.001 m^3 / 8.314 J/mol*K * 298 K n 3.43 x 10^-6 molNow, we can calculate the fractional coverage : = n / 0.0357 mol 9.61 x 10^-5Now, we can use the Langmuir adsorption isotherm equation to find the Langmuir adsorption constant K : = P * K / 1 + P * K 9.61 x 10^-5 = 8.5 x 10^-3 atm * K / 1 + 8.5 x 10^-3 atm * K Solving for K:K 1.13 x 10^-2 atm^-1Now, we can use the Clausius-Clapeyron equation to find the enthalpy of adsorption H_ads :ln K = -H_ads / R * 1/T + Cln 1.13 x 10^-2 = -H_ads / 8.314 * 1/298 + CTo find the constant C, we need more data points at different temperatures. However, since we only have data at 298 K, we can't determine the exact value of H_ads. In practice, experimental data at different temperatures would be used to determine the enthalpy of adsorption.